The Decision to Patent (Contributions to Economics)

Contributions to Economics

For further volumes: http://www.springer.com/series/1262

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Alexandra Zaby

The Decision to Patent

Alexandra Zaby Wirtschaftswissenschaftliche Fakultät Lehrstuhl für Wirtschaftstheorie Mohlstraße 36 72074 Tübingen Germany [email protected]

ISSN 1431-1933 ISBN 978-3-7908-2611-1 e-ISBN 978-3-7908-2612-8 DOI 10.1007/978-3-7908-2612-8 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010933979 c Springer-Verlag Berlin Heidelberg 2010  This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

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For Anna, Luis and Mia

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Acknowledgements

If I have seen a little further it is by standing on the shoulders of Giants. (Sir Isaac Newton, 1676)

This famous saying of Sir Isaac Newton applies to this book in two ways. First of all, without the excellent research of many other economists, the present analysis of the decision to patent would not have been possible. I greatly acknowledge and enjoy the work within this global research community. The second application of Sir Newton’s statement concerns the support I experienced during my time as a Ph.D. student at the University of T¨ ubingen. I am deeply grateful to my doctoral advisor, Manfred Stadler. Throughout the sometimes quite eventful years I spent writing my Ph.D. thesis, I could always count on his absolute support. He gave me the freedom to find and investigate the puzzling question why in the world firms would possibly not patent. Now it is answered—at least to some extent—in the present book. Without his constant encouragement, constructive comments and useful criticism this would not have been possible. Thanks also go to my secondary advisor, Kerstin Pull, for her support and time investment. Further, I would like to thank Werner Neus, who accompanied me when I passed the starting line and was there when I finally reached the finishing line. Economic research—and probably research in general—is not possible without many people to discuss new ideas with. My colleagues and friends at the University of T¨ ubingen, especially Barbara and J¨orn Kleinert, Tobias Sch¨ ule and Tobias Schreij¨ ag, always had a willing ear. I am grateful for uncountable discussions on economic puzzles and for their ongoing belief in me and my work. I would also like to thank our student assistant Elena Tskitishvili and our secretary, Hilda Volkert, for their support. My theorist’s dream of an empirical investigation of the theoretical findings came true when I met my co-author Diana Heger. She ended my Odyssey of trying to find adequate data. I cannot thank her enough and hope that I will have the pleasure to work with her in the future. Special thanks go to my dearest friend Kristin Chlosta. She supported me whenever and wherever she could, and accompanied me through all the ups and downs that life had ready for me in the last years.

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Acknowledgements

Throughout the years of becoming an economist up to now, where the next step is taken, my parents always encouraged me in what I did. It was them who implanted curiosity in my head, which in my eyes is the essential basis for all research activity. I am greatly indebted for the support I was and I am experiencing from them. The light of my days and joy of my life are my children, Anna, Luis and Mia, my dearest thanks go to them. They have to cope with a mother who is often absorbed with economic problems that draw seemingly all of her attention and time. Just one smile on their faces can make my day a good one. Writing this book would not have been thinkable without the ongoing and boundless support of my friend, partner and loving husband Henning. Meeting him was probably the best thing that ever happened to me and I thank him with all my heart for walking the path of life with me. T¨ ubingen, May 2010

Alexandra Zaby

Contents

1

2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 The Patent System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Disclosure Requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Research Exemption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 Patent Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.4 Patent Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.5 Inventive Step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 The Economic Analysis of the Propensity to Patent . . . . . . . . . 1.2.1 The Decision to Patent in the Light of the Protective Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 The Decision to Patent in the Light of the Disclosure Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 A New Theoretical Approach to the Propensity to Patent . . . 1.4 Empirical Insights on the Propensity to Patent . . . . . . . . . . . . . 1.5 Outline of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 6 10 12 13 13 14 17

20 25 29 34

The Decision to Patent with Vertical Product Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 The Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Price Competition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Quality Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Quality Choices if the Invention is Kept Secret . . . . . . . 2.3.2 Quality Choices if the Invention is Patented . . . . . . . . . 2.4 The Patenting Decision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Licensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Welfare Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 Welfare with Secrecy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2 Welfare with a Patent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.3 Welfare with Licensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.4 Welfare Maximizing Appropriation Choice . . . . . . . . . . . 2.7 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37 38 40 42 45 50 53 57 63 64 64 65 65 67

18

ix

x

3

4

5

Contents

An Empirical Investigation of the Decision to Patent with Vertical Product Differentiation . . . . . . . . . . . . . . . . . . . . . 3.1 Hypotheses and Their Empirical Implementation . . . . . . . . . . . 3.2 Sample Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Variable Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71 71 74 76 80 85

The Decision to Patent with Horizontal Product Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 The Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Price Competition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Market Entry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 The Patenting Decision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Licensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Welfare Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.1 Welfare with Secrecy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.2 Welfare with a Patent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.3 Welfare with Licensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.4 Welfare Maximizing Appropriation Choice . . . . . . . . . . . 4.7 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87 89 91 97 102 109 112 112 113 117 117 120

An Empirical Investigation of the Decision to Patent with Horizontal Product Differentiation . . . . . . . . . . . . . . . . . . 5.1 Hypotheses and Their Empirical Implementation . . . . . . . . . . . 5.2 Sample and Variable Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

123 123 126 127 130

6

Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

A

Appendix to Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

B

Definition of Industry Dummies . . . . . . . . . . . . . . . . . . . . . . . . . . 149

C

Appendix to Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

List of Symbols

a

lower bound of consumers’ tastes

α

impact of the disclosure requirement

αN

critical threshold of the impact of the disclosure requirement

Ah

auxiliary variable, Ah ≡ (2b − a)2 /9

Al

auxiliary variable, Al ≡ (b − 2a)2 /9

b

upper bound of consumers’ tastes

β

patent breadth

CS

consumers’ surplus

c

auxiliary variable, c ≡ a/b

Dk

total demand for firm k

Δ+

protective effect of a patent

Δ−

disclosure effect of a patent

ΔP

overall effect of a patent

Δp+l

overall effect of a patent and license

ΔWF P

overall effect of patenting on social welfare

Fu (ql , qh ) overall profits of follower u f

fixed costs of market entry

γ

technological lead

h

right neighbor of the innovator

i

inventor/innovator

j

non-inventor

xi

xii

List of Symbols

k

left neighbor of the innovator

κ

auxiliary variable, κ ≥ 1 l

(·)

with licensing

max

maximum license fee

lmin

minimum license fee

lsmax

maximum license fee if secrecy is the alternative

lsmin

minimum license fee if secrecy is the alternative

l

Lu (ql , qh ) overall profits of leader u λ

spillover parameter

N

total number of firms operating in the market

n

number of the innovator’s competitors

n

e

even number of entering firms

n

u

uneven number of entering firms

PS P

producers’ surplus

(·)

with a patent

p

price

φ

patent height

φ φ

patent height of a weakly protective patent

φ

patent height of a delaying patent

q

quality

qh

high quality

ql

low quality

patent height of a strongly protective patent

r

interest rate s

(·)

with secrecy

σi1

strategy choice of firm i on stage 1

List of Symbols

xiii

ti (q) research time function of firm i tl

early adoption date with low quality

th

late adoption date with high quality

τ

P

patent duration

θ

consumer’s tastes

Ux

net utility of consumer x

μ

probability

v

outside option

WF

social welfare

xz

location of firm z on the unit circle

x ˆk, h consumer indifferent between k and h from viewpoint of k x ˆh, k consumer indifferent between k and h from viewpoint of h x ˆ0h, k location of the consumer indifferent between k and h measured from 0 x ˆi, out consumer indifferent between i and outside option from viewpoint of i

Chapter 1

Introduction

Firms do not patent every invention. In many cases they rather rely on trade secrecy or other non-legal means to protect their intellectual property, i.e. the returns on their investments in research and development (R&D). A patent confers to its owner the exclusive rights to prevent third parties from making, using, offering for sale, selling, or importing for these purposes the patent protected product (Art. 28, Agreement on Trade-Related Aspects of Intellectual Property Rights (TRIPs)). In exchange for the temporary monopoly which is secured by this protection, the patentee has to disclose the invention in a manner sufficiently clear and complete for it to be carried out by a person skilled in the art (Art. 83, European Patent Convention (EPC)). Thus every patent has the drawback of a possible loss of a technological leadership caused by the mandatory disclosure of formerly proprietary knowledge. The patentee has to fear that this transfer of enabling knowledge included in the patent description may benefit his rivals by facilitating their rapid catch-up. The relevance and actual enforcement of the disclosure requirement is underlined by the European Commission’s Green Paper on Innovation (European Commission (1996)). In the so-called Route of Action 8 on the promotion of intellectual and industrial property it is stated that a desirable action should be the “promotion of patent information services as a method of technology watch based, in particular, on the information system set up by the European Patent Office” (European Commission (1996), p. 42). Thus, the European Commission proposes policies which actively encourage firms to make more use of patent databases as a source of technological information for their innovative activities. Due to this use of patent information non-inventors could be able to “invent around” a patent at an earlier point in time as compared to a situation without mandatory disclosure. The term inventing around a patent is thereby understood as the fact that the innovator’s competitors may develop a product or process which does not infringe on the innovator’s patent but still allows rival firms to enter the same market, either with an imitative product (horizontal product differentiation) or with a follow-up innovation (vertical

1

2

1 Introduction

product differentiation). Necessarily inventing around is facilitated by the required disclosure of the patented invention (Landes and Posner (2003), p. 295). In their seminal empirical study Cohen et al (2000) find that the two key reasons for firms not to patent their non-tangible assets are (i) the amount of information disclosed in a patent application and (ii) the ease of legally inventing around a patent. With data from the 1993 European Community Innovation Survey (CIS) for up to 2849 R&D-performing firms Arundel (2001) explicitly analyzes the relative importance of secrecy versus patents. His findings support the results of Cohen et al (2000): A higher percentage of firms in all size classes rate secrecy as more valuable than patents. Using data of innovative Swiss firms Harabi (1995) even comes to the conclusion that patents are the least used mechanism to appropriate the returns from R&D. Galende (2006) finds the same for Spanish manufacturing firms. Following from the empirical investigation of the propensity to patent, today it is commonly acknowledged that patents are not a very adequate measure of inventive activity—as many inventions and innovations are not patented but are rather protected by non-legal appropriation mechanisms, e.g. secrecy, lead time advantages or technical complexity.1 The aim of this book is to provide a closer look at the forces behind the patenting decision of a successful inventor, i.e. the factors influencing his propensity to patent. In economic theory two theories of patents can be distinguished (see Denicol`o and Franzoni (2004a)). The reward theory of patents understands a patent as a means to reward a successful inventor for his risky investments in R&D and thus yields at providing sufficient incentives for firms to undertake research. This interpretation is the most prominent approach to the economic analysis of patents and focusses on the non-exclusive nature of technological knowledge by assuming that unpatented innovations are easily imitated. Following this perspective, the absence of a patent system would lead to firms underinvesting in R&D. The intention of a patent system in this sense is thus to encourage R&D effort. Contrasting this approach, the contract theory of patents interprets a patent as a contract between a successful inventor and society: the inventor is granted a temporary monopoly in exchange for the disclosure of his invention. This approach focusses on the fact that once knowledge is created it can be shared at no cost. A patent system in this sense is understood as a means to promote the diffusion of innovative knowledge. The analyzes presented in this book follow the latter approach. Thus, from the perspective of a successful inventor a patent has two effects: On the one hand, he profits from the temporary monopoly power which arises from the protective effect of the patent, on the other hand he faces the drawback of the required disclosure (disclosure effect). The patenting decision of an 1

For a review of the empirical literature concerned with the propensity to patent see Section 1.4 of this book.

1 Introduction

3

inventor therefore has to balance the tradeoff between the benefits of temporary monopoly power on the one hand and the drawback of the mandatory disclosure of enabling knowledge on the other. For the impact of the protective effect the scope of patent protection is crucial, i.e. the possibility for competitors to enter the market with non-infringing products. To disentangle the counter-effects of the protective effect and the disclosure effect, the present book proposes two theoretical approaches which allow a thorough analysis of the countering effects of protection and mandatory disclosure from the viewpoint of a successful inventor: the model presented in Chapter 2 focusses on vertically differentiated products, while the theoretical approach presented in Chapter 4 analyzes the patenting decision in a setting with horizontally differentiated products. In the latter case rivals may enter with non-infringing, horizontal variations of the innovative product while in the setting with vertical product differentiation competitors may enter with so called follow-up innovations despite of a patent. In both cases the impact of the disclosure effect influences the ability of competitors to enter the innovative market by making inventing around the patent easier. Complementing the theoretical analysis, Chapters 3 and 5 provide some empirical insights on the theoretical results. The theoretical definition of the propensity to patent goes back to the work of Horstmann et al (1985), who define it as the proportion of innovations which are actually patented, i.e. the percentage of patented innovations. This definition is used by most of the subsequent theoretical attempts to explain the driving forces behind the propensity to patent (see the literature review in Section 1.2). Throughout this book we will follow this definition and thus will refer to the propensity to patent as the percentage of innovations which are patented.2 A deeper insight into the factors influencing the propensity to patent can reveal important and useful information for economists and policy makers. As Arundel and Kabla (1998) state “the effectiveness of changes to patent legislation to make patenting easier, and thereby either entice firms to patent a higher percentage of their innovations or even to invest more in innovation, should not be taken for granted. Such changes [...] could increase patent propensity rates in some sectors that currently have low rates while having little effect on firms or sectors where a majority of innovations are already patented ” (Arundel and Kabla (1998), p. 128). Putting it the other way around, policy changes aiming at increasing the effectiveness of a patent system, i.e. providing sufficient incentives to invest in R&D and promote the dissemination of innovations in order to enhance social welfare, could—in the worst case—lead to a decreasing propensity to patent in some industry 2

Actually, in the theoretical approaches we analyze the patenting decision concerning one innovator and one of his innovations. Assuming that all innovators in the economy face the same protection decision, we can speak of an increasing or decreasing propensity to patent when analyzing the driving forces behind the patenting behavior.

4

1 Introduction

sectors. This may happen whenever the measures which are subject to policy changes disregard the factors which influence an innovator’s patenting decision, modifying them in a way which leads (some) firms to refrain from patenting. This is especially interesting in the context of the discussion on so-called “research exemptions”. A research exemption for a patented invention allows other researchers to use the invention without infringing the rights of the patentee. While in Europe the use of patented knowledge for the purpose of further research is generally allowed by patent law, the United States (U.S.) common law only admits a very narrow use of patented knowledge for research purposes.3 The analysis presented in this book follows the assumption that the knowledge disclosed in the patent application can be used by the patentee’s competitors without infringing the patent—by this we follow European patent law where research exemptions are statutory. From the perspective of countries that have not implemented a research exemption as a statutory part of their patent legislation, e.g. the U.S., the analysis provides some interesting insights on how the implementation of a research exemption would influence the propensity to patent. For our analysis of the propensity to patent, a clear definition of the R&D output of firms is crucial: By investing in R&D firms by chance make inventions which originate from the “world of ideas”. If an invention is introduced into a market, i.e. commercialized, it becomes an innovation. Figure 1.1 depicts this coherence. Whenever an invention/innovation fulfills the patentability requirements, meaning that it is new, incorporates the necessary inventive step and is applicable for industrial use, the inventor/innovator may choose to protect it by a patent.4 Else he may choose to protect it by other, non-legal means, such as lead time advantages, technical complexity, trade secrecy or a combination of these. In the following analysis we abstract from non-patentable inventions/innovations and focus on the decision of a successful inventor/innovator between either patenting a patentable innovation, a situation depicted by the dark shaded area in Figure 1.1 or keeping the patentable innovation secret, a situation represented by the light shaded area in Figure 1.1. In Chapter 2 the analysis focusses on a successful inventor who decides whether or not to patent before commercializing his invention. As means of non-legal protection he can rely on a combination of trade secrets, the technical complexity of his innovation and a lead time advantage. For brevity we will refer to these nonlegal means of protection with the term secrecy. In any case he will thereafter bring his invention to the market, so the situation is one of either a patented innovation (dark shaded area in Figure 1.1) or a non-patented, patentable innovation (light shaded area in Figure 1.1). In Chapter 4 the patenting 3

See the following section for a further elaboration on this issue. Patentability requirements are thoroughly investigated in the following section of this book.

4

1 Introduction

5

Fig. 1.1 Ideas, Inventions, Innovations, and Patents

Ideas Inventions Innovations Patents

Unpatentable inventions Non-commercialized patented inventions Patented innovations

Non-patented patentable inventions

Non-patented patentable innovations Unpatentable innovations Source: adopted from Basberg (1987), p. 133 and M¨ akinen (2007), p. 18

decision of a successful innovator who has already brought his invention to the market is analyzed. He may rely on non-legal means of protection which are fixed costs of market entry and technical complexity. Again for brevity we will refer to these means of protection with the term secrecy. Thus, referring to Figure 1.1 the situation is—as before—either one of a patented innovation (dark shaded area in Figure 1.1) or a non-patented, patentable innovation (light shaded area in Figure 1.1). Before turning to the economic analysis of the patenting decision, some points shall be made on the legal background of patents in the real world.

6

1 Introduction

1.1 The Patent System In this section we present a brief survey of the main features of a patent system, setting off with some historical insights on the evolution of modern patent systems.5 That ideas should freely spread from one to another over the globe, for the moral and mutual instruction of man, and improvement of his condition, seems to have been peculiarly and benevolently designed by nature, when she made them, like fire, expansible over all space, without lessening their density in any point, and like the air in which we breathe, move, and have our physical being, incapable of confinement or exclusive appropriation. Inventions then cannot, in nature, be a subject of property. Society may give an exclusive right to the profits arising from them, as an encouragement to men to pursue ideas which may produce utility, but this may or may not be done, according to the will and convenience of the society, without claim or complaint from anybody [...] T. Jefferson in a letter to Isaac McPherson, August 13th, 1813 (as cited in McCann (2003))

When Thomas Jefferson6 wrote his letter to Isaac McPherson the evolution of the modern patent systems as known today was in full swing. Driven by the spread of the Industrial Revolution, patent laws were passed in several countries. In the United States, where Jefferson lived, a patent system was established by the patent act of 1790. Three years later the three commissioners in charge of examining the applications were no longer able to process the vast number of applications so that examination was replaced by a mere registration system, thus every application resulted in a patent. Naturally this practice led to many unreasonable patents, nevertheless it lasted until 1836 when the U. S. Patents and Trademarks Office (USPTO) was established. This institution—up to today—examines patent applications and decides whether an invention meets the necessary standards to receive patent protection. Germany—at the time of Jefferson’s letter—was a non-unified assemblage of different states. As the first of these states, Prussia, in 1815, introduced a patent law (“Publikandum zur Ermunterung und Belohnung des KunstfleiSSes”). In 1834 the Zollverein was established and following this unification attempt in the year 1842 a single patent law for the entire Zollverein came into force. The German Empire (“Deutsches Reich”) was established in 1871 and while in the first six years the member states adopted their own patent policies, in 1877 a unified national Patent Act was passed which included the establishment of a German Patent Office (see Khan (2008)). This institution, initially labeled “Kaiserliches Patentamt” granted the first German patent on July 2, 1877 on the process of producing red ultramarin paint 5

The historical facts in large part were drawn from the excellent chapter on the evolution of modern patent systems in Guellec and van Pottelsberghe (2006). 6 Thomas Jefferson, (1743-1826), was the third president (1801-1809) of the United States of America. He was the principal author of the Declaration of Independence.

1.1 The Patent System

7

(”Verfahren zur Herstellung einer rothen Ultramarinfarbe”) (DPMA (2009)). The Unified Patent Act already included many features which prevail in European patent law today:7 the “first to file” rule, the pre-grant publication of patent applications, the fact that third parties could oppose the patent prior to grant, the preliminary examination, the necessity of inventive height— predecessor of the inventive step, as well as obliged payments of renewal fees to maintain a granted patent (Guellec and van Pottelsberghe (2006)). The notion of a patent as a reward to encourage innovation arose quite early. In the Greek city of Sybaris in Sicily in 500 BC the king would grant a one year exclusivity to cooks who had invented a new recipe. First privileges rewarding inventions were granted in the independent cities of northern Italy in the late middle ages. Targeted at attracting foreign craftsmen a 20 year “patent” was given to those who settled in the city to perform their art and train local workers. One example of such an early privilege is the Brunelleschi patent for a system to transport marble on the Arno river which was granted by the city of Florence in 1426 (Prager (1946)). The first formalized patent law is the famous patent statute of Venice issued in 1474 which already incorporated some important features of modern patent systems, e.g. the examination of the patent application and a standardized duration of the right to exclude. Initially the right to exclude others from the use of an invention was a royal privilege that only a ruler could grant. Mostly such monopolies served the ruler’s own interests or those of the state he reigned. Later, especially in Britain, attempts were made that these rights should be governed by law and courts. At the end of the nineteenth century most advanced countries had managed to set up working patent laws and institutions. The twentieth century was then mainly characterized by the harmonization of patent law and practice across borders. The first worldwide union for the protection of intellectual property was the Paris Convention of 1883, which by 1903 was signed by 14 countries.8 In the year 1967 the Convention became part of the United Nations (UN) system through the establishment of the World Intellectual Property Organization (WIPO). Further harmonization was reached by the Agreement on Trade-Related Aspects of Intellectual Property Rights (TRIPs), which as part of the General Agreement on Tariffs and Trade (GATT), was signed in 1994. The essential features of the TRIPs are that patents should apply to all fields of technology, that their duration should be minimum 20 years after filing and that working requirements9 should be imposed only in exceptional circumstances (Guellec and van Pottelsberghe (2006), p. 26). In 7

See pp. 9 for an elaboration on the main features of modern patent law. Initial participants were Belgium, France, Guatemala, Italy, Netherlands, Portugal, San Salvador, Serbia, Spain and Switzerland. Later, the United Kingdom, the U. S. Mexico and Germany joined the Convention. 9 The definition of such working requirements is “[...] that the patentee must manufacture the patented product, or apply the patented process, within the patent granting country. By requiring local, or national working, the patent granting country forces 8

8

1 Introduction

Europe the harmonization attempts culminated in a centralized patent granting procedure for members (and non-members) in the European Union (EU), defined in the European Patent Convention (EPC) which was signed by 16 countries in the year 1973 and entered into force in 1977. One year later the European Patent Office (EPO) was established as executive body with the mission to implement the EPC.10 The EPC provides a unitary application and examination procedure which gives patent applicants the opportunity to obtain a bundle of selected national patents. The latest development regarding the harmonization of patent legislation in Europe is the attempt to create a European Community patent. In the year 2007 the European Commission adopted the communication “Enhancing the Patent System in Europe” (European Commission (2007)) which makes clear that the intention of the European Commission is to implement the Community patent as soon as possible. The Commission is of the opinion that the creation of a single Community patent continues to be a key objective for Europe. The Community patent remains the solution which would be both the most affordable and legally secure answer to the challenges with which Europe is confronted in the field of patents and innovation.

Today a European Patent comprises of a bundle of national patents and keeping these in force is nearly nine times as expensive as holding and renewing Japanese or U.S. patents for 20 years (van Pottelsberghe de la Potterie and Francois (2006)). In contrast, a Community patent would provide a “simple, cost-effective and high quality one-stop-shop patent system in Europe, both for examination and grant as well as post-grant procedures” (European Commission (2007), p. 3). Equipped with the knowledge on the evolution of modern patent systems, in the following we will focus on the exact definition of a patent and the underlying filing procedure necessary to obtain patent protection. According to Article 28 of the TRIPs Agreement a patent gives its holder the following rights: 1. A patent shall confer on its owner the following exclusive rights: (a) where the subject matter of a patent is a product, to prevent third parties not having the owner’s consent from the acts of: making, using, offering for sale, selling, or importing for these purposes that product; (b)

where the subject matter of a patent is a process, to prevent third parties not having the owner’s consent from the act of using the process,

the patentee to transfer the patented technology, or the technology needed to produce the patented product, into the country” (Halewood (1997), p. 249). 10 Today the member countries of the European Patent Organisation are Austria, Belgium, Bulgaria, Switzerland, Cyprus, Czech Republic, Germany, Denmark, Estonia, Spain, Finland, France, the United Kingdom, Greece, Hungary, Ireland, Iceland, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Monaco, the Netherlands, Poland, Portugal, Romania, Sweden, Slovenia, Slovakia and Turkey.

1.1 The Patent System

9

and from the acts of: using, offering for sale, selling, or importing for these purposes at least the product obtained directly by that process. 2. Patent owners shall also have the right to assign, or transfer by succession, the patent and to conclude licensing contracts.

(Art. 28, TRIPs) Not every invention is patentable. The European Patent Convention clearly defines for what kind of inventions a patent is applicable. European patents shall be granted for any inventions, in all fields of technology, provided that they are new, involve an inventive step and are susceptible of industrial application.

(Art. 52 (1), EPC) Further the EPC states that discoveries, scientific theories, mathematical methods, aesthetic creations, schemes, rules, methods for performing mental acts, playing games or doing business, as well as programs for computers are not patentable (Art. 52 (2), EPC). The term “industrial application” is further elaborated on in Article 57 of the EPC where it is stated that “an invention shall be considered as susceptible of industrial application if it can be made or used in any kind of industry, including agriculture”. In Europe this industrial applicability is usually interpreted as applicability in the manufacturing industry (and agriculture), a fact that stresses the notion of technicality which is seen synonymous to materiality (Guellec and van Pottelsberghe (2006)). This naturally gives more weight to the understanding that only material inventions are patentable. In the U.S. patent law the interpretation of patentability is based upon the notion of “utility” so non-material inventions are explicitly not excluded from patent protection. Patents are territorial rights as they only apply within the country and jurisdiction where they have been granted. In order to obtain a patent, an inventor has to file an application to a patent office. This government institution examines whether the respective invention fulfils certain legal criteria. In Europe a patent application needs to fulfil the requirements stated in Article 78 of the EPC. It needs to include: a request for the grant of a European patent, a description of the invention, one or more claims, any drawings referred to in the description or the claims and an abstract. The priority filing of a patent provides the first legal date of the application for the patent. Two filing rules can be distinguished: the first-to-file rule and the first-to-invent rule. The first-to-file rule applies in all countries except in the United States and defines that a patent is issued to the first applicant—independently of the priority regarding the actual invention. With the first-to-invent rule, which applies in the United States, a patent will be granted to the first inventor,

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1 Introduction

provided the date of first invention can be documented.11 Once an application is filed at the EPO it passes through several procedural stages: first a search for the relevant prior art is initiated. Then, 18 months after the priority filing, the patent application together with the search report and a non-binding opinion regarding the prospect of the application to be granted are published (Art. 93, EPC).12 After further examination the patent is then eventually granted. According to the Roland Berger (2005) Survey the cost of patenting can be divided into four main categories: process costs, translation costs, external expenses and maintaining costs. Process costs consist of the actual patenting fees, translation costs occur once a patent is granted as it needs to be translated into the languages of all countries where protection is applied for. External expenses arise due to the services necessary for the writing of the patent application and the filing to and communication with a patent office, usually a patent attorney is appointed for this. Maintaining costs are the required renewal fees to keep a granted patent valid, naturally they need to be payed in every country where the patent is to be kept in force. The Roland Berger Survey comes to the result that for a hypothetic patent filed at the EPO with 6 claims and 6 designated countries total patent costs amount to 31 580 Euro if it is kept in force for 10 years.13 Fees paid to the EPO for the patent’s initial grant thereby only amount to 4400 Euro and renewal fees to 5600 Euro.14

1.1.1 Disclosure Requirement The European patent application shall disclose the invention in a manner sufficiently clear and complete for it to be carried out by a person skilled in the art. (Art. 83, EPC)

A patent’s merits are opposed by the inventor’s requirement to disclose the invention. In the United States the disclosure requirement for patentability is stated in Section 112 of the U.S. patent code, “the specification shall contain a written description [...] in such full, clear, concise and exact terms as to enable any person skilled in the art [...] to make and use the same [...]”. 11

See Scotchmer and Green (1990) for a comparison of the economic efficiency of these rules. 12 This mandatory pre-grant publication is in place in all industrialized countries except the U.S. 13 For a patent filed at the EPO excess claims fees have to be paid from the eleventh claim on, at the USPTO excess claims fees accrue for more than three claims. 14 Renewal fees need to be paid from the 3rd year on.

1.1 The Patent System

11

The disclosure of the invention—today key component and justification of a patent system—became mandatory rather late in the evolution of patent systems in Europe. In England until the mid-eighteenth century, even the authority in charge of examining a patent application was not fully aware of the invention due to incomplete disclosure. Only in the late eighteenth century the disclosure requirement evolved as an established feature of the patent system. According to the patent law of 1877, in Germany the disclosure of claims and specifications included in the patent application was mandatory even prior to the grant of the patent (as is the case until today, 18 months after filing the patent). In the United States the disclosure was a key factor from the beginning of patent law. Even before the USPTO was established in 1836, lists of patents were being published from 1805 on. Later in the nineteenth century patent descriptions were made available in regional offices of the USPTO. Differing from the European pre-grant publication, in the U. S. the mandatory disclosure of the patent application does not take place until the patent is actually granted.15 Nowadays, as Guellec, van Pottelsberghe (2006, p. 40) put it “the publication of patent applications and grants is [...] a central mission assigned to patent offices, which invest significant resources for handling it by using the latest techniques”. To provide an effective search tool for the retrieval of patent documents by intellectual property offices and other users and in order to examine the novelty and evaluate the inventive step or non-obviousness of technical disclosures in patent applications the WIPO established an International Patent Classification (IPC) system which entered into force on October 7th, 1975 (§1 and §6 of the IPC Guide). According to §118 of the IPC Guide, the competent authorities, i.e. patent offices, shall indicate “the complete symbols of the Classification applied to the invention to which the patent document relates”. This means that it is mandatory for patent offices to assign proper classification codes to every patent application which represent the respective patent’s relevant invention information. The term invention information hereby relates to all technical information included in a patent document which represents an addition to the state of the art (§77, IPC Guide), i.e., the difference between the subject matter in a patent document and the collection of all technical subject matter that has already been placed within the public knowledge (§78, IPC Guide). Consequently, every granted patent is sufficiently described by the IPC Codes assigned to it.

15

See Aoki and Spiegel (2009) for an economic analysis of the alternative disclosure procedures.

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1 Introduction

1.1.2 Research Exemption National patent law in all EU countries includes a statutory research exemption (also: experimental use exemption) to patent protection, meaning that the knowledge disclosed in a patent application can be used by other researchers without infringing the rights of the patentee (Goddar (2002), Dent et al (2006)). The legal background to these exemptions is twofold. On the one hand member states of the WTO have to comply with the TRIPs Agreement which states in Article 30: Members may provide limited exceptions to the exclusive rights conferred by a patent, provided that such exceptions do not unreasonably conflict with a normal exploitation of the patent and do not unreasonably prejudice the legitimate interests of the patent owner, taking account of the legitimate interests of third parties.

On the other hand, an exemption for experimental use is included in Article 27 (b) of the Community Patent Convention (CPC) where it is stated that the rights conferred by a Community patent shall not extend to “acts done for experimental purposes relating to the subject-matter of the patented invention”. Although the CPC is not in force up to today, the importance of a Community patent for the EU is without controversy. This makes it quite probable that it will be implemented by the EU in the near future (European Council (2008)). In a recent recommendation of the European Commission to the European Council it is emphasized that “the creation of a Community patent and a unified patent litigation system both for future Community and European patents [...] remains a priority for Europe” (European Commission (2009), p. 3). By now most EU countries have already implemented a statutory research exemption, e.g. in Art. 11(2) of the German Patent Act, Art. 27 (b) CPC is literally adopted.16,17 In the U.S. two types of experimental use exemptions to patent infringement exist, a common law research exemption and a statutory research exemption originating from the Hatch-Waxman act of 1984 which only applies to drugs and medical devices (Hagelin (2005)). As courts in the past have interpreted the non-infringing use of patented knowledge for experimental reasons very restrictively, one can say that a research exemption does not exist in the U.S. (Miller (2003)).18 16

The exact German wording is “Die Wirkung des Patents erstreckt sich nicht auf Handlungen zu Versuchszwecken, die sich auf den Gegenstand der patentierten Erfindung beziehen.” 17 An economic analysis of alternative patent regimes with and without a research exemption can be found in Moschini and Yerokhin (2008). The authors focus on the influence of the patent regime on research incentives in a quality ladder model. The patenting decision is not taken into account. 18 The most recent decision concerning experimental use of patented knowledge is the case Madey vs. Duke University, where the court confirmed the outcome of earlier cases in that research exemptions are understood to be extremely narrow (see U.S.

1.1 The Patent System

13

1.1.3 Patent Duration The duration of a patent is the one dimension of protection which is defined clearly and objectively. The statutory life of a patent is nearly uniform worldwide as the signatory countries of the TRIPs are required to fix it at 20 years. In the European Patent Convention the term of a European patent is defined in Article 63. The term of the European patent shall be 20 years from the date of filing of the application.

Guellec and van Pottelsberghe (2006) see the mission that patents as policy instruments have been assigned by society reflected in this difference between the limited duration of intellectual property rights and the infinitely lived property over tangible goods: the validity of a patent should stop when the costs for society start exceeding the benefits. When a patent is granted its duration from the application date is initially two years, after this time span the inventor has to pay renewal fees to maintain the patent. In Europe these fees increase up to the tenth year and then remain constant.19

1.1.4 Patent Scope The scope of a patent defines the boundaries between what is protected by the patent and what is not. Contrary to the objective definition of patent duration across countries, the concept of patent scope has no uniform and objective implementation in patent law. In the European Patent Convention the extent of patent protection is defined as follows. The extent of the protection conferred by a European patent or a European patent application shall be determined by the claims. Nevertheless, the description and drawings shall be used to interpret the claims. case law Madey vs. Duke University 307 F 3d 1351, Federal Circuit 2002). Madey, a tenured faculty member at Duke University sued the Duke University for patent infringement as it continued using a research instrument (a free-electron laser oscillator) which was protected by a patent of his after he had resigned his position as director of the university’s research lab due to disagreement over the management of the laboratory. Madey won the case, underlining earlier decisions in that research exemptions are only possible for experiments “for amusement, to satisfy idle curiosity, or for strictly philosophical inquiry” (see U.S. case law, Roche Products Inc. vs. Bolar Pharmaceutical Co. 733 F 2d 858, 863, Federal Circuit 1984). 19 Article 2 (4) EPC defines these fees as follows: for the 3rd year 400 Euro, for the 4th year 500 Euro, for the 5th year 700 Euro, for the 6th year 900 Euro, for the 7th year 1000 Euro, for the 8th year 1100 Euro, for the 9th year 1200 Euro, for the 10th and each subsequent year 1350 Euro. According to the FY 2009 Fee Schedule of the USPTO in the U. S. patent maintenance fees are due 3.5 years ($ 980), 7.5 years ($ 2480) and 11.5 years ($ 4110) after a patent is granted.

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1 Introduction

(Art. 69 (1), EPC) In addition, courts may rely on two opposite doctrines that either expand patent scope or restrict it. On the one hand, the doctrine of equivalents extends protection to something outside the claims which can be seen as “equivalent” to the protected invention. On the other hand, the doctrine of literal interpretation states that protection is only given to what is explicitly claimed in the patent application (Guellec and van Pottelsberghe (2006)). Implementing patent scope in economic theory yields different measures that differ subject to the underlying market structure. In a setting with horizontally differentiated goods patent scope is commonly referred to as a patent’s breadth while in a setting with vertically differentiated goods patent scope is understood as a patent’s height.20,21 In defining the borders of a patent’s scope two interpretations are possible (Waterson (1990)). Either the patent’s claims define an exact border of protection, a situation referred to as a fencepost patent system, or the patent’s claims only provide an indicator of protection, a situation referred to as a signpost patent system. Under the fencepost system, a competitor marketing a substitute product infringes the patent whenever the product ˇ claims. In contrast, under a signpost system, the lies within the patenteeSs closer a competitor’s product is located to the original patent, the easier it is to prove infringement using the doctrine of equivalents. As we abstract from infringement issues, the patent system referred to in this book is assumed to be that of the fencepost type in which the patent’s claims define an exact border of protection.

1.1.5 Inventive Step The basic requirement for an invention to be patentable is that it needs to be novel. Patent law characterizes the extent of this novelty as the inventive step, which defines how much an invention needs to differ from prior art to be patentable. 20 Matutes et al (1996) introduce a further parameter of patent design which they call the scope of a patent. The main difference between patent scope and patent height respectively breadth is that where height protects a certain quality range of further developments of a basic invention and breadth protects horizontally related products, scope protects further developments, e.g. applications, that can be sold on independent markets. Thus these applications can neither be ranked in terms of quality relative to the basic technology nor can they be understood as horizontally differentiated versions of the original invention. 21 Yiannaka and Fulton (2006) assume that an inventor can strategically choose the extent of patent protection by setting the breadth of his patent. Throughout this book we abstract from their approach and consider patent breadth as well as patent height as parameter which are subject to policy decisions.

1.1 The Patent System

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An invention shall be considered to be new if it does not form part of the state of the art. The state of the art shall be held to comprise everything made available to the public by means of a written or oral description, by use, or in any other way, before the date of filing of the European patent application.

(Art. 54 (1), (2), EPC) An invention shall be considered as involving an inventive step if, having regard to the state of the art, it is not obvious to a person skilled in the art.

(Art. 56, EPC) The scope of a patent and the inventive step necessary to obtain a noninfringing patent on a related invention are strongly interdependent. Following Scotchmer (2004) the difference between both dimensions is best explained using a figure with—what she calls—donuts, depicting alternative extents of patent scope and inventive step. Fig. 1.2 Patent Scope and the Inventive Step Infringing, patentable

A

Infringing, unpatentable B

Non-infringing, unpatentable (a) narrow, large inventive step

(b) broad, small inventive step Source: Scotchmer (2004), p. 85

Products A and B are depicted by the dots in the middle of either donut, the respective patents are illustrated by the surrounding circles. All points within these circles represent different substitute products. Note that substitutability here is understood in a sense that consumers are to some degree heterogenous and are thus willing to buy either the patented product or a differentiated version—be it horizontally or vertically distinct from the patented original. If a patent’s scope is narrow but the required inventive step is large we have the situation depicted in Figure 1.2(a). Here the inner circle around product A depicts the patent’s scope—it encloses all substitutes which are infringing due to supposed “equivalence”. As the inventive step is assumed to be large, a competitor’s invention needs to be sufficiently novel, i.e. different, to be patentable. Speaking in terms of the illustration, the inventive step is

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1 Introduction

depicted by the outer circle so that any patentable invention has to lie beyond. This means that all substitute products on the shaded area, the donut, are not patentable as they do not reach the necessary inventive step, yet they are non-infringing as they lie outside the patent’s scope. Things are reversed in Figure 1.2(b). Here the patent’s scope is broad but the required inventive step is small. Hence it is the outer circle line that depicts the patent’s scope and all substitute products within this circle infringe the patent. Yet, the inventions on the donut are patentable as the inventive step, defined by the inner circle, is narrow. In this case so-called blocking patents may occur as the owner of a patent that infringes on the original patent on product B requires a license from B to market his invention. Throughout this book we will assume a situation as depicted in Figure 1.2(a), a narrow patent’s scope and a large required inventive step. Thereby we focus our analysis on the patenting decision as a pure means of appropriating the returns from successful research activity.

1.2 The Economic Analysis of the Propensity to Patent

17

1.2 The Economic Analysis of the Propensity to Patent A vast number of theoretical approaches concerning patents is dedicated to the optimal design of the different dimensions constituting a patent, namely the interplay of patent scope, patent duration and the inventive step. An excellent survey of this literature is provided by Encaoua et al (2006). Most of these theoretical approaches assume that a patent already exists and do not question the inventor’s decision on the method of appropriating his returns on research investments. The focus of the present analysis challenges the assumption that every innovation is patented: it aims at analyzing an inventor’s decision to patent. The following overview of the economic literature on the propensity to patent thus omits contributions concerning the optimal design of a patent and focusses on contributions analyzing an inventor’s decision to patent. Horstmann et al (1985) were the first to challenge the assumption that every innovation is patented. Opposing the stylized fact that the number of innovations and patents could be seen as equivalent measures of a firm’s R&D output, Horstmann et al (1985) find that the propensity to patent (the proportion of innovations that are actually patented) actually is below unity. In their setting a patent can transfer private information from the innovator to competitors, while at the same time patent protection is of limited coverage so that competitors can earn positive profits by imitating the patented invention without infringing the patent itself, i.e. inventing around. Thus by a patent a competitor is prevented from copying the exact product or process, but is nonetheless able to enter the market with a differentiated version of the protected innovation. Interestingly, Horstmann et al (1985) show that even if the patent application conveys no explicit information which in itself increases the competitor’s profits (e.g. the required disclosure of information), the propensity to patent is positive but less than one as long as patent breadth does not rule out positive profits for a differentiated version of the protected innovation. If patenting does reveal information which positively influences a competitor’s profit, the propensity to patent is reduced. The innovator’s optimal strategy involves mixing between patenting and not patenting while the follower decides to stay out of the market whenever the innovator patents, and to imitate whenever the innovator decides to keep his invention secret. Since the thought-provoking impulse of Horstmann et al (1985) many attempts have been made to analyze the patenting decision. Much of the theoretical literature concerning this issue disregards the influence of the disclosure requirement which is linked to every patent application. Various approaches rely on the assumption that the disclosure requirement does not come to effect until a patent expires. In proceeding, the theoretical approaches to the patenting decision will be categorized according to their handling of the disclosure effect. Initially, we present the theoretical literature which only takes into account the protective effect of a patent (Section 1.2.1).

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1 Introduction

Subsequently we will turn to the more comprehensive approaches which also include the disclosure effect in an adequate way (Section 1.2.2).

1.2.1 The Decision to Patent in the Light of the Protective Effect The extent of the protective effect of a patent is defined by the patent’s scope. An inventor profits from the protective effect if competitors attempt to copy or imitate, i.e. “invent around”, the patented invention.22 Naturally, whenever the inventor would be a monopolist even without a patent, e.g. due to prohibitively high imitation costs, patenting has no positive effect for him, as protection then is unnecessary. All of the papers presented in this section follow the assumption that a patentee does not immediately face the drawback of the disclosure requirement linked to a patent. Thus the monopoly during the statutory life of the patent is followed by perfect competition after the patent expires since then anyone skilled in the art is able to use the formerly protected knowledge. A central contribution to the literature concerning costly imitation of a patent by rivals is provided by Gallini (1992). She moves away from the assumptions that either imitation of patented innovations is prohibitively costly and therefore never a threat to the innovator23 or that imitation is costless and therefore always a threat to the innovator24 . By introducing imitation costs Gallini can endogenize rivals’ imitation decisions as the incentive to imitate now depends on the length of patent protection awarded to the patentee. The innovator can choose between a patent and secrecy. With a patent, rivals are prevented from duplicating the protected innovation, but can invent around the patent developing a non-infringing imitation at a given cost. If the innovator chooses secrecy he faces a positive risk that some rival firms will learn about his innovation and duplicate it. In this case the innovation becomes available to all firms in the market at zero cost. Whenever secrecy is effective, the innovator enjoys an infinite monopoly. Whether the innovator patents or keeps his invention secret depends on the statutory patent life as well as on imitation costs. The longer the duration of the patent, the more likely competitors will invent around it. Thus, extending patent 22

Two contributions concerned with the consequences of inventing around are Mukherjee and Pennings (2004) and Mukherjee (2006). While the latter focusses on the impact that inventing around has on R&D investments, Mukherjee and Pennings (2004) examine the influence of inventing around on the timing of technology adoption. Both models disregard the patenting decision. 23 See among others Nordhaus (1969), Scherer (1972) and Kamien and Schwartz (1974). 24 See among others Gilbert and Shapiro (1990) and Klemperer (1990).

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19

life may actually lead to a decrease of the inventor’s propensity to patent. Gallini (1992) finds that from a welfare perspective optimal patents should be sufficiently short and sufficiently broad to discourage imitation. Takalo (1998) extends the work of Gallini (1992) in the sense that costly imitation—irrespective of the patenting decision—involves uncertainty about success. He finds that an increase of patent breadth always strengthens the incentive to choose patent protection. In his contribution, Bessen (2005) focusses on the question whether the disclosure requirement—the main justification for the existence of our patent system—actually promotes the diffusion of inventions. As Gallini (1992) he assumes that disclosure takes place only after the statutory life of the patent ends. Additionally Bessen (2005) assumes that another channel for the diffusion of knowledge is the imitation of the original invention by competitors. Thus he evaluates a non-inventor’s probability of successfully imitating or inventing around the patent as equivalent to the probability of diffusion. Bessen (2005) comes to the conclusion that without licensing the probability of diffusion is less or equal to the case with trade secrecy and that with licensing social welfare will be at least as high and possibly even higher without patents. Contrary to Bessen (2005), Denicol`o and Franzoni (2004a) come to the conclusion that patents can be welfare enhancing. In two companion papers Denicol` o, Franzoni assume patent protection to be perfect in the sense that a patent is always broad enough to prevent imitators from inventing around. Alternatively to a patent, innovators may rely on secrecy to protect their innovations. With secrecy, the innovation can either leak out or can be replicated by one duplicator. Denicol` o, Franzoni’s main finding is that early disclosure through the patent system is socially valuable. To find the optimal length of a patent two effects have to be balanced: on the one hand, longer patents will induce additional firms to disclose their innovations while on the other hand, the deadweight loss associated with the patentees’ monopoly power will increase. In the companion paper Denicol`o and Franzoni (2004b) additionally analyze the implications of prior user rights on the incentives to innovate and the propensity to patent. With secrecy—as in Denicol`o and Franzoni (2004a)—a follower firm can replicate the innovation. Extending the theoretical model, depending on the actual patent policy, now a follower might even be able to patent the innovation and exclude the first inventor from its use. As Denicol`o and Franzoni (2004b) assume perfect patent protection and abstract from issues of patent invalidity or imitation, they focus on patent length as the relevant policy variable. Thus, a policymaker can induce patenting rather than secrecy by choosing patent life adequately. The innovator’s patenting decision is driven by the limits of patent protection (complete disclosure after the expiry of the patent) on the one hand and the risks he faces with secrecy on the other. Denicol`o and Franzoni (2004b) come to the conclusion that the introduction of prior user rights increases the incentives to innovate

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1 Introduction

but reduces the first inventor’s propensity to patent so that the welfare effect of introducing prior user rights is ambiguous. Most interestingly and opposing the results of Bessen (2005), they find sufficient conditions ensuring that it is socially desirable that innovators patent, meaning that trade secret protection is only socially preferable in limited circumstances. Waterson (1990), in a completely different model setting, also comes to the conclusion that society may profit from a patent. He argues that “the main impact of a product patent is not to create a monopoly but rather to affect the variety choices that rivals make” (Waterson (1990), p. 860). To capture this proposed effect of a patent he introduces patenting into a framework with horizontally differentiated products. In this setting he assumes a signpost rather than a fencepost system of patents: Defining product space as a onedimensional line of finite length, a patent will in principle cover the entire product space. Yet, the exact borders of protection are left to court decisions. Thus, a non-inventor entering the market always infringes the patent and the patentee can decide on whether taking the infringer to court or not. If he does so there is some probability that the patent will be ruled invalid. With secrecy the non-inventor is able to duplicate the invention so that he enters the market with the same product as the inventor, while, with a patent, the non-inventor will necessarily differentiate to some extent. Waterson (1990) finds that for some parameter values—if entry of a rival can be prevented by a patent—patenting is the dominant strategy for the innovator and for social welfare. Using numerical calculations Waterson (1990) analyzes the relative welfare effects of secrecy versus patenting with a signpost or a fencepost patent system. Here he comes to the result that a signpost patent system, where an infringing competitor is obliged to pay a penalty in height of the innovator’s loss in profit, outperforms the supposed alternatives. In addition Waterson (1990) comes to the conclusion that where variety is valued very highly, the broad protection of a patent is likely to be socially inferior.

1.2.2 The Decision to Patent in the Light of the Disclosure Effect The contributions which allow for an immediate impact of the disclosure effect are presented in this section. Mostly this literature focusses on cumulative innovations, a setting which constrains the usability of the disclosed knowledge to subsequent inventions, thereby disregarding the possibility of “inventing around” the original invention without improving it qualitatively.25 25

The cumulative innovations approach is chosen by Scotchmer and Green (1990), Erkal (2005), Bhattacharya and Guriev (2006) and Aoki and Spiegel (2009). Only Harter (1994) uses a framework with differentiated goods which accounts for inventing around.

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21

The impact of the disclosure effect crucially depends on the way it is implemented theoretically. Empirically the extent of the disclosure requirement depends on factors such as policy decisions26 , the use of patent applications as a means to obtain technological knowledge input, and the industry-specific usability of knowledge spillover. This makes it self-evident to model the impact of the disclosure requirement as exogenously given. Nevertheless variations of this parameter may lead to changes in the interplay of the counter-effects of patenting, i.e. protection versus disclosure, which in the end may result in an alteration of the propensity to patent. Thus, implementing the possibility of a varying extent of the disclosure requirement may reveal interesting insights. In the work of Scotchmer and Green (1990) and Erkal (2005) the extent of the disclosure requirement remains fixed whereas in Bhattacharya and Guriev (2006), Aoki and Spiegel (2009) and Harter (1994) the impact of the required disclosure may vary. However, the latter contributions do not explicitly focus on the consequences that a varying impact of the disclosure requirement has on the counter-effects of patenting and in the end on the propensity to patent. Instead, they consider the influence of alternative filing procedures on the propensity to patent (Aoki and Spiegel (2009)), the choice of alternative licensing contracts (Bhattacharya and Guriev (2006)) and Harter (1994) even comes to the conclusion that the propensity to patent is not at all influenced by the impact of the disclosure requirement. A related strand of literature is concerned with the strategic disclosure of enabling information. Here the disclosure does not stem from the mandatory disclosure requirement due to patenting, but originates as a means to strategically influence competitors’ behavior. In Bhattacharya and Ritter (1983) partial disclosure of enabling knowledge may reduce the cost of capital, while at the same time the rivals in a patent race are strengthened. Anton and Yao (2003, 2004) regard the disclosure of proprietary knowledge as an instrument to signal low costs of production to a rival. Apart from the strategic use of disclosure as a signalling instrument, firms may also publish their research findings in order to establish new prior art and thus strategically affect the patentability of related innovations. Ponce (2002), Bar (2006) and Baker and Mezzetti (2005) follow along this line. We will set off our literature review with the work of Scotchmer and Green (1990) who focus on the influence that the novelty requirement has on the pace of innovation. In their model an inventive firm faces the tradeoff between the profit of marketing a small technological advance and the value of maintaining a competitive advantage in technical knowledge. Scotchmer and Green (1990) assume that a firm cannot market a discovery without disclosure. So unless an innovation is patented, the firm will not earn a flow of profit from it. They study a simple case in which there is a basic technological knowledge invention that enables two possible innovations - one of them adds 26

A major policy issue temporarily discussed is the implementation—or absence—of research exemptions. See also Section 1.1.2 and Chapter 6 of this book.

22

1 Introduction

one unit of social value to the basic invention while the other adds two units of value. If the novelty requirement is strong, the more advanced technology can be patented without infringing a patent on the basic invention, if - on the other hand - the novelty requirement is weak, even the smaller improvement can be patented without infringing the patent issued on the basic technology. Their model setup is such that the smaller innovation requires one Poisson hit in a Poisson discovery process, whereas the discovery of the more advanced technology requires two Poisson hits. To capture the effect of the disclosure requirement Scotchmer and Green (1990) further assume that if a successful firm achieves the first “hit” and decides to disclose its invention by patenting it, then the other firm can immediately learn from the disclosed technology and only requires one additional hit to achieve the more advanced technology. One interesting conclusion of this paper is that firms may decide not to patent interim technologies in a multistage race since they cannot profit from the cost reductions the disclosure of technical information provides to competitors. These informational externalities even impose direct disadvantages on the patentee, since they make future competitors more potent. As a main result, Scotchmer and Green (1990) find that the disclosure of the first invention, e.g. patenting, is always socially desirable because it accelerates the discovery of the second invention and thereby reduces the aggregate research cost. This is due to the fact that Scotchmer and Green (1990) have omitted the monopoly pricing distortions a patent induces. This assumption excludes a major drawback of patents from the viewpoint of social welfare: the granting of a temporary monopoly. Therefore a more comprehensive analysis of the welfare effects of patenting should take into account both, the positive effects of disclosure and the negative effects of temporary monopoly a patent induces on social welfare.27 A different approach is chosen by Erkal (2005), who extends the setting of a repeated R&D race as introduced by Denicol`o (2000). The winner of the first race has a higher probability of winning the second race compared to his rivals. Yet if he decides to patent his invention he loses his headstart and consequently all firms face the same probability of success subsequently. Erkal (2005) focusses on the behavioral implications and welfare properties of three policy regimes. The first regime considers broad patent protection, where a second innovation infringes the patent of the first innovation. With narrow patent protection, two other possible regimes exist: either the antitrust authorities can have a policy of collusion or a policy of no collusion in the sense that they either permit or prohibit collusive licensing deals between holders of competing but non-infringing patents. Erkal (2005) finds that broad patent protection gives early innovators the highest incentives to patent. Thus, from a welfare point of view the desirability of a patent regime with broad patent protection depends on how attractive secrecy is for innovators. Naturally, as 27

A more comprehensive welfare analysis is provided in Sections 2.6 and 4.6 of this book.

1.2 The Economic Analysis of the Propensity to Patent

23

the rival firm’s probability of success in case of secrecy increases, innovating firms have increased incentives to patent their innovations. One of her main results is that having broad patent protection increases social welfare by encouraging earlier disclosure of innovations. Although Erkal’s model incorporates the disclosure requirement in a plausible way, a major drawback of the race setting is that the prize for the winner—the value of the patent—is exogenously determined. As the patent’s value clearly is one of the main decisive factors concerning the choice between a patent and secrecy, a more comprehensive approach should define it endogenously.28 Bhattacharya and Guriev (2006) develop a model of two-stage cumulative R&D where a so called research unit (RU) produces non-verifiable interim knowledge that can be used by a so called development unit (DU) to create a marketable product. The licensing of the interim knowledge can either take place as an “open sale”, based on a patent or as a “closed sale”, based on trade secrets. If the RU bases its knowledge transfer to the DU on a patent, legal support for an exclusive disclosure is only provided to one DU. However, a patent leads to the leakage of a given portion of the knowledge to the public due to the required disclosure in the patent application. In this case the knowledge disclosed via a patent facilitates inventing around the patent which may lead to a patentable follow-up innovation. Alternatively, the RU may decide to sell the knowledge privately, thereby relying on trade secrets. Here Bhattacharya and Guriev (2006) find that the RU needs to obtain a share in the licensed DU’s postinvention revenues to preclude further sales of the non-patented knowledge to other DU’s. As a main result Bhattacharya and Guriev (2006) come to the conclusion that the RU is more likely to rely on trade secrets if the interim knowledge is very valuable and intellectual property rights are not very well protected. Aoki and Spiegel (2009) examine the implications of pre-grant publication of patent applications in the context of a cumulative innovation model. Recall that pre-grant publication is compulsory after 18 months from the date of application (this requirement is in place in every industrialized country except the U.S.). The work by Aoki and Spiegel (2009) takes into account that the risk that arises from pre-grant publication, namely that proprietary knowledge is disclosed even if eventually a patent application is rejected, may discourage innovations. They compare a patent regime with pre-grant publication to a regime with confidential filing, where disclosure takes place only after a patent is granted. To capture the headstart of a successful inventor, Aoki and Spiegel (2009) assume that the leading firm in the R&D process has 28

The present analysis of the patenting decision offers two alternative approaches. In Chapter 2 patent value is determined by the monopoly profits a patentee can realize until an imitator enters the market whereas in Chapter 4 a patent’s value is determined by the extent of the patent’s scope as well as by the impact of the disclosure requirement.

24

1 Introduction

lower costs of developing the new technology. Deciding whether to patent, the innovative firm faces the trade-off between applying for a patent—which allows to sue a rival for patent infringement—and revealing information about the innovation through the application—which boosts the rival’s chances to develop the new technology. Aoki and Spiegel (2009) show that the implications of pre-grant publication depend on the strength of patent protection. In their model setting patent strength is captured by two factors: the likelihood that a patent will be granted on the one hand, and the likelihood that the patentee will win a patent infringement suit on the other. If patent protection is weak, so that a patent is unlikely to be upheld in court, Aoki and Spiegel (2009) find that the innovator does not file for patents under neither patent regime. When patents provide strong protection, the leading firm will file for a patent in both patent regimes. However, since the public disclosure hurts the patentee, it weakens the incentive to innovate. If the strength of patent protection is intermediate, the innovator will only file for a patent when patent applications are confidential. Aoki and Spiegel (2009) state two main conclusions: On the one hand, pre-grant publication discourages patent applications and weakens the incentives to invent if patent protection is intermediate, while on the other hand—holding the number of inventions fixed—pre-grant publication may raise the likelihood for new technologies to reach the product market thereby benefiting consumers and enhancing social welfare. Besides Waterson (1990), Harter (1994) provides the only contribution which models the patenting decision of a successful innovator in a setting with horizontally differentiated products. Other than in Waterson’s model, in the model of Harter (1994) the disclosure effect of a patent is taken into account. Product space is defined by the unit interval. Assuming a fencepost patent system, a patent protects a given product space situated around the innovation, thus forcing a competitor to locate his product at least as far away as the patent is broad. With a patent, the disclosed information leads to a reduction of the non-innovator’s imitation cost. Harter (1994) assumes that a non-inventor has four options after becoming aware of the innovator’s appropriation choice: he may exit the market, stay and continue his research, stay and re-focus his research or stay and imitate the innovation. The central result of the model is that “if imitating is not the non-innovator’s response when a patent is granted, then the innovator will patent the innovation” (Harter (1994), Theorem 1, p. 198). When we follow the contract theory of patents and understand that patenting has two opposing effects, Harter ’s result is quite straightforward: Both, the protective and the disclosure effect have to be balanced in the decision to patent. Naturally, the disclosure requirement will only have an impact if the non-innovator’s strategy is to imitate the innovation. For all other strategy choices (exit, stay, move), the patent only has a protective effect so that patenting is profitable for the innovator. The second result of Harter (1994) follows along the same line—he finds that if the non-innovator chose to imitate whenever the innovator preferred secrecy, the innovator would rather patent his innovation (Harter (1994), Lemma 4,

1.3 A New Theoretical Approach to the Propensity to Patent

25

p. 199). In this case the innovator can strongly profit from the protective effect of the patent as it forces the non-innovator to adjust his differentiation strategy by moving further away from the patented product—a strategy which increases the patentee’s profits. Thus the mechanism behind Harter ’s result is that the disclosure effect is outweighed by the protective effect so that patenting becomes profitable. Although Harter (1994) in principle allows for a variation of the extent of the disclosure requirement, he comes to the conclusion that it has no influence on the propensity to patent. This is, on the one hand, due to the fact that the original choices of product variety are not derived endogenously so that the impact of the disclosure effect on the variety choice of the non-innovator and its effect on the innovator’s profit is ignored.29 On the other hand, the result originates from the fact that Harter (1994) only considers one potential market entrant. Economic intuition suggests that with decreasing market entry costs an increasing number of firms is enabled to enter the market. In Chapter 4 of this book we present a more comprehensive approach that accounts for this aspect.

1.3 A New Theoretical Approach to the Propensity to Patent As the preceding literature review has revealed, two modeling approaches to the patenting decision can be distinguished. While one strand of the literature concentrates on cumulative inventions, the other focuses on so-called stand-alone inventions which face the threat of being invented around. In the first case it is the timing of the follow-up innovation which crucially depends on the impact of the disclosure requirement, in the latter case it is the extent to which inventing around takes place. Following this distinction, this book provides two alternative approaches to the patenting decision in the light of the disclosure requirement. In Chapter 2 the decision to patent is introduced into a dynamic model of vertically differentiated goods where the quality of a first innovation is superseded by a follow-up innovation. In Chapter 4 the patenting decision is analyzed within a setting of horizontally differentiated products where a successful innovator introduces a drastic product innovation. As patent protection is not perfect, competitors may be able to invent around the patent. The main focus of our analysis is the examination of the disclosure requirement’s significance for the propensity to patent. Following patent law, we assume that a patent requires the immediate and full disclosure of all technical 29

In a companion paper Harter examines the effects a patent system has on the product varieties chosen by potential duopolists (Harter (2001) in combination with Harter (1993)). As here he abstracts from the patenting decision and from a disclosure requirement, no additional insights concerning the focus of this book are gained.

26

1 Introduction

details concerning the patented discovery.30 This transfer of enabling knowledge benefits a non-inventor instantaneously. In the setting with vertically differentiated products it boosts the non-inventor’s research so that he may be able to accomplish a follow-up innovation at an earlier point in time, while in the setting with horizontally differentiated products the disclosed information facilitates inventing around by reducing market entry costs. In both cases the profits of the innovator will decrease due to the disclosure effect. Following the contract theory of patents this negative disclosure effect is opposed by a positive protective effect of patenting. The strength of this effect is subject to a patent’s scope: With vertically differentiated products the scope of a patent can be understood as a patent’s height in the sense that the patent defines the minimum level of quality enhancement that the competitor has to realize in order to enter the market without infringing the patent. In a setting with horizontally differentiated goods patent scope translates into patent breadth and defines a given range of product space surrounding the original innovation which is protected from the entry of competitors. In both modeling approaches we assume a fencepost rather than a signpost patent system and abstract from patent infringement issues. This implies that competitor’s will only enter the market with products that lie outside the patent protected product space. The patenting decision of the inventor has to balance the tradeoff between the benefits of temporary monopoly power (with vertically differentiated products) or an extended degree of product differentiation (with horizontally differentiated products) on the one hand, and the drawback of the complete disclosure of enabling knowledge on the other. Naturally, the positive effect may be enhanced by stronger property rights while the negative effect is subject to the impact of the disclosure requirement. Both modeling approaches have specific advantages. Due to the dynamic character of our model in Chapter 2, we are able to analyze the effects of patenting with regard to the timing of technology adoption. As the noninnovator is forced to realize a given level of product quality to enter the market without infringing the patent, his date of market entry is possibly postponed by a patent. From the viewpoint of the innovator one can say, that the threat of market entry (TOM) is mitigated by patenting. To keep the analysis tractable, only one potential entrant is considered here. The setting with horizontally differentiated products in Chapter 4 allows a varying number of entering firms. Subject to the impact of the disclosure effect, which leads to decreasing market entry costs, a patent may lead to a change of the underlying market structure, i.e. an innovator formerly operating as monopolist by patenting could possibly end up with an excessive market entry by rivals.

30

See Johnson and Popp (2003) for empirical evidence concerning this assumption.

1.3 A New Theoretical Approach to the Propensity to Patent

27

As the effects concerning knowledge disclosure due to patenting are central to our analysis, we will elaborate on the theoretical implementation of this parameter before proceeding with the respective analyzes. Necessarily we need to distinguish unintended knowledge spillover on the one hand and mandatory knowledge disclosure on the other. If an innovator chooses secrecy, he faces the possibility of unintended knowledge spillover due to either the leakage of information or due to reverse engineering. Both aspects are interdependent as existing knowledge spillover are only of use for those firms capable to appropriate them.31 Thus it is probable, that in an industry where reverse engineering is simple, this is due to the fact that spillover of information are easily appropriated. Therefore, whenever the invention is marketed, the usability of knowledge spillover can be interpreted as an industry-specific factor reflecting the easiness of reverse engineering.32 We capture this by the spillover parameter λ, 0 ≤ λ ≤ 1. If the innovator chooses to patent, he suffers from mandatory knowledge disclosure. We will refer to the impact of the disclosure requirement as α. As empirical evidence suggests that the relevance of the disclosure requirement as a reason not to patent varies throughout different industries (see Arundel et al (1995)), we partly allow for a variation of this parameter, 0 ≤ α ≤ 1. The theoretical implementation of these parameters given the alternative appropriation choices secrecy or patent, is summarized in Table 1.1, where γ is the measure for the inventor’s headstart in the setting with vertical differentiation and f are the fixed market entry costs in the setting with horizontal differentiation. The alternative situations patent or secrecy are distinguished by the subscripts p(atent) and s(ecrecy). The initial parameter situation concerning market entry costs or the technological headstart is marked by a swung dash, e.g. γ˜ is the extent of the inventor’s headstart before it is reduced by either unintended spillover or by the required disclosure of information.

31

See Kamien and Zang (2000) for an extensive theoretical approach to this issue. Industry-specific differences concerning the usability of knowledge flows could account for varying patent rates throughout different industry sectors (as found e.g. by Arundel et al (1995)). See Chapters 3 and 5 of this book for an empirical investigation of this matter.

32

28

1 Introduction Table 1.1 The Spillover Effect and the Impact of the Disclosure Requirement

vertical differentiation

patent

secrecy

γ p = α˜ γ

γ s = (1 − λ)˜ γ λ≤α

(Chapter 2)

horizontal differentiation (Chapter 4)

fp = αf˜

fs = (1 − λ)f˜ λ≤α

A central assumption in our analysis is that the innovator can exploit his innovation and realize positive profits even if he decides to rely on secrecy.33 This assumption is plausible when looking at industries where reverse engineering is prohibitively costly, e.g. the sectors aerospace or precision instruments, where products are extremely complex. Arundel et al (1995) find that in the three industry sectors aerospace, precision instruments and telecommunications equipment innovative firms even rely on the technical complexity of their products as an appropriation mechanism for their innovations. Moving away from the extreme case, a possible justification for the marketability of non-patented inventions is that a rival firm will never be able to immediately market a copied product. Instead, imitating competitors will need to invest some amount of time and resources until they are able to produce something similar to the initial innovation. In our analysis of the patenting decision this is implemented as follows: in our model approach with vertically differentiated goods we assume that the inventor has a technological lead compared to his rival and that in the absence of a patent the rival needs a given time span to catch up with the inventor. In the setting with horizontally differentiated products the difficulty of imitation is captured within the fixed market entry costs that non-innovators face.

33

We share this assumption with Anton and Yao (2004). Other than this one could also assume that the innovation cannot be marketed if the inventor relies on secrecy, since by launching the new product all formerly proprietary knowledge would spill out to the public allowing the immediate imitation of the original innovation so that profits go to zero due to perfect competition. Scotchmer and Green (1990) and Langinier (2005) follow along this line.

1.4 Empirical Insights on the Propensity to Patent

29

1.4 Empirical Insights on the Propensity to Patent Within this book we aim at empirically testing several hypotheses derived from the theoretical results. To do this we use German firm and countrylevel data from the year 2005 which is part of the Community Innovation Survey (CIS IV). The CIS was initiated in 1992 by the European Commission and deals with questions concerning the protection of intellectual property. Among other things in the CIS firms are asked to evaluate legal and nonlegal methods of intellectual property protection distinguishing product and process innovations. The importance of the alternative appropriation mechanisms are thereby scored on a five-point Likert scale.34 The empirical approaches to the firm’s patenting behavior can be subdivided into four clusters. These are: 1. 2. 3. 4.

Country-level surveys on the propensity to patent Firm-level surveys on the propensity to patent Empirical analyzes of the propensity to patent using firm-level data Empirical analyzes of the propensity to patent at the innovation level

The first approach provides insights on the relationship between R&D and patents at the country level so that the impact of differing patent policies on research productivity and on the propensity to patent can be analyzed. Referring to one specific country, the second approach includes firm-level surveys that analyze firms’ uses of alternative appropriation strategies of their intellectual property. The third approach builds on these firm-level surveys to gain further empirical insights on the patenting behavior of firms, while with the fourth approach—contingent on very detailed data—an investigation whether and why specific innovations have been patented or not is possible. We will look at the respective empirical literature in the following.

Country-level Surveys on the Propensity to Patent de Rassenfosse and van Pottelsberghe de la Potterie (2009) estimate an empirical model on the country-level which explicitly distinguishes the factors affecting the productivity of researchers from the factors affecting the propensity to patent. By this they can analyze the impact of different patent policy tools on research productivity as well as on patent propensity. de Rassenfosse and van Pottelsberghe de la Potterie (2009) come to the conclusion that both, 34 As Hussinger (2006) points out, a major drawback to the first wave of the CIS is the fact that firms were asked to evaluate the different appropriation tools regardless of their use. This was taken into account in the fourth CIS wave from which the data underlying our estimations is drawn. Here ratings were only accepted from firms that actually used the respective appropriation mechanisms.

30

1 Introduction

the propensity to patent as well as the research productivity play an important role in explaining cross-country variations in the number of patents per researcher. For the propensity to patent, the design of the relevant IP system plays a crucial role: whereas the strength of a patent system leads to a higher propensity to patent, de Rassenfosse and van Pottelsberghe de la Potterie (2009) find that the extent of patenting fees has a negative and significant impact. Firm-level Surveys on the Propensity to Patent The major firm-level surveys concerned with the intellectual property protection strategies of firms are Mansfield’s 1986 survey of 96 U.S. manufacturing firms (Mansfield (1986)), the PACE Survey of Europe’s largest industrial firms (Arundel et al (1995)) and the Carnegie Mellon Survey of 1478 U.S. R&D labs in the manufacturing sector (Cohen et al (2000)). Where only the two latter surveys provide data on the effectiveness of the different appropriation mechanisms as perceived by the innovative firms. Further evidence is provided by the so-called Yale Survey (Levin et al (1987)) for the United States and by the Community Innovation Survey (CIS) for several European countries. Other firm-level surveys have been carried out for Switzerland (Harabi (1995)), Japan (Cohen et al (2002)) and Spain (Galende (2006)). The following table summarizes the results concerning the effectiveness of the alternative appropriation mechanisms. Table 1.2 The Relative Importance of Different Appropriation Mechanisms Levin et al. Cohen et al. Cohen et al. 1987 2000 2002 US

US

N=650 prod.proc.

Japan

Harabi 1995

Arundel et al. 1995

Arundel 2001

Galende 2006

Switzerland

Europe

7 European Countries

Spain

N=1118/1087 N=567/522 N=358 prod.proc. prod.proc. prod.proc.

N=840 prod.proc.

N=2849 prod.proc.

N=152 prod.

Patents

3

4

4

4

2

3

4

4

2

3

4

4

4

Secrecy

4

3

2

1

4

1

3

3

3

1

2

3

2

Lead Time

2

1

1

2

1

2

2

1

1

4

1

1

-

Sales

1

2

3

3

3

4

1

2

-

-

-

-

-

Continuous Innovation

-

-

-

-

-

-

-

-

-

-

-

-

1

Complemen tary Resources

-

-

-

-

-

-

-

-

-

-

-

-

3

Complexity

-

-

-

-

-

-

-

-

4

2

3

2

-

&

Service

Perceived importance is ranked from the the most important (1) to the least important (4) prod.=product innovation proc.=process innovation Source: Adapted from M¨ akinen (2007)

Obviously firms perceive a patent neither as the only, nor as the most important appropriation mechanism for their R&D output. Other non-legal

1.4 Empirical Insights on the Propensity to Patent

31

mechanisms such as secrecy, lead time advantages, superior sales and service capabilities, continuous innovation, complementary resources or complexity of the innovation are often seen as the better means to protect intellectual property. Further, the relative effectiveness of appropriation mechanisms varies between process and product innovations. Overall, across all firm-level surveys summarized in Table 1.4, 50% come to the conclusion that patents are perceived as the least important appropriation mechanism for product innovations while even 71% find that they are perceived as least important for process innovations. This clearly points to the fact that firms heavily rely on alternative appropriation strategies for their intellectual assets.

Empirical Analyzes of the Propensity to Patent Using Firm-level Data In the empirical literature three definitions of the propensity to patent coexist (see Arundel and Kabla (1998)). In his early empirical studies Scherer introduced the definition of the propensity to patent as the number of patents per unit of R&D expenditure (Scherer (1965, 1983)). A major drawback to this approach is that this measure is influenced by the efficiency of R&D, i.e. technological opportunities of a firm. Nevertheless this approach has the advantage that it can be widely used as most countries provide public statistics of R&D expenditures and of the number of patents. Another existing measure for the propensity to patent is the percentage of innovative firms in a sector that have applied for at least one patent in a defined time period (Grefermann et al (1974), Kabla (1996), Licht and Zoz (1998)). The disadvantage of this approach is that most large manufacturing firms have at least one patent so that this definition of the propensity to patent is only adequate for small firms. The approach which is most closely related to the theoretical approach by Horstmann et al (1985) defines the propensity to patent as the percentage of patentable inventions that are patented (Mansfield (1986)), where “patentable” means that an invention (or innovation) meets the necessary inventive step and the industrial applicability to qualify for patent protection. In Section 1.1 these patentability requirements were extensively discussed. Arundel and Kabla (1998) follow the same definition, but rather refer to innovations than inventions and further move away from the restriction to patentable innovations. By this they actually measure the propensity to apply for a patent.35 35 In their paper Arundel and Kabla (1998) thoroughly discuss why this measure is still an appropriate measure for the propensity to patent. Their main argument is that differences in national grant rates which could lead to an overestimation of the propensity to patent should not markedly influence the results as most of the firms in the sample of Europe’s largest industrial firms had applied for at least one non-domestic patent either via the EPO or in the U.S. or Japan (Arundel and Kabla (1998), pp. 131).

32

1 Introduction

An early empirical approach is provided by Scherer (1965) who measures the propensity to patent in terms of the number of patents a firm obtains per million dollars of R&D expenditures. He finds that the propensity to patent is positively correlated with R&D investments of a firm. As a further quite interesting result Scherer (1965) states that the number of patents held by a firm is correlated higher with an estimate of the number of in-house attorneys than with the number of R&D employees. Later studies such as Scherer (1983) using a quite similar approach by defining the propensity to patent as the number of patents obtained per unit of R&D expenditure find inter-industry variations in the propensity to patent. The subsequent empirical literature analyzing the relationship between patents and R&D is very extensive. In a survey of the earlier literature concerned with the empirical relationship of firm size, R&D activity and patents, Cohen and Klepper (1996) come to the conclusion that the number of patents and innovations per dollar of R&D spendings decreases with firm size and/or the level of R&D. Using the first wave of the German part of the CIS, K¨onig and Licht (1995) investigate the importance of patents compared to non-legal appropriation methods of research output. To do this they specify a patent production function as a product of a propensity to patent function and an invention production function. They find that the non-legal intellectual protection tools are more effective than patents. Moreover, opposing empirical evidence for other European countries (see Arundel (2001)), K¨ onig and Licht (1995) find that patents are more important for larger firms than for small and medium enterprises (SMEs). Furthermore they conclude that firms rather rely on a bundle of legal and non-legal appropriation mechanisms instead of solely patenting. As M¨ akinen (2007) points out, a drawback to their approach is that the explanatory variables in their empirical model may have an impact on the productivity of R&D as well as on the propensity to patent. Brouwer and Kleinknecht (1999) follow a more comprehensive approach by controlling for R&D output rather than R&D input by using the sales accruing from innovative products as a control variable. In line with economic intuition they find a positive relationship between the sales of innovative products, i.e. R&D output, and a firm’s patenting behavior. Further, for a given R&D output, Brouwer and Kleinknecht (1999) state that smaller firms have a lower probability of applying for a patent than larger firms. With data from the 1993 European Community Innovation Survey (CIS), Arundel (2001) explicitly analyzes the relative importance of secrecy versus patents. His main finding is that a higher percentage of firms in all size classes rate secrecy as more valuable than patents. In a direct comparison of the use of patents versus secrecy Hussinger (2006), using data from the year 2000 CIS on German manufacturing firms, finds that patents are an effective means to protect innovations, i.e. commercialized inventions, while secrecy is rather important for inventions which are in the pre-market phase. She implements the measure sales of new products—which reflect the market success of innovations—as

1.4 Empirical Insights on the Propensity to Patent

33

dependent variable and thereby obtains a new measure of the importance of intellectual property protection. Arundel and Kabla (1998) use the data from the PACE survey of Europe’s largest industrial firms to calculate the sales-weighted patent propensity rates for 19 industries. They find that the patent propensity rates for product innovations vary from 8.1 % in textiles to 79.2 % in pharmaceuticals leading to an average of 35.9 % of patented product innovations. For process innovations the patenting propensity varies from 8.1 % in textiles to 46.8 % in precision instruments with an overall average of 24.8 % patented process innovations. Further Arundel and Kabla (1998) state that only four industry sectors reveal patent propensities which exceed 50 %. These are pharmaceuticals, chemicals, machinery, and precision instruments. Regression results show that large R&D intensive firms do not patent a higher percentage of their innovations than large firms with lower R&D intensities. Thus Arundel and Kabla (1998) come to the conclusion that firms with different R&D intensities only reveal minor differences in their valuation of patents. Other than this they find that firm size has a consistently positive and significant effect on the propensity to patent for process as well as product innovations, a statement which equivocates earlier investigations of the propensity to patent (see Cohen and Klepper (1996)). Overall empirical evidence based on firm-level surveys finds that the percentage of innovations which are patented varies by industry sector due to differences in the valuation of patents as a means to appropriate returns from R&D. Patents are most valued in sectors where the cost of copying an innovation is considerably smaller than the initial cost of invention. These sectors are pharmaceuticals, chemicals and machinery. Opposing this, patents are least valued in sectors where high costs of imitating create a natural entry barrier—here alternative appropriation methods such as secrecy, lead time advantages or technical complexity are preferred. This is found to be the case in the sectors aerospace or precision instruments.

Empirical Analyzes of the Propensity to Patent at the Innovation Level Naturally, only very scarce data exists on the innovation level where patented inventions or innovations can be distinguished from those that are kept secret or are subject to a different non-legal appropriation mechanism. According to M¨ akinen (2007) three data sets allow such an investigation. A Canadian data set (De Melto et al (1980), a Dutch data set (Kleinknecht and van der Panne (2009)) and a Finnish data set (M¨ akinen (2007)). The first is the outcome of a survey conducted by De Melto et al (1980) of 170 Canadian firms. Here data on the major innovations the firms developed in the time span from 1960 to 1979 was collected. In the end the Canadian data set included about 300 innovations. De Melto et al (1980) find that scientific breakthroughs resulting in entirely new innovations are protected more frequently by patents

34

1 Introduction

than incremental improvements of existing innovations. In addition they find a higher use of patents for original innovations than for innovations that attempt to imitate others.36 The Dutch data set consists of 398 innovations. Using a multivariate analysis Kleinknecht and van der Panne (2009) find that inventions resulting from scientific breakthroughs tend to be patented more often than incremental improvements of existing technologies. Also innovations which are new to the market and not only new to the firm tend to be protected by patents rather than by non-legal appropriation alternatives. The Finnish data set M¨ akinen (2007) uses includes information on 791 Finnish innovations. He finds that scientific breakthrough innovations yield a higher propensity to patent than minor innovations. Moreover, M¨akinen (2007) comes to the conclusion that technologically complex innovations are patented less often than other innovations. Overall his results indicate that the propensity to patent varies across technology classes, i.e. industry sectors.

1.5 Outline of the Book The present book consists of four main chapters. Chapters 2 and 4 theoretically analyze the driving forces behind the propensity to patent within two alternative modeling approaches, while in Chapters 3 and 5 we deduce several hypotheses from the results obtained in the theoretical analyzes which are then tested empirically. The theoretical analysis in Chapter 2 introduces the patenting decision of a successful inventor into a dynamic model of vertical product differentiation. Here the inventor has a technological headstart compared to a rival firm, allowing him to enter the market as monopolist. If the inventor chooses to patent, he faces two effects: On the one hand, the patent protects a given range of product space from the entry of the rival firm. On the other hand, due to the disclosure requirement, the inventor’s rival is able to accomplish a non-infringing follow-up innovation at an earlier point in time, thereby terminating the inventor’s monopoly. In the other theoretical Chapter 4 we analyze the patenting decision within a market of horizontally differentiated products. Consequently, not the timing of inventing around but the number of firms which are enabled to invent around the patent is decisive for the impact of the disclosure effect. Hence, the innovator does not lose his technological lead completely by patenting, but only faces a partial loss of his proprietary knowledge. Essentially both theoretical chapters have the same structure: After presenting the respective game theoretic model setup (Sections 2.1 and 4.1) the games are solved by backward induction, starting with the analysis of price competition on the last stage of the respective game in 36

Note that a possible explanation for this result could be that imitations lack the necessary inventive step to be patentable. See also Section 1.1.5 of this book.

1.5 Outline of the Book

35

Sections 2.2 and 4.2. In the case with vertically differentiated products we then proceed with the analysis of the firms’ quality choices (Section 2.3), in the case with horizontally differentiated products we proceed with the analysis of firms’ market entry decisions (Section 4.3). In Sections 2.4 and 4.4 the equilibrium outcomes of both approaches reveal the strategic decision of an inventor between a patent and secrecy. Subsequently, in Sections 2.5 and 4.5 we investigate whether the introduction of the additional possibility of licensing affects our main findings. Some welfare considerations presented in Sections 2.6 and 4.6 regarding the alternative appropriation mechanisms and a comparison of the strategies’ welfare effects provide insights on the question whether the patenting behavior of a successful inventor is socially desirable. Both theoretical chapters end with some concluding remarks in Sections 2.7 and 4.7. In Chapters 3 and 5 of the book the theoretical results are tested empirically using data from the Mannheim Innovation Panel of the year 2005.37 The empirical investigation proceeds for both theoretical approaches separately, but follows the same structure. In a first step in Sections 3.1 and 5.1, we deduce several hypotheses from the theoretical analyzes. In a second step, in Sections 3.2, 3.3 and 5.2 we describe how we implement the theoretical parameters in the empirical data. Section 3.4 and 5.3 provide the estimation results and Sections 3.5 and 5.4 conclude the empirical investigations. A summary and discussion of our overall results in Chapter 6 completes the book.

37

The empirical analysis was conducted under the co-authorship of Diana Heger from the Centre for European Economic Research, ZEW, Mannheim.

Chapter 2

The Decision to Patent with Vertical Product Differentiation

In this chapter we introduce the patenting decision of a successful inventor into a market with vertically differentiated products.1 The analysis of the patenting decision in this setting follows Zaby (2009a). The theoretical approach presented in this chapter builds on Dutta et al (1995) who model the strategic market entry decisions of two rival firms in a vertically differentiated product market. Due to the dynamic setting in Dutta et al (1995) and their assumption that the quality of an innovation increases costlessly over time, a first adopter can realize monopoly profits offering a low-quality product until the rival firm enters and offers a product with higher quality. Then both compete in an asymmetric duopoly. Both firms strategically choose their optimal adoption dates, that is, the quality at which they decide to cease their research activities and launch a new product which embodies the achieved quality. Dutta et al (1995) do not consider aspects of patent protection. They propose that two alternative equilibria evolve depending on the extent of consumer diversity: a preemption equilibrium, where both firms engage in a race for being the first, and a maturation equilibrium, where firms postpone adoption to reach a higher quality level. Extending their model we consider two firms which are asymmetric in their adoption capabilities: one firm is a successful inventor and possesses the complete technological knowledge about its invention. Its rival, the non-inventor, has failed to make the invention, but has accumulated some know-how. Assuming that the quality of the invention increases costlessly over time, the decision when to market the new technology, i.e. when to innovate, is equivalent to the decision at which quality level to market it. Note that due to the assumed asymmetry between firms in our model setting the terms “maturation” and “second mover advantage” cannot be used equivalently as in the 1

The idea of analyzing the effects of patent protection in a model of vertical product differentiation goes back to van Dijk (1996). Two related papers concerned with patent protection in vertically differentiated markets are Yiannaka and Fulton (2006) and Lambertini and Tedeschi (2007). All of these contributions do not consider the patenting decision itself.

37

38

2 The Decision to Patent with Vertical Product Differentiation

symmetric setting of Dutta et al (1995). The first adopter of a new product will realize monopoly profits offering the innovative technology at a relatively low quality up to the point in time when a rival firm enters and offers the new technology incorporated in a product of higher quality. Subsequently, both firms compete in an asymmetric duopoly. Additionally to the adoption decision the inventor faces the choice between a patent and secrecy to protect his discovery. A patent protects a given quality range from the entry of a rival. As we consider vertically differentiated goods, the intensity of patent protection is measured by the height of a patent. Assuming that patent protection is not perfect in the sense that it cannot cover all possible product qualities, the non-inventor may still enter the market with a non-infringing product in spite of a patent. In the case that the inventor himself is the first to innovate, he profits from temporary monopoly power until a competitor is able to enter with a sufficiently improved—non-infringing—version of the basic innovation. At the same time the innovator faces the drawback of the disclosure requirement linked to the patent which may enable the competitor to accomplish a follow-up innovation at an earlier point in time. We model the strategic decisions in a three stage game: On the first stage the inventor decides whether to patent or to rely on secrecy, on the second stage both firms simultaneously choose their qualities and on the last stage of the game they compete in prices. Due to our dynamic setting, patent protection may eventually come into operation even before the inventor decides to market the new product, thus leaving him more time to improve the basic invention in order to make a delayed market entry more profitable without facing the threat of a rival’s entry. The rest of this chapter is organized as follows. After laying out the model setup in Section 2.1, we start solving the game by backward induction in Section 2.2, setting off with the last stage by analyzing the price decision of firms. In the following Section 2.3 we analyze the quality choices of the firms on the second stage of the game for the case that the inventor decides to keep his invention secret (Section 2.3.1) and for the case that he patents (Section 2.3.2). We derive the subgame perfect Nash equilibrium in Section 2.4, considering alternative intensities of patent protection. In Section 2.5 we extend our model and consider the possibility of licensing. Some welfare considerations are stated in Section 2.6. Section 2.7 concludes. All Proofs can be found in Appendix A.

2.1 The Model Setup The patenting decision of a successful inventor and the market entry decisions of the two considered firms are modeled as a three stage game. On the first stage the inventor, henceforth denoted by subscript i, chooses the protection

2.1 The Model Setup

39

method for his discovery. His strategy, σi , can either be to protect it by a patent, σi1 = P , or to keep his invention secret, σi1 = S. In the following the superscript of σ denotes the stage of the game for which a strategy is relevant. On the second stage both firms choose whether to market a product of low quality, σu2 = ql, u , u = i, j, or a product of high quality, σu2 = qh, u , u = i, j, given the inventor’s protection decision. Hereby either firm may be the first adopter, i.e. the non-inventor may enter the market first despite of his technological disadvantage. On the third stage firms compete in prices, σu3 = pu , u = i, j. We will solve this three stage game by backward induction, setting off with the last stage where firms compete in prices, given their quality choices and the method of protection. Before we proceed with the analysis, we will take a closer look at the dynamic nature of product quality. Following Dutta et al (1995) and Hoppe and Lehmann-Grube (2001) we assume that spending more time on research activities suffices to improve the quality of the new technology over time. More precisely, the quality of the invention, q, increases proportionally to time without involving any further research costs. Thus, the inventor’s research time is given by ti (q) = q ,

(2.1)

implying that the inventor has to invest the time span ti (¯ q ) = q¯ in order to q ) obviously dereach a certain quality level q¯. Thus, the adoption date ti (¯ fines the adopted quality level, q¯. To capture the fact that the inventor has a technological headstart compared to his rival, we further assume that at the date of the invention (t = 0) he has a technological lead in height of γ which is assumed to be common knowledge. This means that the non-inventor will have to invest a time span which exceeds that of the inventor by γ to reach a given quality level, so that his research time to arrive at the same technology level can be specified by tj (¯ q ) = q¯ + γ. Furthermore the research capability of the non-inventor is positively influenced by unintended leaks of information. As mentioned earlier we will measure the spillover of information by an exogenously given spillover parameter λ. Due to the existence of a spillover effect, the initial headstart of the inventor, say γ˜ , has to be distinguished from his effective headstart, γ, where the latter accounts for a positive spillover effect. Whenever the inventor chooses secrecy, the extent of his technological lead at any point in time t > 0 will differ from his initial headstart if λ > 0. The extent of the inventor’s effective technological lead—given he keeps his invention secret—can thus be defined as γ s ≡ (1 − λ) γ˜ . Naturally, the noninventor profits from the spillover of information as this shortens his research time. Whenever λ > 0 it can be specified by tj (q) = q + (1 − λ)˜ γ.

(2.2)

If the inventor decides to patent he faces the mandatory disclosure of information we measure by α, with γ p ≡ α˜ γ . For tractability reasons in this chapter we assume that the disclosure effect is always maximal so that

40

2 The Decision to Patent with Vertical Product Differentiation

patenting leads to α = 0. In this case the inventor loses his lead completely by patenting as then γ p = 0. Proceeding with the analysis we will start solving the three stage game, setting off with the last stage.

2.2 Price Competition On the third stage of the game firms set their prices, σu3 = pu , u = i, j, given their strategic quality decisions on the previous stage. Thus, three scenarios are possible: (i) the inventor offers the low quality while the non-inventor offers the high quality, (ii) the non-inventor offers the low quality while the inventor offers the high quality or (iii) both firms enter with the low quality.2 Following Dutta et al (1995) we assume for simplicity that costs of production are zero. Subsequent to the unique quality decision of the firms on the second stage of the game, price competition will take place at every point in time up to infinity. Consequently, we first need to derive the profits a firm realizes in one period so that in a second step we will be able to derive the discounted overall profits the two firms would realize either as second adopter (follower), Fu (qh , ql ), or as first adopter (leader), Lu (qh , ql ), u = i, j. Let us proceed with the per period profits. The demand that firms face is modeled following Mussa and Rosen (1978). At most two firms can earn positive profits. Consumers differ in their tastes θ for improvements of the basic invention and are uniformly distributed with unit density f (θ) = 1 in the interval [a, b] where b > 2a > 0. This assumption assures a minimum level of consumer heterogeneity so that it is potentially possible for both firms to enter the market and earn positive profits. Each consumer will buy one unit of the product in every period as long as his net utility, U = θq − p, is greater than zero. To assure that the market is completely covered, i.e. all consumers buy one unit of the product, we will introduce a market coverage condition below. Firms strategic choices thus lead to a subdivision of an overall constant demand between them. As we assume that quality rises costlessly over time, an early adopter will necessarily offer the relatively lower quality ql . All consumers with a quality preference θ ≥ pl /ql will buy one unit of the product with quality ql from the temporary monopolist in every period until the rival firm enters with a higher quality qh at a later point in time. Straightforward computation yields the monopoly profit that the early adopter realizes in every period until his rival enters the market πm = Am ql (2.3) 2

The firms will only attempt to enter simultaneously with the same quality if a technological lead is absent, γ = 0. Then the preemption equilibrium analyzed by Dutta et al (1995) emerges. See Proposition 2.1 and Footnote 9 for further details.

2.2 Price Competition

41

with Am ≡ b2 /4. The adoption of the high quality qh by the rival firm constitutes an asymmetric duopoly. By definition qh > ql . Then the consumer indifferent between buying high or low quality is situated at θ0 = (ph − pl )/(qh − ql ), h, l = i, j ; i = j. The market share for the firm offering the low quality is [a, θ0 ] while the high quality offered by the late adopter has a market share of [θ0 , b]. Standard computations deliver the duopoly prices pl = (qh − ql )(b − 2a)/3

(2.4)

ph = (qh − ql )(2b − a)/3 and the corresponding profits per period πh = Ah (qh − ql ) πl = Al (qh − ql )

(2.5) (2.6)

with Ah ≡ (2b − a)2 /9 and Al ≡ (b − 2a)2 /9. To assure that the market for differentiated quality goods is completely covered, the consumer with the lowest taste parameter has to realize a positive net utility from buying the low quality good, aql − p l ≥ 0. Inserting p l as stated in Equation (2.4), rearranging terms yields −1/2

ql ≥ qh /(aAl

+ 1)

(2.7)

as market coverage condition. Using the per period profits derived above we can determine the overall profits firms can realize as early or late adopter of the innovative product. We denote the point in time when the early adopter enters the market with a low quality by tl and the point in time when the late adopter enters with a higher quality by th , respectively. Further we assume that all future profits are discounted with the interest rate r > 0. The early adopter’s overall profit consists of two parts: the monopoly profits he realizes from his adoption in tl until the second firm enters in th and the subsequent duopoly profits. Thus the lifetime profits of either firm if it is the leader amount to  th, u (qh∗ )  ∞ e−rt πm dt + e−rt πl dt, u = i, j . (2.8) Lu (ql , qh ) = ∗) th, u (qh

tl, u (ql )

The late adopter earns duopoly profits πh per period starting with his entry into the market in th with a high quality qh . Thus the lifetime profits of either firm as follower amount to  ∞ Fu (qh ) = e−rt πh dt, u = i, j . (2.9) th, u (qh )

42

2 The Decision to Patent with Vertical Product Differentiation

2.3 Quality Choices Moving one stage backwards, we proceed to the second stage where firms simultaneously choose their qualities given the protection decision of the inventor on the first stage. As mentioned before, three scenarios concerning the quality decisions are possible: (i) the inventor offers the low quality, σi2 = ql, i , σj2 = qh, j , (ii) the non-inventor offers the low quality, σi2 = qh, i , σj2 = ql, j , or (iii) both attempt to enter with the low quality. Both firms will make their strategic quality decisions given the inventor’s protection decision on the first stage where he either (a) chooses to protect his invention by a patent or (b) chooses to keep his invention secret. To solve this stage of the game we will again proceed in two steps: first we will derive the optimal quality decisions for either cases (i) and (ii) so that in a second step we can analyze which situation prevails given the protection decision of the inventor on the first stage of the game, (a) or (b). As we will see it is then straightforward to solve the subgame for case (iii). A late adopter has to decide when to adopt the new technology after his rival has already adopted a low quality ql . Inserting πh as defined in Equation (2.5) into the discounted overall profit function of a late adopter, Equation (2.9), optimization with respect to the quality level qh yields the optimum differentiation strategy given the early adopter’s quality decision, ql , qh∗ = ql +

1 r

∂th, u (qh ) ∂qh

,

u = i, j .

(2.10)

According to our specification of the research time functions the non-inventor will need γ additional periods to reach the quality qh , so that his entry date as late adopter would be th, j (qh ) = qh + γ. Due to his technological lead the inventor would be able to adopt this quality earlier, namely at th, i (qh ) = qh . Obviously, in both cases the derivative of the research time function with respect to the level of quality equals one, ∂th, u (qh )/∂qh = 1, u = i, j. This reduces the profit maximizing differentiation strategy as defined in Equation (2.10) to qh∗ = ql + 1/r for both firms and gives us a constant optimum level of differentiation, qh∗ − ql = 1/r, which is independent of the order of adoption. We can now derive the possible adoption dates by inserting this differentiation level into the respective research time functions (2.1) and (2.2). We get th, i (qh∗ ) = ql + 1/r and th, j (qh∗ ) = ql + 1/r + γ so that the respective lifetime profits amount to Fj (ql ) = e−1−r(ql +γ) πh /r if the non-inventor is the late adopter (Case (i)) and

2.3 Quality Choices

43

Fi (ql ) = e−1−rql πh /r if the inventor is the late adopter (Case (ii)). The early adopter anticipates the optimum differentiation strategy of his rival, qh∗ . Inserting πm and πl defined by equations (2.3) and (2.6) and taking into account the optimum level of differentiation, qh∗ − ql = 1/r, as well as the fact that ∂th, u (qh∗ )/∂ql = 1, optimization of (2.8) with respect to ql yields the reaction function for a first adopter ∗

ql,∗ u =

∗

1 − e−r(th, w (qh )−tl, u (ql )) (1 + Al /Am ) , ∗ ∗ r(1 − e−r(th, w (qh )−tl, u (ql )) )

u, w = i, j;

i = j . (2.11)

Recall the two possible scenarios: (i) the inventor takes the lead or (ii) the non-inventor is the first adopter. Let us first consider Scenario (i). The inventor’s research time as first adopter amounts to tl, i (ql ) = ql and the noninventor as second adopter would follow in tl, j (ql ) = ql + 1/r + γ. Inserting these relations into the profit function (2.8) and solving the integrals yields the overall profit of the inventor as early adopter Li (ql ) =

(1 − e−1−rγ ) πm + e−1−rγ πl r erql

(2.12)

with the corresponding profit maximizing quality level ql,∗ i =

1 − e−1−rγ (1 + Al /Am ) . r(1 − e−1−rγ )

(2.13)

This changes in Scenario (ii). As early adopter the non-inventor j could enter the market in tl, j (ql ) = ql + γ and the inventor as second adopter would follow with qh∗ = ql + 1/r in th, i (qh∗ ) = ql + 1/r.3 Inserting these adoption dates into Equation (2.8) and solving the integrals yields the overall profits of the non-inventor as early adopter Lj (ql ) =

(e−rγ − e−1 ) πm + e−1 πl r erql

with the corresponding profit maximizing quality level ql,∗ j =

1 − e−1+rγ (1 + Al /Am ) . r(1 − e−1+rγ )

(2.14)

To assure that tl, j (ql ) < th, i (qh∗ ) we assume that γ < 1/r holds throughout the rest of the paper.

3

44

2 The Decision to Patent with Vertical Product Differentiation

Since the non-inventor faces a technological disadvantage he is able to realize positive profits only after γ periods of time have elapsed, so that Lj (ql ) > 0 ∀ t > γ and Lj (ql ) = 0 ∀ t ≤ γ. So far we derived the lifetime profit functions for the possible scenarios solely depending on the adoption quality of the first adopter, Li (ql ), Lj (ql ), Fi (ql ) and Fj (ql ). Note that the asymmetric adoption capabilities of the firms were taken into account by inserting the respective research time functions ti (q) and tj (q) as specified in Equations (2.1) and (2.2). Therefore—due to our assumption that quality is proportional to time—the quality level ql can be replaced by time, ql = t. Fig. 2.1 The Preemption Equilibrium Lu (t), Fu (t)

300

Fi (t)

250 200

Fj (t)

150

Lj (t)

Li (t)

100 50

t∗l, i

4

6

8

10

t

tIj γ = 0.5, a = 6, b = 25, r = 0.5

In Figure 2.1 these profit functions are plotted for a relatively low value of the technological lead γ, where the dashed lines represent the possible lifetime profits of the inventor and the solid lines represent those of the non-inventor.

2.3 Quality Choices

45

Whenever Lu > Fu , firms prefer to be the first adopter (σu2 = ql, u ) and whenever Fu > Lu firms prefer to wait until a rival has entered and then enter as second adopter (σu2 = qh, u ).4 Alternative values of the technological lead as well as the protection decision of the inventor on the first stage yield different equilibrium outcomes. As we will see, the actual quality choices of the inventor and his rival on the one hand depend on the extent of the inventor’s technological headstart, γ, and on the other hand on his protection decision on the first stage of the game, σi1 = {P, S}. If he chooses to patent his invention, a given range of quality levels will be protected by the patent with the consequence that the non-inventor can only enter the market with a quality that exceeds the protected range. This positive aspect of the patent is accompanied by the drawback that the inventor loses his technological lead due to the disclosure requirement. If he chooses secrecy he maintains his headstart but misses the benefits of patent protection. Proceeding with the second stage of the game, we need to distinguish the subgames secrecy and patent.

2.3.1 Quality Choices if the Invention is Kept Secret Whenever the inventor decides to keep his invention secret on the first stage of the game, σi1 = S, the strategy space concerning the non-inventor’s quality choice is not constrained. Let us first consider the case where the technological lead of the inventor, γ, is small, see Figure 2.1. A reason for this could either be a small initial headstart, a high value of the spillover parameter or a combination of both. With γ low, both firms prefer to be the first adopter at their profit maximizing entry date t∗u ≡ tl, u (ql,∗ u ), u = i, j, as this would maximize their overall profits Lu (t∗u ), u = i, j. Since both anticipate that the other will follow the adoption strategy adopt first (σu2 = ql ) in the area where Lu > Fu , neither firm is able to realize the adoption date that would yield the highest overall profits as compared to alternative adoption dates. The argumentation behind this is straightforward. Suppose the inventor i intends to adopt quality ql,∗ i in t∗l, i . Then the non-inventor, j, anticipating this, would adopt at t∗l, i − , where is an infinitesimally small amount of time, as this yields higher profits for him, Lj (t∗l, i − ) > Fj (t∗l, i ). Now the inventor in turn has an incentive to preempt. Following this argument the behavior of both firms will be preemptive as long as Lu (t − ) > Fu (t) ∀ t < t∗u , u = i, j. So evidently either firm will stop preempting its rival as soon as it reaches the adoption date at which early and late adoption yield the same profits. This is the case at the intersection point tIu with Lu (tIu ) = Fu (tIu ), u = i, j. Therefore, the loser of the race for being the first will be the firm who’s intersection point 4

Note that the potentially higher profits at the far left of the Fu -curves cannot be reached since neither firm will enter as first adopter as long as Fu > Lu . No firm can become a follower if none decides to be the leader.

46

2 The Decision to Patent with Vertical Product Differentiation

is located closer to the maximum of the overall profit function, t∗u , u = i, j. A comparison of the intersection points of the inventor and the non-inventor leads to the following lemma. Lemma 2.1. Whenever both firms follow the strategy adopt first, σi2 = ql, i , σj2 = ql, j , the inventor will win the preemption race, σi2∗ = ql, i and σj2∗ = qh, j . This means that in a situation where the technological lead of the inventor is low, his equilibrium choice will be the adoption date tIj since then the noninventor has no incentive to continue the race for being the first as Lj (tIj − ) < Fj (tIj ).5 Following Dutta et al (1995) we will characterize this equilibrium as a preemption equilibrium since both firms engage in a race for being the first. Obviously the incentive for the preemptive behavior that leads to this equilibrium can be ascribed to the fact that the profit maximizing adoption date as first adopter, t∗u , lies on the right of the intersection point tIu . If the order of both points is reversed, the strategy of the firms changes from adopt first, σu2 = ql , to wait, σu2 = qh , u = i, j. The position of the dates t∗u and tIu , u = i, j, crucially depends on the extent of the technological lead, γ, as the following lemma points out. Lemma 2.2. If the technological lead is smaller than the threshold γˆ , both firms follow the strategy adopt first, σu2 = ql ∀ γ ≤ γˆ , u = i, j. As the technological lead rises above the critical value γˆ , the non-inventor’s strategy changes from adopt first to wait while the inventor’s strategy remains unchanged, σj2 = qh ∧ σi2 = ql ∀ γ > γˆ . While the inventor himself is always best off by adopting at his profit maximizing entry date t∗l, i , in case of a high technological lead the noninventor may have the incentive to wait and be the second adopter. This situation is depicted in Figure 2.2.

In this subgame equilibrium the low quality takes the value ql = qjI . We can assure that the market is covered by constraining the domain of consumer diversity. As ∂qjI /∂γ > 0, if the market coverage condition holds for the minimum value qjI γ=0  it is always fulfilled if γ > 0. Inserting qjI γ=0 into the critical condition (2.7) and rearranging terms leads to the restriction for consumer diversity: it has to exceed a critical level that can be approximated as c ≥ 0.2384 with c ≡ a/b, for the market to be covered. Thus we define the domain of consumer diversity as c ∈ [0.2384, 0.5[ to assure the existence of this subgame equilibrium. 5

2.3 Quality Choices

47

Fig. 2.2 Payoff Functions of the Non-Inventor when the Technological Lead is High Lj (t), Fj (t) Fj (t)

80

Lj (t)

Lj (t∗l, j )

20

tcrit

t∗l, j

3

4

5

6

t

γ = 1.2, a = 6, b = 25, r = 0.5

Since we know from Lemma 2.2 that the strategy and thus the relative positions of the adoption dates t∗l, i and tIi are not affected by an increase of the technological lead, for clearness only the alternative payoff functions of the non-inventor are plotted. As we can see in Figure 2.2 the profit maximizing strategy of the non-inventor is wait as long as t ≤ tcrit holds due to Fj (t) ≥ Lj (t) ∀ t ≤ tcrit . For any date after tcrit the non-inventor could gain from adopting at t∗l, j since Lj (t∗l, j ) > Fj (t) ∀ t > tcrit . Let us think about the strategy of the inventor. To maximize his profits he will try to reach t∗l, i . It is easy to show that the profit maximizing adoption date of the inventor always exceeds that of the non-inventor, t∗l, i > t∗l, j for γ > 0.6 Let us first suppose that t∗l, i ≤ tcrit . Then the non-inventor will wait long enough for the inventor to reach t∗l, i . Since both cannot gain from deviating this constitutes another subgame equilibrium.7 Following Dutta et al (1995) we will denote this a maturation equilibrium as the behavior of the firms results in so called staggered innovations (Dutta et al (1995), p. 564): the inventor unilaterally adopts at t∗l, i while his rival has no incentive to preempt 



We know that t∗l, i γ=0 = t∗l, j γ=0 and obviously ∂t∗l, i /∂γ > 0 and ∂t∗l, j /∂γ < 0 so it must be that t∗l, i > t∗l, j ∀ γ > 0.

6

7 Following the same argument as in Footnote 5 the critical value that consumer diversity has to fulfill to assure market coverage can be approximated as c > 0.2108. This is fulfilled by the earlier assumption that c ∈ [0.2384, 0.5[.

48

2 The Decision to Patent with Vertical Product Differentiation

him. Instead, he will wait to develop the technology further and will then enter the market with a product of higher quality. Now let us suppose t∗l, i > tcrit so that the non-inventor is better off adopting at t∗l, j before the inventor reaches his profit maximizing adoption date since Lj (t∗l, j ) > Fj (t) ∀ t > tcrit . Recall from Lemma 2.2 that tIi < t∗l, i is always fulfilled and that Li (t) > Fi (t) ∀ t > tIi . Consequently, the inventor will preempt his rival by adopting at t∗l, j − since Li (t∗l, j − ) > Fi (t∗l, j ). Thus, this situation leads to another possible preemption equilibrium.8 As the preceding argumentation showed we have to deal with two critical conditions to find out which of the possible alternative equilibria will emerge. Subject to the extent of the technological lead γ the non-inventor’s strategy can either be adopt first or wait and—if his dominant strategy is wait —he will either wait long enough for the inventor to reach t∗l, i or not. The following lemma sorts this out analytically. Lemma 2.3. If γ > γˆ so that the non-inventor’s optimum strategy is wait (σj2 = qh ) he will wait beyond t∗l, i only if the technological lead exceeds the threshold γˆ ˆ , t∗l, i ≤ tcrit iff γ > γˆ ˆ. Last we will turn to Case (iii) where both firms follow the same adoption strategy. From the preceding analysis we know that for all γ > 0 the inventor succeeds in entering the market as first adopter. Thus Case (iii) will only prevail if γ = 0 meaning that both firms are symmetric in their adoption capabilities. From Lemma 2.2 we know that for small values of the technological lead both firms follow the strategy adopt first. Following Dutta et al (1995) we assume that in this case firm i is successful with probability μ and firm j is successful in adopting first with probability (1 − μ). Analogously to our analysis of Cases (i) and (ii) in this preemption equilibrium the succeeding firm will adopt quality quI and the remaining firm adopts the quality level quI + 1/r.9 The situation thus is the following: as the technological lead rises, the nature of the non-inventor’s payoff functions is changed. This alternates the 8 In this subgame equilibrium the low quality takes the value q = q ∗ − . Other than l l, j ∗ −)/∂γ < 0. Substituting q = q ∗ − into the market covin the above cases here ∂(ql, l j l, j erage condition as stated in Equation (2.7) yields a critical condition for the techno  3e(5c−1) ≡ γc. logical lead subject to the level of consumer diversity, γ < 1r ln 16c3 −16c 2 +19c−3 c We assume that γ < γ holds throughout the rest of our analysis. 9 This corresponds to the preemption equilibrium analyzed by Dutta et al (1995). For all γ > 0 our results differ from those derived by Dutta et al (1995), but are consistent with the findings of Hoppe and Lehmann-Grube (2001). They show that the maturation equilibrium proposed by Dutta et al (1995) actually does not exist as the market coverage condition is not fulfilled (see Hoppe and Lehmann-Grube (2001), Proposition 1, p. 425). In our model it is the asymmetry between firms that leads to the existence of a maturation equilibrium: it will only exist if this asymmetry is high enough. Contrarily, if the asymmetry between firms vanishes, γ → 0, they engage in a race for being the first adopter, as Hoppe and Lehmann-Grube (2001) propose.

2.3 Quality Choices

49

order of the decisive dates tIj and t∗l, j and as a consequence leads to the different equilibrium outcomes. The following proposition characterizes the four alternative unique equilibria of the subgame secrecy as described above. Proposition 2.1. If the inventor chooses to keep his invention secret, σi1 = S, the subgame secrecy has four alternative Nash equilibria (i) a preemption equilibrium where firm i is the first adopter with probability μ and firm j is the first adopter with probability (1−μ); the successful first 2∗ adopter choosing σu2∗ = q I , the remaining firm choosing σw = q I +1/r > 2∗ σu with u, w = i, j, u = w whenever γ = 0, (ii) a preemption equilibrium with σi2∗ = qjI and σj2∗ = qjI + 1/r > σi2∗ whenever 0 < γ < γˆ, (iii) a preemption equilibrium with σi2∗ = ql,∗ j − and σj2∗ = ql,∗ j − + 1/r > σi2∗ whenever γˆ ≤ γ < γˆ ˆ, (iv) a maturation equilibrium with σi2∗ = ql,∗ i and σj2∗ = ql,∗ i + 1/r > σi2∗ whenever γˆ ˆ ≤ γ. Figure 2.3 depicts the quality levels which are realized by the respective first adopters in the alternative equilibria.

Fig. 2.3 Quality Levels of the First Adopter with Secrecy preemption (i)

preemption (ii)

q 0

qI

γ=0

qjI

ˆ 0 tj (φ + ). This makes patent height the only dimension of patent protection relevant for the subsequent analysis. To avoid confusion henceforth choice variables will carry the superscript S if the inventor chooses secrecy and the superscript P if he patents his invention. The inventor has an incentive to patent in every situation where he is not able to adopt his profit maximizing quality level, ql,∗ i . This is due to the fact that ∂Li /∂q > 0 ∀ q < ql,∗ i , so that the inventor will profit from a patent that allows him to choose a higher product quality whenever qiS < ql,∗ i . As the precedent analysis has shown, this is the case in any preemption equilibrium. Let qiS = {q I , qjI , ql,∗ j − } denote these subgame equilibrium outcomes we derived above. We will distinguish three patent types according to their protectional degree: weakly protective patents, strongly protective patents and delaying patents, see Figure 2.4. Patents of height φ ∈ ]qiS , ql,∗ i [ are defined as weakly protective patents since they accommodate the optimum differentiation strat∗ egy of the non-inventor, σj2∗ = qh, j , while having the positive effect of

2.3 Quality Choices

51

∗ protecting the quality range up to φ. Patents of height φ ∈ [ql,∗ i , qh, j [ are defined as strongly protective patents as they allow the inventor to reach his profit maximizing quality ql,∗ i , still admitting the non-inventor to follow his best differentiation strategy. The strongest protectional degree is reached ∗ with delaying patents. They are defined as patents of height φ ≥ qh, j so that additionally to the protective effect they affect the differentiation strategy of the non-inventor: he is forced to postpone adoption further into the future.10

Fig. 2.4 Alternative Intensities of Patent Protection weakly protective patent q qis

φ

∗ ql, i

∗ qh, j

∗ ql, i

∗ qh, j

strongly protective patent q qis

φ

delaying patent q qis

∗ ql, i

∗ qh, j

φ

Given that the inventor patents his invention, three alternative Nash equilibria are possible in the subgame patent depending on the strength of protection. They are summarized in the following proposition.

10 In the extreme case of φ ≥ b market entrance would be deterred for the non-inventor by a delaying patent. In this case the inventor will always patent since this assures him monopoly profits without any disadvantage from disclosure. Consequently this case is not of interest for the analysis of the patenting decision and we exclude it by assuming φ < b throughout the rest of the paper.

52

2 The Decision to Patent with Vertical Product Differentiation

Proposition 2.2. If the inventor chooses to patent his invention (σi1 = P ) the subgame patent has three alternative unique and stable Nash Equilibria depending on the extent of patent protection, φ. If (i) qiS < φ < ql,∗ i a patent is weakly protective and the inventor adopts the quality σi2∗ = φ while the non-inventor can follow his profit maximizing strategy with σj2∗ = φ + 1/r. The threat of entry is weakened. ∗ (ii) ql,∗ i ≤ φ < qh, j a patent is strongly protective and the inventor adopts the 2∗ quality σi = ql,∗ i while the non-inventor can follow his profit maximizing strategy with σj2∗ = ql,∗ i + 1/r. The threat of entry is weakened. ∗ 2∗ (iii) qh, j ≤ φ a patent is delaying and the inventor adopts the quality σi = ∗ ql, i while the non-inventor is forced to wait until he reaches the quality σj2 = φ + . The threat of entry is strongly mitigated. Figure 2.5 depicts the quality levels the inventor as first adopter realizes in the respective cases.11

Fig. 2.5 Quality Levels of the First Adopter with a Patent weak patent (i)

strong/delaying patent (ii)/(iii)

q 0

qiS

φ

∗ ql i

φ

∗ qh j

φ

So far we looked at the inventor’s quality choices given the strength of patent protection, omitting the impact of the disclosure requirement on the adoption date of the non-inventor. In the following section we will include this aspect and can then finally derive the subgame perfect Nash equilibrium of the three stage game by comparing the inventor’s alternative payoffs subject to the chosen protection mechanism.

11

Note that regarding the high quality level of the second adopter we have the ∗ + 1/r < q ∗ relations φ + 1/r < ql, i h, j < φ + .

2.4 The Patenting Decision

53

2.4 The Patenting Decision On the first stage of the game the inventor decides whether to patent, σi1 = P , or to keep his invention secret, σi1 = S. Naturally he will choose to patent whenever this yields higher profits than he could realize by keeping the invention secret. As a patent has the drawback of the disclosure requirement linked to it, he has to consider the tradeoff between a positive and a negative patent effect. The positive protective effect of a patent can be described by the difference between the inventor’s profit when he is able to choose the higher quality qiP due to patent protection and his equilibrium profits without a patent. Recall γ , where the parameter α is a measure for the impact that we defined γ P = α˜ of the disclosure effect. For simplicity we assume that α = 0, so that whenever the inventor patents, the impact of the disclosure effect is at its maximum and we have γ P = 0. The positive protective effect of a patent can then easily be isolated by setting α = 1 (γ P = γ˜ ), we have Δ+ = Li (qiP )|α=1 − Li (qiS )|α=1 .

(2.15)

This positive protective effect is opposed by the negative disclosure effect. Due to the disclosure requirement linked to a patent the inventor loses his lead which means that due to α = 0 the effective headstart of the inventor with a patent, γ P , becomes zero. Consequently, as the non-inventor is now S able to enter at an earlier point in time, tP j (q) = q, instead of tj (q) = q + γ, the duration of the monopoly of the patent holder is narrowed. This negative patent effect can be measured by the difference between the profit of the inventor with and without a technological lead, Δ− = Li (qiP )|α=1 − Li (qiP )|α=0 .

(2.16)

Combining the protective and the disclosure effect yields the overall effect that patenting has on the profit of the inventor, ΔP = Δ+ − Δ− . Inserting equations (2.15) and (2.16) this patent effect can be derived as ΔP = Li (qiP )|α=0 − Li (qiS )|α=1 .

(2.17)

Whenever the patent effect ΔP is positive, the protective effect overcompensates the disclosure effect and the inventor has an incentive to patent as this increases his overall profits. Figure 2.6 depicts the patent effect for strongly protective patents, φ ≥ ql,∗ i . In the region left of γˆ ˆ a preemption equilibrium would result if the inventor chose secrecy. From Proposition 2.1 we know that then he would realize the quality qiS = qjI . By patenting the inventor could increase his profits since he would be able to choose qiP = ql,∗ i > qjI due to the protective effect of the patent.

54

2 The Decision to Patent with Vertical Product Differentiation

Fig. 2.6 The Overall Effect of Patenting ΔP ΔP

5

ˆ γ ˆ

γ ˘

0.2

0.3

0.4

0.5

0.6

γ

-5

-10

-15

ΔP

∗ a = 6, b = 25, r = 0.5, φ = ql, i

Obviously the patent effect increases as the technological lead decreases. The intuition for this is straightforward: a decrease of the technological lead will attenuate the disclosure effect of a patent, while the protective effect is left unchanged - this must lead to a rise of the patent effect ΔP , which is equivalent to a leftward shift on the ΔP − curve in Figure 2.6. As we can see the patent effect ΔP takes positive as well as negative values as it crosses zero exactly once. The intersection point of the ΔP − curve with the x-axis defines a critical value of the technological lead, γ˘. For γ = γ˘ the protective and the disclosure effect compensate each other and the patent effect equals zero. If the technological lead is small, γ < γ˘ , the protective effect dominates the disclosure effect and the inventor profits from patenting his basic invention. If the technological lead exceeds the critical value γ˘ the disclosure effect outweighs the protective effect so that the patent effect is negative and the inventor prefers to keep his invention secret. The following proposition generalizes these findings, finally stating the unique and stable subgame perfect Nash equilibria of the considered three stage game.

2.4 The Patenting Decision

55

Proposition 2.3. The patenting decision of the inventor crucially depends on the extent of his technological headstart. He will choose to (i) (ii)

patent if a preemption equilibrium would prevail with secrecy and his technological lead is small, σi1 = P iff γ ≤ γ˘ < γˆˆ keep his invention secret, σi1 = S, if (a) (b) (c)

a γ˘ a γ˘ a γˆ ˆ

preemption equilibrium would prevail with secrecy and if < γ < γˆ < γˆ ˆ preemption equilibrium would prevail with secrecy and if < γˆ ≤ γ < γˆ ˆ maturation equilibrium would prevail with secrecy and if ≤ γ.

If the inventor chooses to patent (Case (i)), the adoption dates depend on the extent of patent protection, see Proposition 2.2. We have the adoption date pairs {(σi2∗ ; σj2∗ )} = {(φ; φ + 1/r), (ql,∗ i ; ql,∗ i + 1/r), (ql,∗ i ; φ + )}. Note that in the absence of a technological headstart, i.e. with symmetric firms (Case (i) of Proposition 2.1), the inventor will always choose to patent as the disclosure requirement has no impact and thus a patent solely has a protective effect. If the inventor chooses secrecy (Case (ii)) the adoption dates depend on the technological lead of the inventor, see Proposition 2.1 ((ii)−(iv)). Whenever the inventor’s headstart is low, Case (ii(a)) will result. Here the quality choices of the firms are {(σi2∗ ; σj2∗ )} = {(qjI ; qjI + 1/r)}. For an intermediate level of the technological headstart, γ ≥ γˆ , Case (ii(b)) will prevail with the quality choices {(σi2∗ ; σj2∗ )} = {(ql,∗ j − ; ql,∗ j − + 1/r)}. If the technological lead of the inventor is high, Case (ii(c)) will result, see Proposition 2.1 (iv). The quality choices of the firms are then given by {(σi2∗ ; σj2∗ )} = {(ql,∗ i ; ql,∗ i + 1/r)}. Figure 2.7 depicts a possible order of the alternative early adopter’s quality levels.12

12

∗ −  could also be reversed. Note that the order of φ and ql, j

56

2 The Decision to Patent with Vertical Product Differentiation

Fig. 2.7 Quality Levels of the First Adopter with a Patent or Secrecy Case (ii(a)): secrecy

Case (i): patent

q 0

qjI

φ

qj∗ −

∗ l, i

Case (ii(c)): secrecy

Case (ii(b)): secrecy

Obviously the earliest market entry occurs if the inventor’s technological headstart is low, but already exceeds the critical threshold which makes patenting unprofitable due to the disclosure effect. In Case (ii(a)) the inventor chooses secrecy and as the asymmetry between firms is rather low, the preemptive threat the non-inventor imposes on him is high, leading the inventor to enter the market early with quality qjI . The latest market entry occurs if the inventor’s technological headstart is very high (Case (ii(c))). The intuition behind this follows along the same line: As now the asymmetry between firms is high, the preemptive threat is completely absent. Recall that for a very high technological lead the non-inventor has no incentive to preempt the inventor but rather waits to realize a higher quality level, thereby giving the inventor the opportunity to realize the quality level which yields the highest overall profits for him, ql,∗ i . The above proposition states that the disclosure requirement plays a decisive role for the patenting decision of an inventor. If his discovery incorporates a substantial amount of proprietary knowledge the drawback of a patent as appropriation mechanism is immense. Naturally the value of the spillover parameter may influence this result as the following corollary states. Corollary 2.1. As the spillover of information, λ, rises, the propensity to patent increases since the effective technological lead, γ = (1 − λ)˜ γ , declines without patent protection and ∂ΔP /∂γ < 0.

2.5 Licensing

57

Recalling the interpretation of λ as the easiness of reverse engineering, this leads to the interesting conclusion that the propensity to patent increases as reverse engineering becomes easier. Thus a firm operating in an industry sector where reverse engineering is a substantial threat will rather choose to patent than rely on secrecy as even a large initial technological headstart will diminish due to the high value of the parameter λ. Consequently, following our results stated in Proposition 2.3, the protective effect of the patent then outweighs the disclosure effect which is weakened due to the high value of λ, leading the inventor to the decision to patent his invention. Intuitively an increase of the strength of protection should cause the same effect of increasing the inventor’s propensity to patent. The following corollary confirms this analytically. Corollary 2.2. The inventor’s propensity to patent increases if the height ∗ of a weakly protective patent, φ ∈ ]qiS , ql,∗ i [, or a delaying patent, φ > qh, j, increases. It remains unchanged if the height of a strongly protective patent, ∗ φ ∈ [ql,∗ i , qh, j ], increases. The intuition is clear for protective patents. A change of patent height has no impact on the disclosure effect of a patent, but naturally it influences the protective effect. A rise of φ would result in an upward shift of the ΔP − curve in Figure 2.6. By this the critical value γ˘ would move to the right so that the area in which the inventor decides to patent would grow larger. The protective effect can only increase if a weak patent’s protectional range rises, since then the inventor is able to reach a higher quality level. With a strongly protective patent the inventor already realizes his profit maximizing quality level and a further increase of patent height has no influence on the protective effect of a patent, leaving the propensity to patent unchanged. The case is different for delaying patents. They postpone the non-inventor’s entry date further into the future so that the profit of the inventor rises due to a longer duration of his monopoly. This again leads to an increase of the protective effect of a patent resulting in a rise of the propensity to patent.

2.5 Licensing An important aspect the preceding analysis has ignored so far is the possibility of licensing. Besides the advantages that the sequential approach of first analyzing patenting and subsequently including licensing has from a modeltheoretic point of view (as it allows a comparison of the separate strategies), our proceeding is supported by the fact that licensing may not take place if transaction costs are very high, for instance due to information asymmetries between firms and the absence of a market for licenses. Moreover, at the time the patenting decision takes place it will normally not yet be obvious whether

58

2 The Decision to Patent with Vertical Product Differentiation

an invention will turn out to be profitable enough to make licensing attractive. Thus, so far we have implicitly assumed that transaction costs are very high or that the profitability of the invention is not obvious so that licensing was no realizable option for the inventor. In the following we move away from this setting by assuming that transaction costs are low. Consequently patent and license becomes a feasible strategy for the inventor. Intuitively one would think that the additional income the inventor may obtain by licensing the patent to a competitor will lead to a situation where the invention is always licensed. In the following we will see that this is actually not the case: whenever the technological lead of the inventor is high, we find that he refrains from patenting and licensing the invention. Our analysis will proceed in two steps. First we will examine a patentee’s incentive to license his patent or not given that he has already patented, and then we will turn to the influence of licensing on the propensity to patent. With a license, the non-inventor may enter the market with a quality that lies within the patent protected quality range in exchange for the payment of a license fee. He has an incentive to do so whenever this yields higher profits for him.13 From Lemma 2.1 we know that the non-inventor will always be the second adopter, entering with the higher quality. He maximizes his profits whenever he is able to choose his optimal differentiation strategy, ∗ ∗ qh, j = ql, i + 1/r (Equation (2.10)). Recall from Section 2.3.2 that we distinguish three patent types according to their protectional degree: weakly protective patents, strongly protective patents and delaying patents. Weakly protective patents (φ ∈ ]qiS , ql,∗ i [) and strongly protective patents (φ ∈ [q ∗ , q ∗ [) accommodate the optimum difl, i

h, j

∗ ferentiation strategy of the non-inventor. Only delaying patents (φ ≥ qh, j) affect his differentiation strategy as he is forced to postpone adoption further into the future. Consequently, the non-inventor has an incentive to buy a license solely when the degree of patent protection is very high. In this case he can increase his profits by realizing his optimum differentiation strategy which lies within the patent protected quality range.

Lemma 2.4. If a delaying patent protects the invention, the non-inventor can increase his profits by buying a license. The maximum license fee which he is willing to pay corresponds to his increase in profit ∗ P ∗ P lmax = Fjl (ql,∗ i , qh, j ) − Fj (ql, i , qj ). Inserting the respective profit functions from Equation (2.9), decomposing the integrals using t∗h, j < tP j simplifying yields 13

In the following we assume that the innovator possesses the complete bargaining power and that he offers a license at a fixed license fee. Alternative approaches are to sell licenses via an auction or to collect a royalty per unit of output. See Kamien and Tauman (2002) for a comparison of the three licensing methods.

2.5 Licensing

59

 l

max

=

tP j

t∗ h, j

e−rt πh dt

(2.18)

as maximum license fee. To assure that the patentee in turn has an incentive to offer a license to his competitor, this license fee has to exceed the drawback that the patentee faces by licensing. Due to the advanced market entry of his competitor, the patentee’s monopoly is terminated earlier whenever he sells a license. This decrease of the patentee’s profits can be interpreted as a minimum license fee that makes licensing just profitable for him. It amounts to ∗ P l ∗ ∗ lmin = LP i (ql, i , qj ) − Li (ql, i , qh, j ) . Inserting the respective profit functions from Equation (2.8) and again decomposing the integrals by using t∗h, j < tP j simplifying yields  l

min

=

tP j

t∗ h, j

e

−rt

 πm dt −

tP j

t∗ h, j

e−rt πl dt

(2.19)

as minimum license fee. Equipped with these results we can now set up the critical condition for licensing: the patentee’s profit deficit has to be outweighed by his revenue from licensing so that lmax > lmin. As in equilibrium the per period profits πm , πh and πl are independent of t, the critical condition can be rewritten as πh > πm − πl . Inserting the per period profits from Equations (2.3), (2.5) and (2.6) we find that this condition is always fulfilled due to our assumption that c ≡ a/b ∈ [0, 0.5]. Summarizing these results we come to the following lemma. Lemma 2.5. A patentee always profits from selling a license. Summarizing our results so far we come to the following proposition. Proposition 2.4. If the inventor chooses to patent and license his invention (σi1 = l) the subgame license has three unique and stable Nash equilibria. (i)

(ii)

The inventor sells a license at a positive fee if the patent is delaying, ∗ 2 ∗ φ ≥ qh, j . He adopts the quality σi = ql, i and the non-inventor as second adopter realizes σj2 = ql,∗ i + 1/r. The inventor sells a license at a zero fee (a)

(b)

∗ if the patent is strongly protective, ql,∗ i ≤ φ < qh, j . He adopts 2 ∗ the quality σi = ql, i and the non-inventor as second adopter realizes σj2 = ql,∗ i + 1/r. if the patent is weakly protective, qiS < φ < ql,∗ i . He adopts the quality σi2 = φ and the non-inventor as second adopter realizes σj2 = φ + 1/r.

60

2 The Decision to Patent with Vertical Product Differentiation

The quality levels of the inventor as first adopter are the same as those depicted in Figure 2.5. Note that if we compare the resulting adoption dates stated in the above proposition to the results obtained in Proposition 2.2, the only difference is that in the case of a delaying patent the non-inventor is now able to realize his first-best adoption strategy, as it is possible for him ∗ to enter within the protected product space, qh, j < φ due to a license. The following figure depicts the alternative adoption dates of the non-inventor in the alternative cases patent or patent and license.

Fig. 2.8 Adoption Dates of the Non-Inventor with a Delaying Patent or with Licensing q 0

∗ ql, i

+ 1/r

φ+

patent

license

Abolishing the assumption that the inventor has already decided to patent, in a next step we will turn to the analysis of the influence that licensing has on the propensity to patent. We will analyze the non-inventor’s incentive to buy a license first. As the non-inventor’s strategy choice is neither constrained if secrecy prevails, nor if he owns a license, in both cases he is able to realize his profit maximizing adoption date. From his point of view, a license leads to γ = 0 due to the underlying patent, but it also leads to a postponement of his market entry date since the inventor will wait to reach his profit maximizing entry date, t∗l, i . We find that the overall effect of licensing leads to a decrease of the non-inventor’s profits, as the following lemma states. Lemma 2.6. The non-inventor realizes higher profits with secrecy than with licensing. Thus the non-inventor will never accept a licensing contract offered to him in the case that his alternative is secrecy. This changes if the alternative to licensing is a patent without licensing: in this case the non-inventor profits from licensing whenever patent protection is very strong and thus lmax > 0.

2.5 Licensing

61

Analogously to the preceding analysis, the inventor will choose to patent and license whenever he is able to realize the minimum license fee ∗ lsmin = Lsi (qis , qjs ) − Lli (ql,∗ i , qh, j ).

Note that the minimum license fee in this case corresponds to the negative of the overall patent effect as stated in Equation (2.17) with a delaying patent, ∗ φ > qh, j.

Fig. 2.9 The Overall Effect of Patenting when Licensing is an Option

ΔP , ΔP +l γ ˘

γ P +l ˆ γ ˆ

5

0.3

0.4

-5

0.5

γ

ΔP +l

-10

-15

ΔP

∗ a = 6, b = 25, r = 0.5, φ > qh, j

From the analysis of the patenting decision in Section 2.4 we know that the inventor will patent whenever the overall patent effect is positive, see Figure 2.9. Consequently, if ΔP > 0 and the inventor chooses to patent, we have lsmin < 0 meaning that the inventor would profit from licensing even if he had to pay a fee. This confirms Lemma 2.5. The interesting case is ΔP < 0 where the inventor initially refrains from patenting due to a strong disclosure effect. Now the minimum license fee is positive, lsmin > 0, and licensing would become the inventor’s preferred strategy only if lsmin is outweighed by the license fee that he can collect from his competitor. As the non-inventor can only decide whether to accept or decline a licensing contract and has no further bargaining power, the maximum license fee the inventor could collect is the same as in the case ΔP > 0.

62

2 The Decision to Patent with Vertical Product Differentiation

The critical condition for licensing to be profit enhancing, lsmin < lsmax , can be rewritten as ΔP +l ≡ ΔP + lsmax > 0 . (2.20) Economic intuition is straightforward. Whenever the overall negative effect of patenting is overcompensated by the license fee, the inventor will choose to patent and license rather than keep his invention secret. Figure 2.9 depicts ΔP +l in comparison to the overall patent effect ΔP . As lsmax is independent of the technological headstart, γ, licensing simply leads to an upward shift of the overall patent effect. By this, the option to license can lead to an increase of the propensity to patent: If the technological headstart is higher, but close to the critical threshold γ˘ which is decisive for patenting, the inventor will initially prefer secrecy. Due to the option to license and the resulting upward shift of the overall patent and license effect, this critical threshold moves to the right, γ P +l > γ˘ . Consequently the inventor’s appropriation choice changes from secrecy to patent and license. The following proposition summarizes the analysis of the inventor’s licensing behavior. Proposition 2.5. The licensing decision of the inventor crucially depends on the extent of his technological headstart. He will choose to (i)

patent and license his invention whenever (a) (b)

(ii)

γ ≤ γ˘ < γ P +l γ˘ < γ < γ P +l

keep his invention secret whenever γ ≥ γ P +l > γ˘ .

Comparing these results to the patenting strategies we found in the preceding section we can finally analyze how the option to license changes the inventor’s propensity to patent. As we stated earlier, the actual adoption dates of the inventor and the non-inventor do not change substantially except in the case of a delaying patent. Only then the license has an effect on the non-inventor’s adoption strategy as it is now possible for him to enter within the patent protected product space. All other results regarding the adoption dates of both firms remain unchanged, see Propositions 2.1 and 2.2. The inventor’s propensity to patent (and license) in the case of licensing is subject to the critical threshold γ P +l . As this threshold exceeds the threshold decisive for patenting in the case that the option to license is absent, γ˘ < γ P +l , we can state the following corollary Corollary 2.3. The propensity to patent increases due to the option to license. Having analyzed all possible subgames regarding the appropriation strategies of the inventor we will now turn to the consequences which the inventor’s strategy choices have on social welfare.

2.6 Welfare Considerations

63

2.6 Welfare Considerations The preceding analysis of the inventor’s patenting decision opens the question whether a patent is socially desirable or not. Naturally, a first step to analyze the welfare effects of patenting and licensing has to be the determination of a social welfare function. This will be our first attempt. Then we will derive social welfare given the alternative appropriation choices of the inventor: secrecy, patent and/or license.14 Finally we will link these results to the actual appropriation behavior of the inventor. Recall from Lemma 2.1 that the inventor will always be the first adopter entering the market as monopolist in tl with a low quality, whereas the noninventor will subsequently enter in th adopting a high quality. This unambiguousness allows us to drop the subscripts i and j in this section. Consumers thus first face a monopolistic market and subsequently a duopoly so that consumers’ surplus amounts to 

th

CS = tl



∞

+ th

e

−rt



b

pm /ql

e−rt



a

θ0

(θql − pm ) dθ dt  (θql − pl ) dθ +

b

θ0

 (θqh − ph ) dθ dt

where the first summand depicts the consumers’ surplus during monopoly and the second summand their surplus during duopoly. The producers’ surplus consisting of the overall profits of the two firms over time equals  ∞  th e−rt πm dt + e−rt (πl + πh ) dt . PS = tl

th

Inserting equilibrium prices, quality levels and profits derived in the previous sections, solving the integrals, summing up and collecting terms yields the social welfare WF(tl , th ) = [ 3 b2 e−rtl + (b2 − 4a2 ) e−rth ]/(8 r) .

(2.21)

It is easy to show that ∂WF(tl , th )/∂tl < 0 and ∂WF(tl , th )/∂th < 0. Note that except in the case of a delaying patent the non-inventor can follow his profit maximizing differentiation strategy, t∗h = tl + 1/r + γ, where γ = 0 if the inventor patents. Inserting t∗h into the social welfare equation we have social welfare solely depending on the inventor’s adoption date, WF(tl ) = [ 3 b2 e−rtl + (b2 − 4a2 ) e−r(tl +1/r+γ) ]/(8 r) . 14

(2.22)

Note that we focus on the effect that the inventor’s actual patenting and licensing behavior has on social welfare—meaning that we disregard issues such as compulsory licensing.

64

2 The Decision to Patent with Vertical Product Differentiation

Comparative statics yield two general relations: ∂WF(tl )/∂tl < 0 and ∂WF(tl )/∂γ < 0. Thus social welfare is higher, the earlier the inventor commercializes his discovery and the smaller his technological lead is.

2.6.1 Welfare with Secrecy If the inventor decides to keep his invention secret we know from Proposition 2.1 that three alternative equilibria are possible, subject to the extent of the technological headstart. In a preemption equilibrium the inventor will enter with quality qis = qjI or qis = ql,∗ j − , in a maturation equilibrium he will enter with quality qis = ql,∗ i . For the ease of exposition let qipre = {qjI , ql,∗ j − }. Thus, in a preemption equilibrium we have tl = qipre and th = qipre +1/r+γ. Substituting these adoption dates into Equation (2.21) results in the social welfare realized in a preemption equilibrium when the basic invention is not patented, pre

WFSpre = [ 3 b2 e−rqi

pre

+ (b2 − 4a2 ) e−r(qi

+1/r+γ)

]/(8 r) .

(2.23)

In a maturation equilibrium we have tl = ql,∗ i and th = ql,∗ i + 1/r + γ. Inserting these adoption dates into Equation (2.21) results in the social welfare realized in a maturation equilibrium when the basic invention is not patented, ∗

∗

WFSmat = [ 3 b2 e−rql, i + (b2 − 4a2 ) e−r(ql, i +1/r+γ) ]/(8 r) .

(2.24)

Note that due to ql,∗ i > ql,∗ j > qjI and ∂WF(tl )/∂tl < 0 social welfare is higher in a preemption than in a maturation equilibrium.

2.6.2 Welfare with a Patent If the inventor decides to patent, adoption dates depend on the height of the patent. As defined in Section 2.3.2, different levels of patent height lead to weakly protective patents, strongly protective patents or delaying patents. With a weakly protective patent we have tl = φ and th = φ + 1/r. As the non-inventor can follow his profit maximizing adoption strategy we can use the welfare function stated in Equation (2.22). Substituting the adoption date tl yields 2 −rφ WFP + (b2 − 4a2 ) e−r(φ+1/r) ]/(8 r) . weak = [ 3 b e

(2.25)

With a strongly protective patent the inventor is able to realize his profit maximizing adoption date so that tl = ql,∗ i and thus th = ql,∗ i + 1/r. Again

2.6 Welfare Considerations

65

using Equation (2.22), social welfare amounts to ∗

∗

2 −rql, i WFP + (b2 − 4a2 ) e−r(ql, i +1/r) ]/(8 r) . strong = [ 3 b e

(2.26)

¯ social welfare is higher with a weakly Due to ∂WF(tl )/∂tl < 0 and ql,∗ i > φ, than with a strongly protective patent. With a delaying patent the non-inventor is forced to postpone his market entry so we have tl = ql,∗ i and th = φ. Using Equation (2.21) we get ∗

2 −rql, i + (b2 − 4a2 ) e−rφ ]/(8 r) . WFP delay = [ 3 b e

(2.27)

Relative to the social welfare with a strongly protective patent only the adoption date of the non-inventor changes with a delaying patent, φ > ql,∗ i + 1/r. Consequently, due to ∂WFP (tl , th )/∂th < 0, social welfare is higher with a strongly protective patent than with a delaying patent. Concluding our welfare analysis in the case of a patent we can state Lemma 2.7. Social welfare in the case that the inventor patents decreases with the intensity of patent protection.

2.6.3 Welfare with Licensing With a license both, the inventor and the non-inventor, follow their profit maximizing adoption strategies irrespective of the strength of patent protection. The non-inventor has to pay a license fee which the inventor collects. As this is only a relocation of profits without any deadweight loss, the extent of this fee is irrelevant for the analysis of social welfare. Inserting tl = ql,∗ i into Equation (2.22) social welfare with licensing yields ∗

∗

WFl = [ 3 b2 e−rql, i + (b2 − 4a2 ) e−r(ql, i +1/r) ]/(8 r)

(2.28)

which corresponds to social welfare with a strongly protective patent, WFP strong . According to Lemma 2.7 we can thus conclude that social welfare with a weakly protective patent is higher than with licensing, and that social welfare with a delaying patent is lower than with licensing.

2.6.4 Welfare Maximizing Appropriation Choice Having derived social welfare for the alternative appropriation strategies of the inventor, we will now link these results to his actual strategy choices. As the derivatives of the general welfare function (Equation 2.21) with respect to the adoption dates th and tl are both negative, an early date of the first

66

2 The Decision to Patent with Vertical Product Differentiation

technology adoption as well as a small level of differentiation are socially desirable. Intuitively a patent should then have a welfare reducing effect: on the one hand it postpones the first quality adoption by its protective effect and on the other it possibly even increases the level of quality differentiation.15 Let us take a closer look. From Proposition 2.3 we know that the inventor will choose to patent whenever γ > γ˘ , as then the overall patent effect is positive, ΔP > 0. = The effect that patenting has on social welfare can be computed as ΔWF P WFP − WFs . As in the preceding analysis we have to distinguish alternative intensities of patent protection. Integrating the analysis of weakly and strongly protective patents we have tl = φ and th = φ + 1/r with φ = [φ, ql,∗ i ]. Inserting these adoption dates into Equations (2.22) and (2.23) the effect of patenting on social welfare yields16

pre



I

2 −r φ ΔWF − e−rqj ) + (b2 − 4a2 )(e−1−rφ − e−r(qj +1/r+γ) ) . weak, strong = 3 b (e φ, (2.29) = 0, for a patent height This patent effect on welfare is zero, ΔWF weak, strong φ,

of φWF with

φ

WF

≡

qjI

2  1 4a − b2 (1 + 3e1+rγ ) . + γ − ln r 4a2 − b2 (1 + 3e)

(2.30)

Since ∂ΔWF weak, strong /∂ φ < 0 the patent effect on social welfare will be posφ,

itive for all patent heights φ < φWF . It is simple to show that the overall patent effect is negative for a patent of height, φWF . Since the propensity to patent decreases when patent height decreases (see Corollary 2.2), an inventor who chooses secrecy for the patent height φWF will also choose secrecy for any patent height below this level, φ < φWF . This leaves us to derive the effect of patenting on social welfare with a P delaying patent. From Lemma 2.7 we can deduce that WFP delay < WFstrong . Thus whenever a strongly protective patent has a negative effect on social welfare, a delaying patent will as well. The analysis of the welfare effects of patenting is summarized in the following proposition. Proposition 2.6. Regardless of the intensity of patent protection patenting is never welfare enhancing. Things change if licensing is taken into account. Following the above findings licensing can have a positive effect on social welfare only if leads to an earlier adoption date of the non-inventor, ∂WF(tl , th )/∂th < 0. From ∗ , which forces the non-inventor to As is the case with a delaying patent, φ > qh, j delay his entry. 16 As the inventor never patents if a maturation equilibrium prevails with secrecy, it suffices to use WFspre from Equation (2.23) with qis = qjpre . 15

2.7 Concluding Remarks

67

Lemma 2.4 we know that the non-inventor only accepts a licensing contract if the invention is protected by a delaying patent. This is due to the fact that in this case his market entry is postponed beyond his optimal entry date. By buying a license the non-inventor can enhance his profits as he is enabled to enter the market earlier with his profit maximizing adoption strategy. Analyzing social welfare according to the inventor’s actual strategy choices if licensing is an option yields Proposition 2.7. Licensing is only welfare enhancing if patent protection is very strong. Concluding our analysis of social welfare we find that from a welfare point of view, secrecy is the preferred appropriation strategy. This counter-intuitive result is due to the fact that the parameters which positively influence the inventor’s propensity to patent have a negative impact on social welfare. The results regarding social welfare have to be interpreted with great care, as the positive effect of patenting, namely the dissemination of knowledge, cannot be taken into account properly in a duopoly model.

2.7 Concluding Remarks To capture the fact that the inventor has a technological lead compared to a rival who has not yet successfully invented, we introduced the patenting decision into a dynamic setting with vertically differentiated products where firms face asymmetric research capabilities. In this duopolistic setting the technological lead of the inventor was modeled as a time advantage. With secrecy an innovator faces the disadvantage of unintended spillover of information while with a patent the impact of the disclosure requirement results in a complete loss of his headstart (disclosure effect). In exchange for the disclosure the patentee is granted temporary monopoly power (protective effect). However, the duration of his monopoly is shortened due to the fact that the mandatory disclosure facilitates R&D for the competitor. With vertically differentiated products the intensity of patent protection, i.e. the patent’s scope, is given by the height of the patent. Increasing patent height constrains the strategy space of the competing firm in the sense that its date of market entry is (possibly) postponed into the future. Our main results are summarized in Table 2.1.

68

2 The Decision to Patent with Vertical Product Differentiation Table 2.1 Summary of the Theoretical Results with Vertical Differentiation

ptp

spillover

technological lead

patent height

λ↑

γ↑

φ↑

+

–

+

ptp = propensity to patent TOM = threat of market entry

The central parameters of our analysis of the propensity to patent in a setting with vertically differentiated products were the technological lead of the inventor, γ, the unintended spillover of information, λ, and the intensity of patent protection, patent height φ. We found that while the unintended spillover of information as well as the height of the patent have a positive effect on the inventor’s propensity to patent, the extent of his technological lead has a negative impact. These results are partly quite straightforward: An increase of unintended information spillover makes the appropriation strategy secrecy less attractive so that the inventor rather chooses to patent as the negative effect of the required disclosure now appears less drastic. If the intensity of patent protection increases, the protective effect of a patent will more likely dominate the disclosure effect and thus the propensity to patent rises. Regarding social welfare we found that a patent without licensing is never desirable and that even with licensing a positive effect can only be found for delaying patents. As we pointed out, these results need to be interpreted very cautiously as within the underlying duopolistic setting the complex implications a patent has on social welfare cannot be treated properly. Two specific drawbacks of the modeling approach with vertically differentiated products should be pointed out. The first is that we assume the spillover parameter λ to remain constant over time. Thus it does not increase even if the invention is marketed. In a more elaborated model, one could assume that λ(t) is increasing over time with λ (t) > 0 and limt→∞ λ(t) = 1. However, this would not change the qualitative nature of our results but would lead to a more complex analysis. The second specific drawback of the setting with vertically differentiated goods is that the impact of the disclosure requirement is always at its maximum, an assumption implemented to facilitate our analysis. Including a varying impact of the disclosure requirement would result in a technological lead specified as γ(α, λ) = α(1 − λ)˜ γ and as ∂γ/∂α > 0 a decrease of the impact of the disclosure requirement (α ↑) would lead to an increase of the critical threshold decisive for the profitability of a patent. This would be equal to a rightward shift of the overall patenting effect depicted in Figure 2.6 which is equivalent to an increasing propensity to patent. Nevertheless, this extension of the model does not change the qualitative nature of

2.7 Concluding Remarks

69

our results, namely the critical interplay of the protective and the disclosure effect of a patent. In the next chapter we will investigate whether our theoretical findings are supported by empirical evidence. To do this we deduce several hypotheses from the theoretical results and test these empirically.

Chapter 3

An Empirical Investigation of the Decision to Patent with Vertical Product Differentiation

The basis for the empirical analysis presented in this chapter is the Mannheim Innovation Panel (MIP) of the year 2005. The MIP is an annual survey which is conducted by the Centre for European Economic Research (ZEW) Mannheim on behalf of the Federal Ministry of Education and Research. The aim of the survey is to provide a tool to investigate the innovation behavior of German manufacturing and service firms. Regularly—currently every two years—the MIP is the German contribution to the Community Innovation Survey (CIS). Our empirical investigations are based on about 740 firms. In the year 2005, the survey contained additional questions concerning the firms’ perception of their competitive situation. Questions concerning the characteristics and the importance of specific competitive factors like price or quality were asked as well as the perceived competitive situation with respect to the number of competitors and their relative size. Due to this thorough investigation of the competitive environment we are able to specify the relevant market as perceived by firms. The empirical analysis proceeds as follows: After summarizing the theoretical results in multiple hypotheses (Section 3.1), the data sample and the implementation of the theoretical parameters in the data are described (Sections 3.2 and 3.3). The results of the empirical estimations are presented in Section 3.4. Section 3.5 concludes the empirical investigation. The empirical estimations presented in this chapter in large parts follow Heger and Zaby (2009).

3.1 Hypotheses and Their Empirical Implementation In this section, we derive hypotheses based on the model in Chapter 2 in order to verify our theoretical results. Contrary to the theoretical procedure which uses backward induction we will use a chronological approach for the empirical analysis, i.e. we will first empirically investigate the driving factors

71

72

3 Empirical Analysis of the Model with Vertical Product Differentiation

behind the patenting decision and will then, in a second step, examine the theoretical results concerning rival’s timing of market entry, i.e. the threat of entry the innovator faces. Some crucial assumptions were made to solve the theoretical model: The framework in which the model and its results are valid is one of vertically differentiated products, i.e. the firms compete in prices and quality. Recall the results on the first stage of the three-stage game: The patenting decision entails two opposing effects: a protective effect and a disclosure effect. Obviously, a firm decides to patent if profits generated by the protective effect exceed the reduction of profits by the disclosure effect, otherwise the results of the R&D activities are appropriated by secrecy. Both effects are driven by the three parameters “extent of the technological lead”, γ, “usability of technological spillover”, λ, and “intensity of patent protection”, φ. The spillover are expected to be higher in industries where reverse engineering is easy. While, for example, in pharmaceuticals the patenting rate is rather high, in an industry sector such as precision instruments the patenting rate is found to be rather low. Relating this observation to the fact that a patent forces the disclosure of technological knowledge and therefore facilitates the research efforts of rival firms, some industry-specific differences concerning the usability of the disclosed information have to exist, which account for the difference in patenting rates. In the theoretical model, we captured this aspect by linking the technological headstart of a successful inventor to an industry-specific parameter that reflects the easiness of reverse engineering (see Arundel et al (1995)). Summarizing the theoretical results concerning the patenting decision, we derive the following hypotheses: Hypothesis 3.1 Whenever the disclosure requirement has an impact, the protective effect of mitigating the threat of entry may be overcompensated by the disclosure effect so that the higher the technological lead of the inventor, the lower is his propensity to patent. Hypothesis 3.2 In industries in which spillover are easy to use, e.g. because they are characterized by easy-to-achieve reverse engineering, the technological lead will diminish and hence the propensity to patent will increase. In the next step, we present how we implement our theoretical results into an estimation equation. From Equation 2.2 we know that the effective technological lead consists of the initial headstart of the inventor which is eventually decreased by an industry-specific spillover effect in the absence of a patent: γ S = γ˜ − λ˜ γ Where γ˜ is the initial technological headstart of the inventor and λ is the spillover parameter. Note that the effective headstart consists of two terms: the sole extent of the technological lead, γ˜ , and the product of the spillover parameter and the technological lead, λ˜ γ.

3.1 Hypotheses and Their Empirical Implementation

73

As stated in Hypotheses 3.1 and 3.2, the decision to patent is mainly driven by the initial headstart. We capture this theoretical result with the following empirical equation: P = β1 + β2 T L + β3 RE + β4 T L ∗ RE + Controls +  ,

(3.1)

where P denotes the patenting decision, T L the technological lead (γ) and RE the easiness of reverse engineering (λ). In line with the theoretical findings we conjecture a negative influence of the technological lead (T L) and a positive effect of the interaction term of T L and RE. As reverse engineering has no direct effect on the propensity to patent in the theoretical model, we expect to find no significant effect empirically. Given the patenting decision on the second stage of the game, firms decide on when to enter the market. As we find that the inventor always takes the lead, the adoption choice of the non-inventor crucially depends on the extent of the inventor’s technological headstart. Hence, we come to our next hypotheses. Hypothesis 3.3 The rival’s market entry is delayed if the effective technological headstart of the leading innovator is large. Reverse engineering has a detrimental effect on the technological lead and hence increases the threat of rival’s entry. Furthermore, if an inventor chooses to patent, the mandatory disclosure of the invention enables its rival to enter the market at an earlier point in time as the inventor loses his lead. As the disclosure effect is opposed by the protective effect of a patent, the patentee’s competitor might be forced to postpone his market entry in order to develop a non-infringing product. This mitigates the threat of entry that the patentee faces and naturally this effect should be stronger, the higher the level of patent protection is. Thus we propose the following hypothesis. Hypothesis 3.4 The threat of entry decreases with the intensity of patent protection, i.e. patent height. From Proposition 2.2 we know that the threat of entry is weakened with either a weak or strongly protective patent and that the threat of entry is strongly mitigated with a delaying patent. In combination with Hypothesis 3.3 this translates into the following empirical model: T OM = β1 +β2 T L+β3RE+β4 T L∗RE+β5DP +β6 SP +β7 W P +Controls+ , where T OM is the threat of market entry, DP reflects delaying patents, SP strongly and W P weakly protective patents. For a definition of T L and RE see the previous equation. The technological lead, T L, should now have a negative effect on the threat of entry, i.e. the time until entry increases with the extent of the technological headstart. The interaction term with reverse

74

3 Empirical Analysis of the Model with Vertical Product Differentiation

engineering should again reveal the opposite effect while the sole effect of RE should not be significant. In accordance with the theoretical model’s predictions, a delaying patent should have a negative effect on the perceived intensity of the threat of entry, while strong and weak patents should have a negative or an insignificant effect.

3.2 Sample Definition In order to test our hypotheses, we need to restrict our sample to innovative firms, i.e. we exclude firms which did not launch a new product or process within the period 2002 to 2004. Furthermore, the theoretical model is designed for vertically differentiated products, i.e. the competitive situation is characterized by quality competition. In the 2005 survey, one question is aimed at the characterization of the competitive situation on the main product market. The firms are asked to rank the following choices according to their importance: quality, price, technological advance, advertisement, product variety, flexibility towards customers. We keep those observations for which firms have indicated that quality is the most, second or third most important feature of competition. The first part of the empirical analysis deals with the propensity of patenting vs. secrecy and whether it depends on technological leadership (Hypotheses 3.1 and 3.2). In the theoretical model, patenting and secrecy are excluding categories: A firm can either patent or keep the R&D results secret.1 For the investigation of the threat of entry (Hypotheses 3.3 and 3.4), we need to include patent height in the data set. For this we used patent information from the European Patent Office (EPO) for the observation period 2002 to 2004 including the IPC codes stated in every patent application.2 The complete classification codes assign a patent into specific clusters which vary in their aggregational level, see the following table.3 1

For the empirical implementation, this assumption needs to be treated carefully. In the data set, we find several examples of firms which use both, patenting and secrecy. Hence, we observe that firms may have more than one innovation and that these may be treated differently. Assuming that firms which indicate patents as highly important use patenting as their main IP protection strategy, all other protection strategies are ignored. Furthermore, all firms which use other formal mechanisms like trademarks are dropped even if they indicate that they use secrecy. A reason for this procedure is that formal protection dominates strategic mechanisms and we do not account for other formal protection methods besides patenting (Blind et al (2006)). 2 See Section 1.1 for an elaboration on IPC codes. 3 Actually any additional information complementing the invention information which may be useful for search purposes can also be classified by IPC codes through the patent authorities (§123, IPC Guide). To distinguish the Classification symbols referring to the invention information and those referring to additional information, the invention information symbols are displayed in bold font style while the additional

3.2 Sample Definition

75

Table 3.1 International Patent Classification (IPC) Code of the European Patent Office Section

A

Class

01

Subclass

B

Group Main Group

Subgroup

33/0

33/08

As a patent may be codified by more than one IPC Code, the variation of codes is a good indicator for different levels of patent height. The IPC Guide gives a quite clear statement on the relation between the IPC code and the height of the respective patent. The titles of sections, subsections and classes are only broadly indicative of their content and do not define with precision the subject matter falling under the general indication of the title. In general, the section or subsection titles very loosely indicate the broad nature of the scope of the subject matter to be found within the section or subsection, and the class title gives an overall indication of the subject matter covered by its subclasses. By contrast, it is the intention in the Classification that the titles of subclasses [...] define as precisely as possible the scope of the subject matter covered thereby. The titles of main groups and subgroups [...] precisely define the subject matter covered thereby [...]

(§68, IPC Guide) In line with the above quote, since “the class title gives an overall indication of the subject matter covered by its subclasses”, we define the alternative patent heights weakly protective, strongly protective and delaying patents starting with variations at the class level, as variations at the sectional level (including subsections), only “very loosely indicate the scope” of the respective patent. Thus we implement the alternative patent heights from our theoretical model as follows: Whenever a classification symbol differs on the level of classes or subclasses, we characterize the respective patent as delaying. We define a patent as strongly protective, if the IPC codes vary in groups and as weakly protective, if the IPC codes differ in subgroups. Additionally all patents with a single IPC code are classified as weakly protective patents. In a next step we merge this information to the MIP data set we defined above.4 By this we condense the EPO data to the firm level. Hence, we now observe firms holding various numbers of delaying, strongly and/or weakly protective patents. We identified only few firms that stated to hold a patent information symbols are displayed in non-bold font style (§160, IPC Guide). As the average patent is assigned two IPC codes we propose that this distinction is not crucial for our empirical analysis. 4 The merge was conducted by Thorsten Doherr, ZEW, Mannheim, using a computer assisted matching algorithm on the basis of firm names.

76

3 Empirical Analysis of the Model with Vertical Product Differentiation

in the MIP survey but had no equivalent entry in the EPO data set. Due to the missing information we dropped these observations.

3.3 Variable Definition In this section we describe how we define the core variables of the estimations. First, we take a look at our dependent variables: Patenting is measured as a dummy variable indicating whether an inventor uses patenting to protect his intellectual property. In our data set about 60% of the firms applied for a patent in the relevant period (see Table 3.2). To reflect the extent of the threat of market entry (TOM) we refer to a firm’s perception on whether its market position is threatened by the entry of new rivals, which is ranked on a 4-digit Likert scale.5 This ordered variable is our indicator whether technological lead and the opposing effect of reverse engineering induce early market entry by rivals. If the time until the rival’s entry is short, the variable threat of entry should be ranked higher than if the time until market entry is longer and the effective technological lead is larger. Hence, we assume that firms rank the threat of entry higher when they fear rivals’ entry. Next we define the explanatory variables. The central variables of the theoretical model are technological leadership and the easiness of reverse engineering. Both constructs are not straightforward to implement empirically. In MIP 2005, technical leadership is defined by the variable temporal headstart over competitors. Hence, we create a dummy variable indicating whether the importance of technological leadership is high. About 60% of all firms state that technological leadership is a substantial characteristic of the competitive environment in their main product market. The other theoretical concept that has to be transformed into empirical terms is the easiness of reverse engineering. Reverse engineering can also be thought of as the usability of spillover. As stated in Arundel et al (1995), reverse engineering is a characteristic of the industry and not of the firm. We construct a dummy variable which has unit value if the market is characterized by easy-to-substitute products. Hence, we assume that if the firm’s most important product is easy to substitute, reverse engineering is a mechanism that is at work in the industry where it operates. In our data set almost 70% of the innovating firms operate in a market where reverse engineering prevails. From the theoretical model we know that the technological leadership of a firm may be reduced by the possibility of reverse engineering. To implement this fact in our empirical analysis we create the interaction term 5

Respondents could choose between fully applies, rather applies, hardly applies and does not apply.

3.3 Variable Definition

77

tech. lead * rev. eng. From Table 3.2 we know that 38% of all innovating firms state that their competitive environment is characterized by a high relevance of technological leadership and at the same time reverse engineering plays an important role.

Table 3.2 Descriptive Statistics for Patenting Decision Estimation with Vertically Differentiated Products Mean Std. Dev. Min Max patent

0.595

0.491

0

1

technological lead

0.589

0.492

0

1

reverse engineering

0.684

0.465

0

1

tech. lead * rev. eng. 0.382

0.486

0

1

complexity

0.378

0.485

0

1

log(employees)

4.563

1.696

0.693 9.077

human capital

0.267

0.266

0.000 1.000

R&D intensity

0.066

0.130

0.000 1.100

strong competition

0.132

0.339

0

1

medium competition 0.209

0.407

0

1

EU

0.673

0.469

0

1

non EU

0.491

0.500

0

1

subsidy

0.419

0.494

0

1

customer power

0.303

0.460

0

1

obsolete

0.089

0.285

0

1

tech. change

0.465

0.499

0

1

cooperation

0.453

0.498

0

1

diversification

0.658

0.241

east

0.292

0.455

No. of observation

0.003 1.000 0

1

740

For the definition of weak, strong and delaying patents see the above section. According to the descriptive statistics in Table 3.3, 16% of the firms applied for at least one delaying patent, while only 10% applied for a strong, and 18% for a weak patent. Note that it is possible that a firm holds various patents belonging to different categories.

78

3 Empirical Analysis of the Model with Vertical Product Differentiation

Furthermore, we control for several factors that may influence our dependent variables. Firm size is represented by the number of employees in the year 2002, human capital by the share of employees holding a university degree. Market structure is reflected by two dummy variables indicating whether the number of main competitors is between 6 and 15 (medium competition) or exceeds 15 (strong competition). Finally we describe the competitive situation with respect to the geographical dimension of the product market. We control for two world regions, the EU and non-EU. Germany is considered separately as it serves as reference category in the regression. Thus it is not contained in the variable EU. Customer power refers to the fact that the share of sales by the three most important customers exceeds 50% of total sales. In order to capture whether the market is characterized by certain market entry barriers, we control for capital intensity defined as tangible assets per employee and for R&D intensity defined as expenditures for in-house R&D activities per sales.6 If firms cooperate with others, e.g. competitors, customers, universities, in conducting R&D this may influence their IP protection strategy. Therefore we include a dummy variable reflecting whether research cooperations take place. We also control for public R&D subsidies by either regional, national or European authorities. To capture relevant product characteristics, we include an indicator whether a product becomes obsolete quickly. As the fact that a rapid change of production or service generating technologies may play an important role concerning the decision to patent and the perceived threat of market entry, the respective indicator tech. change is included as control variable. Furthermore we control for the individual complexity of product design.7 Additionally a firm’s degree of diversification might be an impact factor in our estimations so that we use a measure reflecting the share of sales originating from a firm’s top-selling product or service. The intensity of the threat of entry may be strongly influenced by the fact that a product is new to the market. Therefore we include a dummy variable reflecting whether the responding firm has introduced such a product in the relevant time period.

6

Note that while capital intensity is taken from the year 2002 due to the lack of adequate data we could not use a lagged instrument variable for R&D expenditures. We try to mitigate the resulting problem of endogeneity by instead using the normed variable R&D activities per sales. 7 Note that we need to distinguish individual complexity and industry-specific complexity which can be described by the substitutability of products in the respective competitive environment of a firm.

3.3 Variable Definition

79

Table 3.3 Descriptive Statistics for the Threat of Entry Estimation Mean Std. Dev. Min Max threat of entry

1.517

0.806

0

3

technological lead

0.413

0.493

0

1

reverse engineering

0.698

0.459

0

1

tech. lead * rev. eng. 0.273

0.446

0

1

delaying

0.160

0.367

0

1

strong

0.096

0.295

0

1

weak

0.183

0.387

0

1

complexity

0.275

0.447

0

1

secrecy

0.525

0.500

0

1

log(employees)

4.147

1.732

0.000 9.077

R&D intensity

0.060

0.281

0.000 6.427

capital intensity

0.124

0.363

0.000 4.554

strong competition

0.191

0.393

0

1

medium competition 0.223

0.417

0

1

new to market

0.434

0.496

0

1

subsidy

0.294

0.456

0

1

obsolete

0.098

0.297

0

1

tech. change

0.484

0.500

0

1

diversification

0.677

0.243

east

0.316

0.465

No. of observations

0.005 1.000 0

1

748

In order to capture regional and sectoral differences we include an indicator whether the firm is located in eastern Germany (east ) and define 11 industry dummies. For the definition of the industry dummies see Table B.1 in Appendix B. The estimation of the threat of entry further incorporates a control variable for the use of secrecy as an IP appropriation mechanism. As secrecy may provide similar protection compared to a patent without the drawback of mandatory disclosure choosing this protection strategy may have a relevant impact on the dependent variable.

80

3 Empirical Analysis of the Model with Vertical Product Differentiation

3.4 Empirical Results To test our hypotheses regarding firms’ patenting behavior, we estimate a probit model and calculate the marginal effects of the technological lead T L and the interaction term T L ∗ RE on the propensity to patent, evaluated at the sample means. The standard errors are obtained by using the delta method. The calculation of the marginal effect of the interaction term is based on Ai and Norton (2003). The results are displayed in Table 5.2. Recall from the theoretical model that the technological lead is defined by γ = γ˜ − λ˜ γ so that the effect of λ, the easiness of reverse engineering, is only included in the interaction term λ˜ γ . For a correct empirical implementation of our theoretical model our estimation equation nevertheless needs to contain the sole effect of λ which is implemented by the variable RE. We in fact find an insignificant effect of RE, so that our theoretical model is confirmed. Our theoretical model predicts that the patenting behavior is negatively influenced by the technological lead of the innovator. This is the basic statement of Hypothesis 3.1. Our empirical results correctly display a negative sign of the respective marginal effect, but it turns out to be insignificant. At first view this is a puzzling result. The insignificance of the effect states that whether there is a technological lead or not does not influence firms’ patenting propensity if the industry is characterized by the absence of easiness of reverse engineering. Suppose a firm’s technological lead is small, then our theoretical model predicts that the propensity to patent is high. In practice, patent law requires a sufficiently high inventive step incorporated in the invention in order to fulfil the patentability requirements (see Section 1.1.5). Consequently a small technological lead is not eligible for patent protection—a fact which is disregarded by the theoretical model. Hence our empirical finding that the technological lead has an insignificant effect can be properly substantiated. Additionally our theoretical model states that in an industry, in which the easiness of reverse engineering is high, the technological lead is reduced so that patenting becomes more attractive to an innovator. This effect is implemented empirically by the interaction term of technological lead and reverse engineering which we expect to have a positive effect (see Hypothesis 3.2). This is confirmed by the empirical findings.

3.4 Empirical Results

81

Table 3.4 Results of the Patenting Decision Estimation with Vertically Differentiated Products Marginal Effect Standard Error technological lead

-0.012

0.040

reverse engineering

0.006

0.043

tech. lead * rev. eng.

0.143*

0.085

complexity

-0.060

0.041

log(employees)

0.081***

0.015

human capital

0.128

0.109

R&D intensity

0.781***

0.219

strong competition

-0.042

0.061

medium competition

-0.021

0.049

EU

0.030

0.050

non EU

0.112**

0.045

subsidy

0.102**

0.050

-0.070

0.046

obsolete

0.000

0.072

tech. change

-0.042

0.041

cooperation

0.099**

0.047

-0.138

0.088

-0.110**

0.049

customer power

diversification east industry dummies

included

Log likelihood

-382.08

McFadden’s adjusted R2

0.235

χ2 (all)

235.05***

χ2 (ind)

42.33***

Number of observations

740

*** (**, *) indicate significance of 1 % (5 %, 10 %) respectively. This table depicts marginal effects of a probit estimation regarding the determinants of the patenting decision. Marginal effects are calculated at the sample means and those of the interaction terms are obtained according to Ai and Norton (2003). Standard errors are calculated with the delta method. χ2 (all) displays a test on the joint significance of all variables. χ2 (ind) displays a test on the joint significance of the industry dummies. For a definition of the industry dummies refer to Table B.1.

82

3 Empirical Analysis of the Model with Vertical Product Differentiation

As pointed out in the literature review in Section 1.4, the patenting behavior of a firm is positively influenced by the size of the firm as well as by its R&D intensity. Our results are in line with those results. Interestingly the control variables reflecting the strength of competition with respect to competitors, customers and regional dimensions are mainly insignificant for the patenting decision. An exception is the positive effect for non EU . An intuition for this surprising result is that firms which are inter alia active in non-EU markets tend to rate protection in their home-market as more important than firms operating solely in the German home-market. A possible explanation is that those firms fear the entry of foreign firms with substitute products. Furthermore we find that R&D cooperation has a positive significant effect on the propensity to patent whereas being located in Eastern Germany has a negative impact. Generally, empirical evidence based on firm-level surveys finds that the propensity to patent varies by industry sectors. Our industry dummies are jointly significant hinting at structural differences between industry sectors. However, due to the fact that we explicitly include the main factors driving these differences in our estimation, e.g. reverse engineering, complexity, technological change, we are not able to confirm significant differences between sectors.8 After the discussion of the results concerning the first stage of our theoretical game we now turn to the findings regarding the second stage where the market entry decision of competitors is analyzed. This decision is empirically implemented by using firms’ statement regarding the perceived importance of the threat of market entry by potential rivals. As threat of entry is measured on a four-point Likert scale we estimate an ordered probit model. Marginal effects are calculated at the sample means and standard errors using the delta method. For the calculation of the interaction effect we rely on Mallick (2009). The results are depicted in Table 3.5. Hypothesis 3.3 stating that the interaction term, T L ∗ RE, has a positive impact on the intensity of the threat of entry is not confirmed by the estimation results. However, we find a positive effect of reverse engineering which has to be interpreted as the effect of reverse engineering in the absence of technological lead. A possible reasoning behind this finding is that the detrimental effect of reverse engineering on technological lead is not sufficiently high to induce a significant impact on the threat of entry, i.e. a significant effect of the interaction term T L ∗ RE. Regarding Hypothesis 3.4 the predictions of the theoretical model are supported by the empirical findings. To test the hypothesis we implement three alternative measures for the intensity of patent protection. The strongest level of protection, i.e. a delaying patent, has a significant negative effect on

8

This result originates from tests on the equality of coefficients of industry dummies.

3.4 Empirical Results

83

the threat of entry while lower intensities of patent protection, i.e. weak and strong patents, reveal no significant effect. Firms’ capital intensity, which can be interpreted as a barrier to market entry for competitors, is found to have a negative significant effect on the threat of entry. However, our control variables reflecting the number of competitors operating in a market show positive significant effects. This opposes our conjecture that more intensive competition decreases the perceived intensity of the threat of entry. Our interpretation of this result is that the number of competitors implicitly reflects the market size. More competitors in the market may be an indicator for the fact that the market has the potential of absorbing even more firms. Furthermore it could also be an indicator for a market with low entry barriers. Following this argument the fact that many competitors operate in a market can either signal low market entry costs or can signal that the market bears no room for further entry. As we find a positive significant effect of a market with a large number of competitors, it must be that market entry barriers are low so that firms perceive a high threat of further market entry. In line with economic intuition the empirical results state that if services or products become obsolete quickly or production technologies change rapidly this has a positive significant effect on the intensity of the threat of entry. Further our estimation results show that the lower the level of diversification in a firm is, the higher this firm rates the intensity of the market entry threat. Table 3.5: Threat of Entry Estimation with Vertically Differentiated Products threat

strong

medium

weak

no

Marg. Eff. Marg. Eff. Marg. Eff. Marg. Eff. (Std. Err.) (Std. Err.) (Std. Err.) (Std. Err.) technological lead

0.020 (0.016)

0.028 (0.022)

-0.029 (0.024)

-0.019 (0.015)

reverse engineering

0.039** (0.015)

0.061*** (0.021)

-0.056** (0.022)

-0.043** (0.017)

tech. lead * rev. eng.

0.009 (0.026)

0.000 (0.041)

-0.014 (0.037)

0.006 (0.031)

delaying

-0.040** (0.018)

-0.067* (0.036)

0.057** (0.025)

0.050 (0.031)

strong

-0.019 (0.023)

-0.029 (0.039)

0.027 (0.033)

0.021 (0.030)

weak

0.011 (0.024)

0.016 (0.031)

-0.017 (0.035)

-0.010 (0.020)

complexity

0.021 (0.017)

0.028 (0.022)

-0.030 (0.025)

-0.018 (0.015)

Table continued on the next page

84

3 Empirical Analysis of the Model with Vertical Product Differentiation

threat

strong

medium

weak

no

Marg. Eff. Marg. Eff. Marg. Eff. Marg. Eff. (Std. Err.) (Std. Err.) (Std. Err.) (Std. Err.) secrecy

-0.022 (0.016)

-0.031 (0.023)

0.032 (0.024)

0.021 (0.016)

log(employees)

0.005 (0.004)

0.007 (0.007)

-0.007 (0.006)

-0.005 (0.005)

R&D intensity

0.026 (0.025)

0.036 (0.035)

-0.037 (0.036)

-0.025 (0.024)

capital intensity

-0.047** (0.022)

-0.066** (0.031)

0.068** (0.033)

0.045** (0.022)

strong competition

0.060** (0.025)

0.069*** (0.022)

-0.086*** (0.033)

-0.044*** (0.015)

medium competition

0.046** (0.022)

0.057*** (0.021)

-0.067** (0.030)

-0.037*** (0.014)

new to market

-0.019 (0.015)

-0.027 (0.021)

0.028 (0.021)

0.019 (0.015)

subsidy

0.012 (0.017)

0.016 (0.022)

-0.017 (0.024)

-0.011 (0.015)

obsolete

0.051* (0.031)

0.058** (0.029)

-0.072* (0.042)

-0.036** (0.018)

tech. change

0.034** (0.015)

0.047** (0.020)

-0.049** (0.022)

-0.032** (0.015)

diversification

0.063** (0.028)

0.089** (0.042)

-0.092** (0.041)

-0.060** (0.031)

east

-0.029 (0.015)

-0.029 (0.022)

0.029 (0.022)

0.020 (0.016)

included

included

included

included

industry dummies Log likelihood

-417.94

McFadden’s adjusted R2

0.037

χ2 (all)

65.21***

χ2 (ind)

8.72

Number of observations

748

*** (**, *) indicate significance of 1 % (5 %, 10 %) respectively. This table depicts marginal effects for an ordered probit of the estimation of threat of entry. Marginal effects are calculated at the sample means and those of the interaction terms are obtained according to Mallick (2009). Standard errors are calculated with the delta method. χ2 (all) displays a test on the joint significance of all variables. χ2 (ind) displays a test on the joint significance of the industry dummies. For a definition of the industry dummies refer to Table B.1.

3.5 Concluding Remarks

85

3.5 Concluding Remarks The preceding chapter intended to empirically test the theoretical results and predictions obtained in Chapter 2. Several hypotheses summarizing the theoretical results concerning the propensity to patent with vertically differentiated products thereby formed the basis of our empirical examination. From the analysis of the propensity to patent in a market with vertically differentiated products we deduced four hypotheses. Two refer to the first stage of the theoretical model, i.e. the patenting decision of the inventor, while the others concern the second stage of the model, i.e. the market entry decisions of the firms. Our empirical results concerning the propensity to patent in a market with vertically differentiated products are summarized in Table 3.6. Table 3.6 Hypotheses tested for the Case with Vertically Differentiated Products Hypothesis description

estimation result

3.1

the higher the technological lead, the lower the ptp

not confirmed

3.2

if rev. eng. is easy, the ptp increases with the technological lead

confirmed

3.3

rev. eng. reduces the technological lead and thereby increases the TOM

not confirmed

3.4

the TOM decreases with the intensity of patent protection

confirmed

ptp = propensity to patent rev. eng. = reverse engineering TOM = threat of market entry

The first, Hypothesis 3.1, proposes that the higher the technological lead of the inventor, the lower is his propensity to patent. This could not be confirmed by our empirical estimation. A possible explanation for this is that the theoretical approach ignores the fact that minor technological advances are not applicable for patent protection. Hypothesis 3.2 states that if reverse engineering is easy to achieve, the technological lead is reduced so that patenting becomes more attractive, i.e. the propensity to patent increases. To test this hypothesis we implemented an interaction term of technological lead and reverse engineering. As the effect of the interaction term is found to be positive and significant, this hypothesis is confirmed.

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3 Empirical Analysis of the Model with Vertical Product Differentiation

Regarding the second stage of the theoretical model, Hypothesis 3.3 suggests that reverse engineering reduces the technological lead so strongly that the threat of entry increases. This finding is not confirmed empirically. Since we find that the single effect of reverse engineering is positive, the effect of reverse engineering on the technological lead is obviously not strong enough to induce a positive effect of the interaction term. Nevertheless we can confirm empirically that the threat of market entry decreases with the intensity of patent protection, which is a result of the theoretical model formulated in Hypothesis 3.4. For a delaying patent, i.e. very strong patent protection, we find a significantly negative effect on the threat of entry. The probably most puzzling and equivocative result of our theoretical analysis is the finding that the propensity to patent decreases, the higher the technological lead of an innovator is (see Proposition 2.3). The commonly perceived intuition suggests the opposite, namely that an innovation is patented, the greater the technological advance it embodies. Our empirical estimation offers the solution to this puzzle: we find that in our model setting the commonly suggested interdependence of technological lead and the propensity to patent only holds if the respective market is characterized by easy-to-achieve reverse engineering. Thus our theoretical findings do not contradict common intuition but constrain its validity to markets where reverse engineering is easy. Consequently, in a market where reverse engineering is difficult, our findings propose that the propensity to patent decreases when the technological lead rises.

Chapter 4

The Decision to Patent with Horizontal Product Differentiation

In this chapter we introduce the patenting decision into an oligopolistic model of horizontally differentiated products. The analysis presented here in large parts follows Zaby (2009b). We assume that a drastic product innovation is released on a new market where rivals may enter with non-infringing products as long as patent protection is not perfect. Product characteristics are assumed to be continuously distributed on a circle of unit-circumference where a patent protects a given range on the circle from the entry of rival firms. Assuming that the information revealed due to the disclosure requirement reduces competitors’ market entry costs, inventing around is facilitated so that possibly more firms are able to enter the market due to a patent. In this model setting we are able to analyze varying intensities of the disclosure requirement’s impact and its influence on the patenting decision of the innovator. Introducing patent protection into a setting with horizontally differentiated products goes back to Klemperer (1990). He defines a patent’s width as “how different competitors’ products must be in order not to infringe the patent ” (Klemperer (1990), p. 116). The main focus of his paper is to analyze a patent’s optimal design with regard to its length and width, the patenting decision per se is not considered. In a very general setting Klemperer (1990) assumes that the patentholder produces the single variety that all consumers prefer. At a given (transport) cost consumers can switch from their most-preferred variety to a substitute product provided by competitors beyond the patent’s borders. Klemperer (1990) assumes a fencepost patent system and includes the disclosure requirement by assuming that there are zero market entry costs for competitors. Free entry then drives the price at the patent boundaries to zero. The welfare losses caused by the granting of a patent are twofold: on the one hand, consumption is switched to less-preferred, unpatented varieties of the patented product inducing additional transport costs for consumers. On the other hand, some consumers might choose not to buy the patented product at all, switching to an outside option. Klemperer (1990) finds that infinitely lived but narrow patents are

87

88

4 The Decision to Patent with Horizontal Product Differentiation

socially desirable when the cost of substitution between varieties is similar across consumers. Furthermore he finds that very short-lived, wide patents are desirable when consumers value the preferred variety and the choice not to buy the product in a similar way. Two subsequent papers analyze the patenting decision in the case of horizontally differentiated products. Waterson (1990) focusses on the comparison of fencepost versus signpost patent systems with regard to social welfare, abstracting from the implications of the disclosure requirement. In a succeeding paper Harter (1994) accounts for a disclosure effect. The major drawback of his modeling approach is that only one potential competitor profits from the merits of the mandatory disclosure. This fact, which largely delimitates the impact of the disclosure requirement, in the end leads Harter (1994) to conclude that there is no causal relation between the required disclosure and the propensity to patent. Economic intuition suggests the opposite: If the disclosure of information leads to decreasing market entry costs, this may enable an increasing number of firms to enter the market, a fact which the inventor will anticipate in his decision to patent. The following analysis confirms this intuition. Two related papers analyze the impact of licensing with horizontally differentiated goods (Wang and Yang (2003), Poddar and Sinha (2004)). Both focus on the incentives of a successful innovator to license his technology to a rival in Hotelling’s linear-city model. If the innovator is a monopolist, he is not able to serve the whole market due to an outside option which consumers located far away from him prefer. Wang and Yang (2003) find that allowing a second firm to offer the new technology by licensing it may be profit enhancing for the innovator due to a market-expanding effect. While Wang and Yang (2003) only consider a fixed license fee and an insider patentee, Poddar and Sinha (2004)) study the effects of different licensing strategies with an insider as well as an outsider patentee. They find that licensing strategies differ in both cases: For an outsider patentee offering a royalty licensing arrangement is best, while for an insider patentee offering no license is best when the innovation is drastic, whereas offering a royalty licensing arrangement is optimal if the innovation is non-drastic. Neither paper considers the patenting decision itself, as both assume that the innovator has already patented his discovery. Moreover their setting is only analytically tractable for the duopoly case as it builds on Hotelling’s linear-city model.1 Our analysis of the patenting decision in a market with horizontally differentiated products proceeds as follows. In Section 4.1 we introduce the strategic protection decision between a patent and secrecy into a setting with horizontally differentiated products. The considered three stage game is solved backward, beginning with the analysis of the price competition in Section 4.2, 1 See e.g. Economides (1993) for the complex analysis of simultaneous entry and Brenner (2005) for the complex analysis of sequential entry of more than two players in the linear city model.

4.1 The Model Setup

89

proceeding with the market entry decisions in Section 4.3 and terminating with the patenting decision in Section 4.4. The following Section 4.5 looks at the changes that arise when the possibility to license a patent is introduced. In Section 4.6 some implications for social welfare are considered. Section 4.7 concludes. All proofs can be found in Appendix C.

4.1 The Model Setup Assume that one firm has successfully accomplished a drastic product innovation and decides to release the new product immediately. As this innovative firm owns the proprietary knowledge concerning the innovation, it will be monopolist in the new market as long as no other firm successfully invents. The new product may be varied horizontally in its product characteristics which are assumed to be continuously distributed on a circle of unit-circumference. The innovator (and any other entering firm) can only offer one variant of the good. We denote the total number of firms that operate in this differentiated oligopoly as N = n + 1, consisting of the innovator and n entering firms. Consumers are assumed to be uniformly distributed over the circle, with density normalized to one. The preference of a consumer is denoted by x ∈ [0, 1] and we assume without loss of generality that the innovator of the new product is located at the beginning of the circle, xi = 0. If a consumer cannot buy a good according to his preference he incurs a disutility that rises quadratically with the distance between his preferred good and the offered good. We will refer to this disutility as mismatch costs. Each consumer purchases one unit of the good as long as his net utility is weakly positive, Ux = v − pz − (x − xz )2 ≥ 0 where xz represents the location of firm z on the circle. We assume throughout the paper that the reservation price v lies within the range 5/16 ≤ v < 3/4 which assures that only in the case of monopoly, N = 1, some consumers prefer the outside option. For N > 1 all consumers buy one unit of the good choosing the variant which is closest to their respective preference. The structure of the model is as follows: on the first stage of a three-stage game the innovator, already located in the new market, decides whether to patent his innovation or to keep it secret, σi1 = {P, S}. A patent protects a given range of product space on the unit circle against the entry of rival firms. The extent of protection is defined by the breadth of the patent, β ∈ ]0, 1[, which is exogenous.2 Following Harter (2001) we assume that the protected product space is situated symmetrically around the location of the patentee’s product. Without loss of generality we set xi = 0 so that this point on the circle defines the middle of the protected product space, see Figure 4.1. From 2

Patent breadth can also be interpreted as a strategic decision variable of the innovator, see Yiannaka and Fulton (2006).

90

4 The Decision to Patent with Horizontal Product Differentiation

there patent protection covers β/2 of the neighboring product space on either side of the innovation. Fig. 4.1 Patent Breadth location of the innovator

β/2

β/2

Whenever the innovator decides to patent his invention he has the possibility to license it to his rivals, allowing them to enter the formerly protected  product space in exchange for a per unit royalty, σi1 = {license, no license}. We will look at licensing in Section 4.5 and will set off the analysis without licensing. On the second stage n potential rivals, n ∈ [0, ∞[, simultaneously decide whether to enter the new market, given the patenting decision of the innovator, σn2 = {entry, no entry}. Upon entry all firms face market entry costs. These can be understood as the costs necessary to achieve the capability to produce a variant of the new product. If the innovator decides to patent his discovery, according to patent law he is required to disclose sufficient information so that anyone skilled in the art is able to reproduce the patented product. Although his competitors are not allowed to copy the protected product, they have the possibility to invent around the patent as long as patent breadth does not deter entry completely, β < 1. Whenever a rival decides to enter the market despite of a patent, he profits from the disclosed information: achieving the capability to enter the new market is now easier and thus less costly. If we denote market entry costs in the case of secrecy by fs , then in the case of a patent they decrease to fp with fp ≡ αfs , 0 ≤ α ≤ 1, where α is a measure for the impact of the disclosure requirement which may differ subject to specific market conditions. Concerning the location of firms, we will use the well established principle of maximum differentiation meaning that firms will locate as far away from each other as possible to soften

4.2 Price Competition

91

price competition.3 Thus, if secrecy prevails firms will locate equidistantly on the unit circle. With a patent potential entrants cannot freely locate on the unit circle due to the range of protected product space. Still, they will try to move as close as possible to their profit maximizing, equidistant locations. Consequently, in the case of a patent, when the choice of location is restricted to the product space 1 − β, the direct neighbors of the patentee will locate at the borders of the patent and all other entrants will locate equidistantly between them.4 On the third stage all firms in the new market compete in prices, σi,3 n = pi .

4.2 Price Competition To find the subgame perfect Nash equilibrium, we solve the game by backward induction, setting off with the last stage. Here we have to distinguish the cases: (i) the innovator has not patented, σi1 = {S}, (ii) the innovator has patented σi1 = {P }. We will consider the cases subsequently, starting with Case (i). (i) the innovator has not patented σi1 = {S} In the case that the innovator refrains from patenting and chooses secrecy to protect his innovation, our model simplifies to the well known Salop (1979) model of a circular city with N s firms which we will briefly analyze in the following: All firms are symmetric so that it suffices to analyze the decision of one representative firm denoted by u. By assumption the outside option only plays a role in the case of monopoly, a market structure that will result if market entry costs are extremely high. We will turn to this case later. With moderate market entry costs, every consumer in the non-protected market buys one unit of the differentiated product from the firm that offers the variant which is closest to his preferences. The consumer indifferent between buying from firm u or a neighboring firm, lets say w, can thus be found by equating the respective utilities he realizes by buying from either of them, U (u) = v − pu − (|ˆ xu, w |)2 = v − pw − (|1/N s − xˆu, w |)2 = U (w).

3

Kats (1995) shows in the case of symmetry that this principle leads to a subgame perfect Nash equilibrium in a price then location game in a circular market. 4 It is easy to check that with a patent even for N p = 3 the incentive to soften price competition leads the entering firms to choose locations as far away from each other as possible so that they locate at the patent’s borders.

92

4 The Decision to Patent with Horizontal Product Differentiation

Solving for xˆu, w we get x ˆu, w =

(pw − pu ) s 1 N + 2 2N s

(4.1)

as the consumer indifferent between buying from u or w. The respective demand for a representative firm operating in the market can be derived as Du = 2ˆ xu, w = (pw − pu )N s + 1/N s . Standard computations then yield equilibrium prices, (4.2) p∗ = 1/(N s )2 , and profits

πn∗ = 1/(N s )3 − fs

(4.3)

for the N s entering firms. Note that the profit of the innovator amounts to πi∗ = 1/(N s )3

(4.4)

as he does not face market entry costs. In the case that only the innovator offers the innovative product due to extremely high market entry costs, we assume that consumers may not buy it if their preferences strongly differ from the characteristics of the offered product. The outside option they prefer may for example be an antecessor product of the innovation. Imagine the time immediately after the innovation has been placed in the market. Some consumers have a strong preference for it, others rather stick with less innovative products offered outside of the market. As soon as the innovation is copied by other firms and offered in differentiated versions, mismatch costs go down and consumers may decide to buy the innovative product rather than an outside option. Technically speaking, consumers will prefer to buy from the innovator in the case N s = 1 as long as v − pi − (ˆ xi, out )2 ≥ 0. Solving for x ˆi, out we get √ x ˆi, out ≤ v − pi , (4.5) where x ˆi, out is the consumer indifferent between buying from the patentee or buying the outside option. This defines the innovator’s demand for the case N s = 1 as Di = 2ˆ xi, out so xi, out by setting the price pi = 2v/3. that he maximizes his profits πis = pi 2ˆ

4.2 Price Competition

93

His profits then amount to5 πis

4v = 3



v . 3

(4.6)

(ii) the innovator has patented σi1 = {P } Now let us turn to Case (ii) and look at the situation when the innovator decides to protect the new product by a patent. As long as the breadth of the patent is rather moderate, β/2 < 1/N p , the patent does not influence the location of rival firms and the symmetric result derived above emerges. Note though, that due to the assumption that the disclosure requirement lowers market entry costs we have fp = αfs where 0 ≤ α ≤ 1 is a measure of the impact of the disclosure requirement. Thus, due to fp < fs , more firms than in the case without a patent might be able to enter the market. We will turn to this fact later. If the protectional degree of the patent is high, β≥

2 ≡ β crit , Np

(4.7)

equidistant location on the entire circumference of the circle is no longer possible as the patent restricts the locations for entering firms to the product space 1 − β. We will define patents in a setting where patent breadth, β, fulfills condition (4.7) as restrictive patents. The following figure depicts firms’ locations with N p = 4 for the cases (a) that the patent is not restrictive (β < 1/2), and (b) that the patent is restrictive (β ≥ 1/2).

As the outside option should restrict the demand of the innovator toDis < 1 as long as N s = 1, the preference parameter v has to meet the condition 2 v/(3) < 1. Solving for v we get v < 3/4 as the lower bound of the preference parameter. For N s = 2 the additional firm k will locate at the opposite of the innovator at xk = 1/2. The indifferent consumer between k and i can be found by substituting N s = 2 in Equation (4.1) as x ˆi, k = 1/4. Prices and profits can be derived by inserting N s = 2 in equations (4.2) and (4.3). We get pi = pk = p∗ N s =2 = 1/4 and πis = should be of no interest for the indifferent 1/8, πks = 1/8 − fs . As the outside option  consumer x ˆi, k , the condition v − p∗ N s =2 − (ˆ xi, k )2 ≥ 0 has to be met. Inserting  ∗ i, k  p N s =2 = 1/4 and x ˆ as derived above, the critical condition simplifies to v ≥ 5/16 so that the domain of the preference parameter that narrows the outside option’s relevance to the case N s = 1 is 5/16 ≤ v < 3/4. 5

94

4 The Decision to Patent with Horizontal Product Differentiation

Fig. 4.2 Firms’ Locations with a Patent, N p = 4 i

i

h

k

h

k

k+1

(a) non-restrictive patent

k+1

(b) restrictive patent

In the case that the innovator patents, firms’ neighborhoods are no longer uniform, but are dependent on the respective location of a firm. To distinguish firms’ locations we will refer to the left and right neighbor of the innovator as firms k and h. Further we will denote the first right (left) neighbor of k (h) by k + 1 (h + 1), the second by k + 2 (h + 2) and so on. Consequently, with a restrictive patent an equilibrium can no longer be derived by analyzing a representative firm, as the respective neighborhood of a firm now plays a crucial role for its pricing decision. We have to distinguish three types of firms, differing by their respective neighborhood: (a)

the patentee has a uniform neighborhood consisting of firms k and h

(b) the border“ firms k and h have an non-uniform neighborhood with the ” patentee on the one side and either each other or, if n > 2, a non-patentee, non-border firm k + 1 or h + 1 on the other side (c) a non-patentee, non-border firm k + κ, κ ≥ 1 always has a non-uniform neighborhood (k + κ − 1 to the left, k + κ + 1 to the right side) as long as it is not the firm with the greatest distance to the patentee. For this firm we need to distinguish two cases that depend on the number of non-patentee firms n • if n is even, which we will denote by ne , then the firm furthest away from the patentee is firm k + (ne /2 − 1) and its neighborhood is non-uniform: to the left firm k + (ne /2 − 2), to the right firm h + (ne /2 − 1) • if n is uneven, nu , then the firm furthest away is firm k + (nu − 1)/2 and its neighborhood is uniform: to the left firm k + (nu − 3)/2, to the right firm h + (nu − 3)/2.

4.2 Price Competition

95

As all non-patentee firms are ex-ante symmetric they will come to the same decision whenever facing the same neighborhood. Thus, if an even number of firms enters, every firm has a symmetric “partner” that faces the same neighborhood. In the following, we will refer to this as semi-circle symmetry. If an uneven number of firms enters the market then the firm located furthest away from the patentee has no symmetric “partner”, we will refer to this case as semi-circle asymmetry. As we are analyzing the last stage of the game we take the number of firms that have entered the market as given. Due to the fact that the neighborhood of every firm is crucial for its individual demand and thus pricing decision, we will have to distinguish the indifferent consumer between every pair of firms, say y and z. From the viewpoint of firm y the indifferent consumer will be denoted by x ˆy,z , from the viewpoint of its neighbor z it will be denoted by x ˆz,y . By standard computations the location of the indifferent consumer can be found by equating the respective utilities a consumer realizes by buying from either of its neighboring firms. We will set off deriving the demand for the different types of firms, starting with the patentee. The indifferent consumer situated between the patentee, i, and his left neighbor, k, is situated at x ˆi,k and can be found by equating the respective utilities the consumer realizes by buying from either of the firms ppi

2

+ (ˆ xi,k ) = x ˆi,k =

ppk

 +

β −x ˆi,k 2

ppk − ppi β + . β 4

2

(4.8)

Necessarily the patentee’s left and right neighbor are semi-circle symmetric so that the indifferent consumers on both sides of the patentee are located at the same distance x ˆi,k = x ˆi,h . Thus the patentee’s demand is given by Dip = 2ˆ xi,k .

(4.9)

If a firm has a non-uniform neighborhood the indifferent consumers on either side are not located equidistantly. This is the case for the patentee’s neighbors, k and h. As they are semi-circle symmetric it suffices to derive the demand for one firm, say k. Due to its non-uniform neighborhood firm k’s demand consists of two different parts: On the one hand, all consumers between firm k and the indifferent consumer to its left, x ˆk, i , will buy from firm k. On the other hand, all consumers between firm k and the indifferent consumer to its right, x ˆk, k+1 , will buy its product.

96

4 The Decision to Patent with Horizontal Product Differentiation

Thus the demand of the firm amounts to Dkp = x ˆk, i + x ˆk, k+1 with x ˆk, k+1 =

(4.10) (ppk+1

ppk )(n

− − 1) 1−β + . 2(1 − β) 2(n − 1)

Note that whenever the difference between the firms’ prices is high, the consumer indifferent between buying from firm k or firm k + 1 is no longer situated in between firm k and firm k + 1 but is located to the left of firm k, as then xˆk, k+1 < 0. This at first sight surprising result is quite intuitive: due to the relatively low price firm k + 1 offers, even consumers situated in the proximate neighborhood of firm k prefer to buy the neighboring firm’s product as the higher mismatch costs they face by doing so are overcompensated by the lower price firm k + 1 offers. We will refer to this shift in demand as consumer migration effect. Last we need to calculate the demand for the non-patentee, non-border firms, k + κ, κ ≥ 1. As mentioned earlier, we have to distinguish between situations in which the number of non-patentee firms in the market is even and those in which it is uneven. If it is even, ne , then the neighborhood of firm k + κ, κ ∈ [1, ne /2 − 1] is non-uniform. The demand of firm k + κ given ne thus amounts to D(ne )p(k+κ) = xˆ(k+κ), (k+κ)−1 + xˆ(k+κ), (k+κ)+1 .

(4.11)

Now let us turn to the case where the number of non-patentee firms is uneven, nu . Then the range of firms k + κ changes to κ ∈ [1, (nu − 1)/2]. For ease of exposition let us denote the firm with the furthest distance to the patentee by k + κmax with κmax = (nu − 1)/2. As all firms k + κ < k + κmax have non-uniform neighborhoods, their demand is equal to D(ne )p(k+κ) . Due to the assumption that firms locate equidistantly within the non-protected product space, the location of firm k + κmax is exactly opposite to that of the patentee so that xk+κmax = 1/2. Other than the neighboring firms, this firm faces a uniform neighborhood and thus for an uneven number of firms the demand for a non-patentee, non-border firm is given by  ∀ κ < n−1 D(ne )p(k+κ) u p 2 D(n )(k+κ) = (4.12) 2x ˆ(k+κmax ), (k+κmax )−1 ∀ κ = n−1 2 Having derived the respective demand functions for the different firm locations, we can now turn to the price reaction functions of the firms. Again we will look at the patentee first. His profits are πip = ppi Dip .

4.3 Market Entry

97

Inserting the demand function from Equation (4.9) and carrying out the optimization we get pp β2 (4.13) ppi (pk ) = k + 2 8 as the patentee’s price reaction function. The semi-circle symmetric border-firms k and h face positive market entry costs so their profits amount to πkp = ppk Dkp −fp . Their price reaction functions can be derived as ppk (pp , pk+1 ) =

β(n − 1) p (1 − β) p β(1 − β) pk+1 + pi + 2Γ Γ 4(n − 1)

(4.14)

with Γ ≡ 2 + β(n − 3). Analogously the price reaction functions of the nonpatentee, non-border firms k + κ with κ ≥ 1 can be derived as pp(k+κ) (ne )

=

pp(k+κ)+1 + pp(k+κ)−1 4

for an even number of non-patentee firms and ⎧ p ⎨ p(k+κ) (ne ) p u  p(k+κ) (n ) = pp(k+κ)+1 β 2 ⎩ + 12 1n − 2 −1

1 + 2



1−β n−1

2

∀ κ
fp, N p +1 . In the following we will describe in detail the derivation of the critical boundaries for N p = [2, 3, 4] as then the computation of all cases N p > 4 should be obvious. Suppose now that one additional firm, say k, enters the market, np = 1, so that N p = 2 firms compete against each other. Recall from Equation (4.7) that β/2 ≥ 1/N p has to be fulfilled for a restrictive patent. For N p = 2 this condition changes to β ≥ 1. As we defined β ∈ ]0, 1[ this condition can never be fulfilled meaning that a patent is never restrictive. Thus—following the assumption of maximum differentiation—the entering firm locates at the opposite of the patentee, xk = 1/2. As prices are equal in equilibrium, the consumer indifferent between buying from firm k or from the patentee can be found by substituting N p = 2 in Equation (4.1) as xˆi, k N p =2 = 1/4. Prices and profits can then be derived as pi, 2 = pk, 2 = 1/4 and πi,p 2 = p 1/8, πk, 2 = 1/8 − fp . The critical threshold where an entering firm realizes zero profits is thus given by fp, 2 = 1/8 so that the necessary condition for a market structure with np = 1 is fp < fp, 2 ≡ 1/8 .

(4.18)

Thus the market structure with one entering rival is defined by market entry costs fp, 2 ≥ fp > fp, 3 . For the case that two additional firms, k and h, enter the market, np = 2, the condition for a restrictive patent changes to β ≥ 2/3. If 2/3 ≤ β < 1, the patent restricts the product space where the two entering competitors can choose to locate to 1 − β. Whenever k and h enter, they have a non-uniform neighborhood with the patentee to their left (right) and each other to their right (left). Thus in the price reaction function of a non-patentee firm derived in Equation (4.14) we can set k+1 = h. Due to semi-circle symmetry we know that ppk = pph . Using ppi from Equation (4.13) we can derive the equilibrium prices β(4 − 2β − β 2 ) (4.19) ppi, 3 = 8(3 − 2β) and

100

4 The Decision to Patent with Horizontal Product Differentiation

ppk, 3 =

β(1 − β)(1 − β/4) 3 − 2β

(4.20)

so that profits amount to β(4 − 2β − β 2 )2 32(3 − 2β)2 (4 − β)2 (2 − β)(1 − β)β = − fp . 32(3 − 2β)2

πi,p 3 =

(4.21)

p πk, 3

(4.22)

Consequently, the critical threshold for market entry costs in the case N p = 3 is (4 − β)2 (2 − β)(1 − β)β fp, 3 ≡ (4.23) 32(3 − 2β)2 and the case with two rivals entering the market is sufficiently defined by fp, 3 ≥ fp > fp, 4 . To derive fp, 4 we need to look at the case where three firms enter simultaneously, np = 3 and 1/2 ≤ β < 1. Recall that as the number of entering firms is uneven, one firm does not have a semi-symmetric partner, for np = 3 this is firm k + 1. Its price reaction function can be derived by inserting κ = 1 into Equation (4.16). Note that the right neighbor of firm k + 1 is firm h so that we have pp(k+κ)+1 = pph . The price reaction function then simplifies to pp(k+1), 4 =

pph (1 − β)2 + . 2 8

(4.24)

As k and h are semi-circle symmetric, in equilibrium we must have ppk, 4 = pph, 4 . Simple computations then yield equilibrium prices and profits. Decisive for the critical threshold of market entry costs is the profit of firm k + 1 which is located at the furthest distance to the patentee. We have fp, 4 ≡

(1 − β) . 32

(4.25)

In the same manner the critical thresholds for market entry costs can be derived for all market structures N p ≥ 4.7 Last let us turn to the limiting case fp → 0, meaning that we have free market entry, np → ∞. The price reaction function of the patentee will not change as it is independent of np , see Equation (4.13). The case is different for the non-patentee firms: in the limit case the border firms’ price reaction function as derived in Equation (4.14) degenerates (using De L’Hˆospital) to  ppk np →∞ = ppk+1 /2. In the limit, price competition between firms will become The respective outcomes for the cases N p ∈ [1, 6] are summarized in Table C.1 in the Appendix.

7

4.3 Market Entry

101

so tough that they end up setting a price according to their cost, in our case ppk+κ = 0. This means that all non-patentee firms will set the same price and have zero-profits.8 We can derive the patentee’s optimal price choice in the limiting case by inserting ppk = 0 in Equation (4.13). This yields the price  p pi np →∞ = β 2 /8 with the corresponding profits  1 3 πip np →∞ = β . 32

(4.26)

We will turn to the question whether a patent is profitable with extremely low market entry costs in the next section. Equipped with these results we are now able to take a closer look at the consumer migration effect mentioned earlier.9 Due to the asymmetric equilibrium prices demand may shift from a border firm, say k, to its neighbor k + 1 as the consumer indifferent between buying from either firm is no longer located in between the firms, but beyond the location of firm k, as depicted in Figure 4.3.10

Fig. 4.3 The Consumer Migration Effect for N = 5 x ˆk, i

Di

x ˆi, h

i Dk

Dh

x ˆh, h+1

x ˆk+1, k

h

k k+1

h+1

Dk+1

Dh+1

x ˆh+1, k+1

We find that the factors leading to consumer migration correspond to the factors which strengthen price competition between the non-patentee 8

Klemperer (1990) comes to the same conclusion. Naturally the argumentation concerning the consumer migration effect holds for both border firms, k and h and their respective neighbors k + 1 and h + 1. For the ease of exposition we refer to firm k in the following. √ 10 In the case N = 5 patent breadth needs to exceed β cme ≡ 1 (−5 + 115) for 5 9 consumer migration to occur. See the proof of Lemma 4.1. 9

102

4 The Decision to Patent with Horizontal Product Differentiation

firms. As more firms enter in the non-protected product space the distance in between firms decreases and price competition becomes fiercer so that lower prices result. Increasing breadth of a patent affects prices in the same way: as the non-protected product space becomes narrower, firms move closer together and again the intensified price competition leads to decreasing prices. The following lemma summarizes these results. Lemma 4.1. Consumer migration takes place whenever price asymmetry is sufficiently high. The effect is higher the more firms are operating in the market and the broader a patent is. The consequence of the consumer migration effect is that even consumers situated in the proximate neighborhood of a border firm prefer to buy the neighboring non-border firm’s product so that the border firm’s demand necessarily decreases. As the following lemma states, consumer migration will never reduce the border firm’s demand to zero. Lemma 4.2. A border firm’s demand is positive for every restrictive patent. From the above lemma we can deduce that consumer migration only influences the innovator’s patenting decision indirectly by driving the border firm’s pricing decisions. Since their demand will always be positive, consumers located in the proximate neighborhood of the innovator will never have the incentive to migrate to firm k + 1. Technically speaking we have x ˆi, k < β/2 − |ˆ xk, k+1 | so that consumers migrate only from the border firms to their non-patentee neighbors.

4.4 The Patenting Decision On the first stage of the three-stage game the innovator decides whether to patent his innovation or to keep it secret, σi1 = {P, S}. His patenting decision is driven by two opposing effects. On the one hand, a patent protects part of the market, β, from the entrance of rival firms (protective effect). On the other hand, the disclosure requirement linked to a patent may lead to decreasing market entry costs for potential rivals, possibly making market entry profitable for a larger number of firms than with secrecy (disclosure effect). Recall from above that we define the reduction of market entry costs as fp ≡ αfs . In the following we distinguish two cases: either the disclosure requirement has an impact, αN ≥ α ≥ 0, or it has no impact, 1 ≥ α > αN .11 Whenever the disclosure requirement has no impact the reduction of market entry costs is too small to change the number of entering firms so that patenting will either lead to N p = N s , or will even reduce the number of firms in The critical threshold αN is subject to the particular patent breadth β and the initial market entry costs f¯N and can be derived as αN ≡ fN+1 /f¯N where fN+1 is the next lower critical threshold of market entry costs.

11

4.4 The Patenting Decision

103

the market, N p < N s . If the disclosure requirement has an impact it leads to a sufficient decrease of market entry costs to make market entry profitable for a larger number of rival firms, N p > N s . Intuitively it should be that whenever patent protection is intense (β high), the protective effect dominates the disclosure effect and the innovator will patent. If patent breadth is rather low, the negative disclosure effect should dominate the protective effect so the innovator will refrain from patenting. To analyze the patenting decision of the innovator it is thus crucial to know how many firms would enter the market with secrecy and distinguish how many firms would possibly additionally enter with a patent. Recall from above that the number of firms entering the market is sufficiently defined by market entry costs with fN ≥ f > fN +1 . Figure 4.4 illustrates the critical thresholds of market entry costs derived in Section 4.3 for alternative levels of patent breadth, β, where the solid lines depict the critical thresholds for the case that the innovator chooses secrecy and the dashed lines depict the critical thresholds for the case that the innovator patents.12

Fig. 4.4 Critical Thresholds of Market Entry Costs fp, N p , fs, N s fs, 3

0.03 fp, 3

0.02 B

A

B

fs, 4

f¯ 0.01

fp, 4

C

fs, 5

fp, 5 D

fp, 6 0.2

¯ β

0.4

β

0.6

¯ β

fs, 6

1.0

β

Note that to maintain clarity we omitted fs, N s for N s < 3 and N s > 6. The former would be located above fs, 3 and all latter below fs, 6 .

12

104

4 The Decision to Patent with Horizontal Product Differentiation

Obviously fp,N p and fs,N s are equal up to the point where patent protection becomes restrictive, β ≥ 2/N s . All combinations of f and β that lie in between the two curves fN and fN +1 lead to a situation where N firms enter the market. Thus in the upper shaded area N p = 3 firms would enter the market with a patent while with secrecy any number N s ≥ 3 could enter in this area. In the lower shaded area N p = 5 firms would enter with a patent while N s ≥ 5 could enter with secrecy. Figure 4.4 shows that given market entry costs and patent breadth, a patent may lead to three different cases: (a)

due to a dominant protective effect less firms enter with a patent,

(b)

due to a dominant protective effect the number of firms stays unchanged,

(c)

due to a dominant disclosure effect more firms enter with a patent.

Take for example the combination f¯, β¯ which leads to point A. With secrecy, market entry costs f¯ allow N s = 4 firms to enter the market, with a patent only N p = 3 firms could enter due to a strong protective effect (Case ¯ the protective effect will only be (a)). If patent breadth is rather low, β, moderate: Given the same height of market entry costs, f¯, we are at point B (B  ) where still N s = 4 but now N p = 4 firms would enter if the innovator patented (Case (b)). Now suppose that the disclosure requirement has an impact and leads to a sufficient reduction of market entry costs to change the number of entering firms. To differentiate between a high and a low impact of the disclosure requirement we assume that for our example value β¯ the reduction of market entry costs with a patent is rather moderate so we come to point C, for the example value β¯ we assume a high impact of the disclosure requirement, so that the reduction of market entry costs leads to point D. As fs = f¯ stays unchanged, with secrecy N s = 4 firms would enter, but with a patent N p = 5 firms would be able to locate in the market for both values β¯ and β¯ (Case (c)). To find out whether the innovator will choose to patent or to keep his innovation secret in the cases considered above, we need to compare the respective profits he can realize given the alternative combinations of market entry costs and patent breadth. In the following figure the profits of the innovator subject to f and β (see Table C.1) are plotted for the cases that he chooses a patent (dashed lines) or secrecy (solid lines). Let us start with the analysis of Case (a) where N s > N p . For our examplary combination f¯, β¯ we need to compare the profits at points Ap and As . Obviously the innovator is better off with a patent in this case, as then he ¯ > π s (β). ¯ Things change in Case (b) where realizes higher profits, πi,p 3 (β) i, 4 N s = N p = 4. In the above figure we can see that the respective profits with a patent and secrecy, marked by the point B s , B p are equal as the patent

4.4 The Patenting Decision

105

Fig. 4.5 Alternative Profits of the Innovator With a Patent/Secrecy p s , πi, Ns i, N p

π

Ap 0.04

p

πi, 3

0.03

s πi, 3

p

πi, 4

0.02

AD

Bp

Bs , Bp

p

πi, ∞

Bs

BC

s πi, 4

p

πi, 5

0.01

As s πi, 5

p

πi, 6

0.2

¯ β

s πi, 6

0.4

β

0.6

¯ β

0.8

β

is not restrictive, β¯ < 1/2. By assumption the innovator then prefers secrecy.13 If patent breadth increases to β  the patent becomes restrictive since β  > 1/2 and the innovator will choose to patent, see points B s and B p . At last we turn to Case (c) where the disclosure requirement has an impact so that, speaking in terms of our example, patenting leads us to the points ¯ BC or AD, respectively. For the relatively low value of patent breadth, β, the innovator compares the profits marked by the points B s and BC and ¯ > π p (β). ¯ Again, as patent breadth will apparently choose secrecy as πi,s 4 (β) i, 5 increases, patenting may become the more attractive strategy: with our example value β¯ the innovator faces As or AD, clearly preferring to patent since ¯ > π s (β). ¯ π p (β) i, 3

i, 4

In Figure 4.5 the profit function the innovator would realize in the case that three rival firms entered with a patent shows some exceptional characteristics. Compared to the profit functions for N p > 3 it is the only curve that has an inner optimum for patent breadth so that for all β > β max the patentee’s profits are downward sloping. For very high values of β secrecy even becomes the more attractive strategy.

13

If we would introduce patent costs into our model, the innovator would clearly refrain from patenting in the case that it led to the same profits as with secrecy.

106

4 The Decision to Patent with Horizontal Product Differentiation

This puzzling result contradicts economic intuition, as one would naturally assume that a patent is the better for its holder, the broader its protective level is. To discover the driving forces behind the patentee’s seemingly uncommon strategy choice in this case, let us take a closer look on how patent breadth influences his profits if N p = 3. A change of β influences the patentee’s profits in two ways: his demand as well as his optimal price choice are altered. The following lemma states in which way. Lemma 4.3. For N p = 3 the patentee’s demand decreases as patent breadth rises, while his price rises as long as β does not exceed a critical threshold β0. The intuition behind the above lemma is the following: As patent breadth increases, the border firms k and h are forced to move closer together. This intensifies price competition between them, resulting in lower prices since ∂ppk, 3 /∂β < 0. This in turn increases the demand of the border firms while lowering that of the patentee. Nevertheless the patentee is initially able to increase his price as the effect of the extending protected product space exceeds the negative effect of decreasing prices. Only for very high values of β the patentee has to match his rivals in reducing prices as else he would lose too many consumers. From this point on a further rise of patent breadth leads to decreasing profits, eventually turning secrecy into the more attractive strategy. The following proposition summarizes our results so far. Proposition 4.1. Whenever the disclosure requirement has no impact, α > αN , so that N s ≥ N p , the innovator’s protection decision depends solely on the protective effect of a patent. If (i) (ii)

(iii)

β ≤ 2/N s the protective effect is low and the innovator always prefers secrecy, 2/N s < β < fp, N p the protective effect is moderate and the innovator always prefers to patent for N p > 3. For N p = 3 the innovator will only patent if β < 0.915, β > fp, N p the protective effect is high and the innovator always prefers to patent.

The above proposition covers the situation where the disclosure requirement has no impact which leaves us to analyze the case where due to the required disclosure of the innovation more firms are able to enter the market with a patent, N p > N s (Case (c)). From our exemplary values β¯ and β¯ we know that the impact of the disclosure requirement may lead to secrecy as well as a patent, depending on the extent of patent breadth. In Figure 4.5 we can see that the patent profit functions πi,p N p for N p > 4 cross at least one secrecy profit function πi,p N s with N p > N s . Let us call the intersection point βˆN s , N p . As the patent profit functions are increasing in patent breadth,

4.4 The Patenting Decision

107

the innovator will prefer secrecy for relatively low values of patent breadth, β ≤ βˆN s , N p , and he will prefer to patent for relatively high values of patent breadth, β > βˆN s , N p . Take, for example, the situation where with secrecy four firms would enter the market and with a patent six firms could enter due to the market entry costs reduction of the disclosure requirement. The relevant intersection point in this case is βˆ4, 6 . Whenever patent breadth is lower than βˆ4, 6 the protective effect of the patent is too weak to outreach the negative effect of the disclosure requirement and the innovator will prefer secrecy as this yields higher profits. If patent breadth exceeds the critical threshold, the protective effect overcompensates the disclosure effect and the innovator is better off with a patent. Generalizing these results we come to our next proposition. Proposition 4.2. Whenever the disclosure requirement has an impact, α ≤ αN , so that N p > N s , the innovator will (i)

prefer secrecy for all N s ≤ 3

(ii)

prefer to patent for all N s > 3 if and only if patent breadth exceeds a critical threshold β > βˆN s , N p . Else the innovator will prefer secrecy.

Note that—keeping the number of firms entering with secrecy, N s , fixed— the critical threshold, βˆN¯ s , N p , increases as the impact of the disclosure requirement increases, i.e. more firms are able to enter with a patent. Thus we come to the following corollary. Corollary 4.1. Whenever the disclosure requirement has an impact, the propensity to patent decreases with the strength of the disclosure effect. Last let us turn to the extreme case where the disclosure requirement has a very high impact, α → 0, so that market entry costs approach zero and an infinite number of firms enters. From Equation (4.26) we know  that in the limit case for np → ∞ the profit of the patentee amounts to πip np →∞ = β 3 /32. A patent will be profitable for the innovator whenever it yields higher profits than secrecy. The following proposition states the result of this comparison. Proposition 4.3. Whenever a patent requires complete disclosure, α → 0, so that np → ∞, a patent is profitable for √ the innovator whenever patent breadth exceeds a critical threshold, β > 2 3 4/N s . For N s ≤ 3 the innovator always prefers secrecy. Notably, even if the market will become extremely crowded with a patent the innovator will nonetheless patent whenever patent breadth is sufficiently high. Due to the strong protective effect with a high β the entering firms have to locate in a rather narrow area of non-protected product space which drives their prices and profits to zero. The distance β/2 between the patentee and each of his neighbors then allows him to set a higher price which—in the

108

4 The Decision to Patent with Horizontal Product Differentiation

case that β is high enough—leads to higher profits than with secrecy where the distance to a neighbor is only given by 1/N s . Summarizing we find that the innovator’s decision between a patent and secrecy in a differentiated oligopoly is mainly influenced by two factors: the potentially substantial change in the number of entering firms due to the disclosure requirement, and the breadth of the patent which is the determining factor for the strength of the protective effect. Whenever the disclosure requirement has a high impact, meaning that more firms will enter due to decreasing market entry costs, the innovator may prefer secrecy. If, however, the disclosure requirement plays a minor role, a patent may be profit enhancing for the innovator, as it forces his rivals to locate their products further away from him. The following table summarizes our results for N p , N s ∈ [1, 6] and N p → ∞. Table 4.1 The Propensity to Patent with Horizontally Differentiated Products: Summary of Results Np

1

2

3

4

5

6

Np → ∞

secrecy secrecy

secrecy secrecy

secrecy secrecy

secrecy secrecy

secrecy secrecy

secrecy

secrecy

secrecy

secrecy

Ns

1 2

secrecy secrecy –∗ secrecy β

3

–

patent

< 0.91

patent β

≥ 0.91

secrecy β ≤ 0.5 se- β

4

–

patent

patent

crecy β

>

≤ 0.65 β

secrecy 0.5 β

patent

> 0.65 β

patent

–

patent

patent

patent

crecy β

>

0.4 β

patent

β

6

–

patent

patent

patent

patent

β

∗

≤ 0.53

secrecy

> 0.33 β

patent

> 0.63

patent

≤ 0.33 β

secrecy

≤ 0.63

secrecy

> 0.48 β

patent

> 0.79

patent

≤ 0.48 β

secrecy

≤ 0.79

secrecy

> 0.71 β

patent

β ≤ 0.4 se- β

5

≤ 0.71 β

secrecy

> 0.53

patent

For N s = 2 we must have fs, 2 ≥ f > fs, 3 whereas for N p = 1 market entry costs have to fulfill fp, 1 ≥ f > fp, 2 . We know that fp, 1 = fs, 1 and fp, 2 = fs, 2 so the latter condition changes to fs, 1 ≥ f > fs, 2 which cannot be fulfilled for any situation with N s > 1.

4.5 Licensing

109

Obviously there are two regions where the protection decision is independent of patent breadth: in the lower left area of the table, where N s < N p the innovator chooses to patent and in the upper right area of the table where N s ≤ 3 and N s < N p the innovator chooses secrecy. In the area in between, patent breadth is the decisive factor for the dominant effect. If β is rather low, the protective effect is weak so that the negative effect of the required disclosure leads to secrecy. If patent breadth is rather high, the protective effect is strong enough to overcompensate the disclosure effect so that the innovator chooses to patent. An important fact that we have ignored so far is that a patent opens the opportunity of licensing to the innovator. Naturally this additional strategic possibility may heighten the innovator’s incentive to patent. We will analyze the influence of licensing on the obtained results in the following.

4.5 Licensing To introduce licensing into our three-stage game we will modify the innovator’s strategy-set on the first stage by adding the strategy“patent and license” so that σi1 = {S, P, l}.14 As extensively analyzed in Section 4.4 a set of market entry costs and patent breadth, (f, β), combined with the particular impact of the disclosure requirement, α, defines the number of firms operating in the market. If the innovator patents and licenses he discloses his innovation to a restricted number of firms. For all licensees we have α = 0 so that their market entry costs are zero. Additionally they can enter the market without any restriction on their choice of location so that—following the principle of maximum differentiation—they will choose to locate equidistantly on the unit circle. We assume that the patentee offers licenses at a fixed fee, L, making a take-itor-leave-it offer to his rivals.15 The individual profits of each licensee will be equal to his profits in the case of secrecy (see Equation (4.3)) with market entry costs set to zero, f = 0, and minus a license fee, L, πlL = 1/(N L )3 − L. To maximize his profits the patentee will choose a fee that minimizes the licensee’s profits, making him just indifferent between buying a license or not, L = 1/(N L )3 . The profits of the patentee consisting of his individual profits 14 For the ease of exposition in the following we will briefly call the strategy “license”, naturally always meaning that the innovator patents and licenses his innovation. See for example Anton and Yao (1994) for an analysis of licensing in the absence of a patent. 15 Hereby we implicitly assume that the innovator possesses the complete bargaining power. Relaxing this assumption would lead to a weakening of our results: as the innovator’s bargaining power decreases he would license his innovation in less cases since the share of profits he can collect from his licensees declines.

110

4 The Decision to Patent with Horizontal Product Differentiation

and the sum of all licensing fees he collects amount to πi,L N L =

1 . (N L )2

(4.27)

Naturally by licensing the patentee cannot influence the extent of protected product space as this is defined by the breadth of the underlying patent. Thus at least as many firms will be able to enter in the case of licensing as in the case of a patent or secrecy. Lemma 4.4. Whenever N s > 1 and the innovator chooses to patent and license his innovation he will offer a license to as many rival firms as would operate in the market without a license. One exception to the above lemma is the situation where the innovator acts as monopolist due to very high market entry costs, f > fs, 2 . By licensing the innovator could enable a restricted number of rival firms to enter. As in a monopoly the outside option detracts consumers from buying the innovative product, this strategy could be profit enhancing. Let us take a closer look. From Propositions 4.1 and 4.2 we know that if licensing is not an option the innovator will prefer secrecy for N s = 1. In this case he realizes monopoly profits πim . The innovator will prefer to license the new product whenever this yields higher profits than in the case of monopoly, πi,L N L > πim . Proposition 4.4. An innovator acting as monopolist (N s = 1) will (i)

always prefer secrecy if the reservation price is high (v ≥ vcrit )

(ii)

patent and sell one license if the reservation price is low (v < vcrit ).

The intuition behind this result is straightforward. Whenever the reservation price is high, the consumers will rather buy the monopolist’s product than an outside option and as a consequence monopoly profits are high. The innovator thus has no incentive to share the market by selling a license and will keep his innovation secret. If the reservation price is low, the outside option becomes more attractive to consumers and monopoly profits go down. In this case it is profitable for the innovator to share the market with one licensee as this has a market-expanding effect: By licensing the innovation the whole market can be served, as consumers located far away from the innovator can now buy a differentiated version of the innovative product better matching their preferences. By collecting the license fee the innovator can extract the additional profits from his rivals so that he realizes higher profits than in monopoly. Whenever competitors operate in the market, the outside option has no relevance.16 In Section 4.4 we analyzed the innovator’s protection decision for 16

This is due to our assumptions on the domain of the reservation price v, see Footnote 5.

4.5 Licensing

111

all possible combinations of market entry costs and patent breadth, f, β, that lead to N s > 1 and N p > 1. If licensing is an additional option, the innovator will change his protection strategy whenever this yields higher profits. Suppose that without the possibility of licensing the innovator chooses secrecy and N s firms operate in the market. If he now licenses his innovation he will sell nL = N s − 1 licenses (see Lemma 4.4) so that the number of firms operating in the market as well as their respective locations remain unchanged. What changes is the profit of the innovator: additionally to his own profits πi,s N s he now also collects N s − 1 times the license fee L, thus clearly he is always better off with this strategy. Proposition 4.5. Whenever the combination of f, β would lead to secrecy as the profit maximizing strategy in the absence of licensing and N s > 1, the innovator will choose to patent and license his innovation. Now suppose that without the possibility of licensing the innovator chooses to patent and N p firms operate in the market, all rival firms located in the non-protected product space. If the innovator chose to license, firms could freely locate on the circle so that due to the principle of maximum differentiation they would be evenly spaced in the market. From Lemma 4.4 we know that N L = N p firms will receive a license. The higher the number of licensees, the fiercer is price competition between neighbors as the distance between them decreases. In the end this leads to decreasing profits for the patentee and licensor. At the same time the extent of patent breadth has a positive effect on the profits the innovator could realize by solely patenting. Combining both effects, we find that licensing becomes unattractive as patent breadth and the number of firms in the market increase. The following proposition summarizes these results. Proposition 4.6. Whenever the combination of f, β would lead to a patent as the profit maximizing strategy in the absence of licensing and N p > 1, the innovator will choose to (i) (ii)

license his patent for all N p < 6 crit license his patent for all N p ≥ 6 if and only if β < βN p .

The possibility of licensing thus has changed our results substantially. The strategy secrecy remains the dominant option for the innovator only in the special case that initial market entry costs are so high that he acts as a monopolist and additionally the reservation price is very high. For all other cases—given that patent breadth is not too high—the innovator will choose to patent and license his innovation. If patent breadth as well as the number of entering firms is relatively high, the innovator solely patents and profits from a strong protective effect.

112

4 The Decision to Patent with Horizontal Product Differentiation

4.6 Welfare Considerations So far we analyzed the best appropriation mechanism from the innovator’s viewpoint. In this section we will take a careful look at the influence of the innovator’s decision on social welfare. Therefore we will first derive social welfare given the alternative appropriation choices secrecy, patent and/or license and then link the obtained results to the actual appropriation choices of the innovator stated in the propositions earlier in this chapter.

4.6.1 Welfare with Secrecy If the innovator decides to keep his innovation secret, we need to distinguish the cases that either the innovator is the only firm offering the innovative product or that he shares the market with one or more competitors. In the latter case our model corresponds to Salop’s well known circular city. As firms are symmetric, the derivation of producers’ surplus is straightforward: Producers’ profit (Equation (4.4)) is multiplied with N s , the number of firms operating in the market, which yields P S = 1/(N s )2 . As firms are located symmetrically on the unit circle with distance 1/N s , the distance between an indifferent consumer and its neighboring firm must be 1/(2N s ). Thus consumers situated between the firm situated at x0 = 0 and the indifferent

1/(2N s ) consumer xˆ0 = 1/(2N s ) realize a surplus in height of CS0 = 2 0 Ux dx with Ux = v−p0 −(x−x0 )2 . Inserting p0 from Equation (4.2), total consumers’ surplus can be derived as s

CS = 2N

s



1/(2N s )

0

=v−

 v−

 1 2 dx − x (N s )2

13 . 12(N s )2

Thus social welfare amounts to WFs = v −

1 . 12(N s )2

(4.28)

Hence, if the innovator chooses secrecy as appropriation strategy, economic welfare is higher, the higher is the reservation price and the more firms operate in the market. In the case that the innovator acts as a monopolist, it may be that consumers prefer to buy an outside option (see pp. 92). This changes the analysis of consumers’ surplus to

4.6 Welfare Considerations M

CS

113



x ˆi, out

=2



0

4v = 9



 v − pi − x2 dx

v 3

which results in social welfare in height of  16v v . WFM = 9 3

(4.29)

4.6.2 Welfare with a Patent Whenever the innovator patents, firms’ locations on the unit circle are no longer symmetric. Consequently social welfare has to be derived subject to the number of firms operating in the market. As in the analysis of the patenting decision earlier in this chapter, we will explicitly refer to the cases N p = [3, 4, 5, 6] and to the limit case N p → ∞. The derivation of producers’ surplus is straightforward: it consists of the profits of all firms operating in the market. Summing up the profits derived in Section 4.3 yields p

p

PS =

N 

πa with a = [i, k, h, k + 1, h + 1, . . . , k + κmax ] .

(4.30)

a=1

Due to the asymmetric locations of firms, the derivation of consumers’ surplus differs subject to the number of firms operating in the market. To begin with we will consider the case N p = 3. Consumers can be distinguished subject to the firm from which they choose to buy. With three firms operating in the market, the unit circle can thus be divided into two regions, see Figure 4.6(a). Region I consists of all consumers buying from the innovator, Region II of all consumers buying from either border firm. Due to semi-circle symmetry we know that the border firms in equilibrium will set equal prices, thus we can write   0 CSp3 = 2

x ˆi, h

0

Ux dx + 2

x ˆh, k

x ˆi, h

Ux dx

with Ux = v − ppz, 3 − (x − xz )2 , z = [i, h]. In solving the integrals it is important to take into account the fact that the value of the parameter x ˆh, k does not correspond to the actual location of the indifferent consumer on the circle. Instead, it measures the distance between the location of firm h

114

4 The Decision to Patent with Horizontal Product Differentiation

and the consumer indifferent between buying from firm h or firm k, xˆh, k . In the basic Salop model this distinction between value and location is obsolete, as due to the symmetry of firms it is sufficient to analyze the surplus of the consumers situated in between two firms and then multiply it with the total number of firms. Nevertheless, the location of an indifferent consumer situated next to a firm, say xz with 0 < z < 1, does not correspond to the value of x ˆz . This parameter actually measures the distance between firm xz and the indifferent consumer next to it. Thus, the correct position of this consumer measured from 0 is x ˆ0z = xz + xˆz . In the considered case N p = 3 0 this means that x ˆh, k = xh + x ˆh, k with xh = β/2. Taking this into account and inserting PSp as well as the respective prices into the social welfare function WFp3 = PSp3 + CSp3 yields WFp3 = v(1 − β) + Γ (β) with Γ (β) ≡

(4.31)

−144+β (1008+β (−2176+β (2436+β (−1488+373 β)))) 192 (3−2 β)2

.

Next we turn to the case N p = 4. To derive consumers’ surplus we distinguish three regions on the unit circle, see Figure 4.6(b). Region I consists of all consumers buying from the innovator. All consumers buying from the border firms k and h are located in Region II and finally Region III consists of all consumers buying the non-border firms’ product. Consumers’ surplus can be formalized as  xˆi, h  xˆ0h, k+1  xˆ0k+1, k Ux dx + 2 Ux dx + Ux dx CSp4 = 2 0

x ˆi, h

x ˆ0h, k+1

with Ux = v − ppz, 4 − (x − xz )2 , z = [i, h, k + 1] . Again we need to carefully distinguish the values of the parameters xˆz and the actual locations measured from 0. The respective locations are x ˆ0i, h = x ˆi, h , x ˆ0h, k+1 = xh + x ˆh, k+1 with xh = β/2 and x ˆ0k+1, k = x0k+1 + x ˆk+1, k with 0 xk+1 = 1/2. Inserting these locations, the respective prices and producers’ surplus from Equation (4.30) into the social welfare function we have   (−1 + β) β 7 p WF4 = v − − (4.32) 192 8 as social welfare in the case N p = 4. For the analysis of social welfare in the case N p = 5 we subdivide the unit circle into three regions, see Figure 4.6(c). Region I and II are analogous to the former cases, Region III consists of the consumers that buy from one of the two non-border firms. Due to semi-circle symmetry we have ppk+1, 5 = ˆh, h+1 , which measures the distance of pph+1, 5 . Additionally the parameter x the consumer indifferent between buying from firm h or firm h + 1 to the

4.6 Welfare Considerations

115

Fig. 4.6 The Derivation of Consumers’ Surplus xi

xi

I

x ˆi, k

x ˆi, h

I

x ˆi, k

x ˆi, h

II

II k

h

k

II

h

k+1 x ˆk+1, k

x ˆh, k

(a) N p = 3

x ˆh, k+1

III

(b) N p = 4 xi

xi I

x ˆi, k

I

x ˆi, k

x ˆi, h

x ˆi, h

II

II II

II

k k

h k+1

x ˆk+1, k

k+1

h+1

k+2

x ˆk+1, k x ˆh, k+1

III

h h+1 x ˆh, k+1

III

x ˆh+1, k+2

x ˆk+2, k+1

(c) N p = 5

(d) N p = 6

border firm h, is equivalent to the parameter x ˆk+1, k , which measures the distance of the consumer indifferent between buying from firm k + 1 or firm k to the border firm k. Due to our assumption that the patentee’s competitors follow the principle of maximum differentiation and thus are evenly spaced in the non-protected product space we have x0h+1 = xh + (1 − β)/3 with xh = β/2. Thus consumers’ surplus amounts to CSp5 = 2

 0

x ˆi, h

 Ux dx + 2

x ˆ0h, h+1

x ˆi, h

 Ux dx + 2

1/2

x ˆ0h, h+1

with Ux = v − ppz, 5 − (x − xz )2 , z = [i, h, k + 1, h + 1].

Ux dx

116

4 The Decision to Patent with Horizontal Product Differentiation

Inserting the respective locations, prices and producers’ surplus into the social welfare function and solving the integrals yields WFp5 = v + Γ  (β)

(4.33)

(3898+β (12304+β (6480+371 β))))) as social welwith Γ  (β) ≡ −(2450+β (−4416+β 15552 (3+2 β)2 fare in the case N p = 5.

This leaves us to analyze the case N p = 6. To derive consumers’ surplus we divide the market into four regions, see Figure 4.6(d). Regions I, II and III are analogous to the above cases while Region IV consists of the consumers that buy from the non-border firm h + 2. Consumers’ surplus can thus be derived by solving CSp6



x ˆi, h

=2 0

 Ux dx + 2

x ˆ0h, h+1

x ˆi, h

 Ux dx + 2

x ˆ0h+1, k+2

x ˆ0h, h+1

 Ux dx +

x ˆ0k+2, k+1

x ˆ0h+1, k+2

Ux dx

with Ux = v − ppz, 5 − (x − xz )2 , z = [i, h, k + 1, h + 1, h + 2] . The actual locations of the non-border firms are x0h+1 = β/2 + (1 − β)/4 and x0h+2 = 1/2. Further the actual locations of the indifferent consumers are x ˆ0h+1, k+2 = (1 + β)/4 + x ˆh+1 and x ˆ0k+2, k+1 = 1/2 + x ˆk+2, k+1 . Again inserting the respective locations, prices and producers’ surplus into the social welfare function and solving the integrals yields WFp6 = v + Γ  (β) with Γ  (β) ≡

−(22+3 β (−14+β (2+β) (−11+9 β (4+3 β)))) 48 (7+9 β)2

(4.34) .

Finally we take a look at the limit case N p → ∞. From our analysis in Section 4.3 (p. 101) we know that in the limit case price competition between the patentee’s competitors becomes so tough that they set a price according to their cost. As we assume c = 0 for all firms we thus have ppzˆ, ∞ = 0 with zˆ = [k, h, k + 1, h + 1, . . . , k + κmax ]. To derive consumers’ surplus we can subdivide the unit circle into three regions. Region I includes all consumers buying from the patentee. These consumers face positive mismatch costs and pay the price ppi, ∞ = β 2 /8 so we have UxI = v − β 2 /8 − x2 . Region II contains all consumers that buy the border firms’ products. They also face positive mismatch costs, but due to the strong competition prices are zero. We have UxII = v − (x − β/2)2 . Region III contains the consumers located in the non-protected product space. As np → ∞ firms enter, these consumers no longer face mismatch costs as they can buy a product that perfectly matches their preferences. Thus we have UxIII = v.

4.6 Welfare Considerations

117

Knowing this, consumers’ surplus can be derived by solving CSp∞ = 2

 0

x ˆi, h

(v − β 2 /8 − x2 ) dx + 2



β/2

x ˆi, h

(v − (x − β/2)2 ) dx + 2



1/2

β/2

v dx .

Since the patentee’s competitors realize zero profits, producers’ surplus solely consists of the patentee’s profit, PSp∞ = β 3 /32. Inserting CSp∞ and PSp∞ into the social welfare function and solving the integrals we get WFp∞ = v +

−7 β 3 192

(4.35)

as the social welfare in the limit case. Concluding the preceding analysis we find that for any number of firms operating in the market with a restrictive patent, β > 2/N p , the intensity of patent protection as well as the reservation price are decisive for the extent of social welfare. On the one hand, we have ∂WFpN p /∂β < 0, meaning that the higher the intensity of patent protection is, the lower is social welfare. On the other hand the reservation price, v, has a positive influence on social welfare as it increases consumers’ surplus without affecting producers’ surplus negatively. Before we proceed to the comparison of the innovator’s actual appropriation choices with the welfare maximizing strategies, we will analyze social welfare in the case that the innovator patents and licenses his innovative product.

4.6.3 Welfare with Licensing From Lemma 4.4 we know that the innovator will offer a license to as many firms as would operate in the market without a license so N L = N p or N L = ¯ ) = W F s (N ¯) N s . As licensees can freely locate on the circle we have W F L (N s p ¯ with N = {N , N }.

4.6.4 Welfare Maximizing Appropriation Choice To compare the innovator’s actual protection choices with the welfare maximizing strategies, we will proceed in two steps. First we will suppose that licensing is not an option so that the innovator may either patent or keep his innovation secret (Case 1). As in our theoretical analysis in Section 4.4, we will distinguish the case that the disclosure requirement has an impact (1(i)) and the case that the disclosure requirement has no impact (1(ii)). In a second step we will then look at the changes that eventually occur due to

118

4 The Decision to Patent with Horizontal Product Differentiation

the possibility of licensing (Case 2). The comparison of the innovator’s appropriation strategies with the welfare maximizing strategies in Case 1(i) brings us to the following proposition. Proposition 4.7. Whenever the disclosure requirement has no impact (Proposition 4.1) and licensing is not an option, the innovator’s protection decision depends on the protective effect of a patent. If (i) (ii)

(iii)

β ≤ 2/N s the innovator always prefers secrecy which is the welfare maximizing strategy, 2/N s < β < fp, N p the innovator prefers to patent for N p > 3. For N p = 3 the innovator will only patent if β < 0.915. Hence he chooses the welfare maximizing strategy only if N p = 3 and β ≥ 0.915, β > fp, N p the innovator always prefers to patent, never choosing the welfare maximizing strategy.

Obviously the innovator’s propensity to patent increases with patent breadth. Hence, the higher the intensity of patent protection, the more will the innovator’s strategy differ from the welfare maximizing appropriation mechanism. In Case 1(i) the innovator only chooses the welfare maximizing strategy, secrecy, if the protective effect of a patent, β, is low. The economic intuition behind this result is straightforward: the advantage of a patent from a welfare perspective is the disclosure of formerly proprietary information. Neglecting the disclosure effect, as is the case in Proposition 4.7, the patent’s drawback of granting a temporary monopoly is not opposed by any positive effect, so that secrecy or licensing become the welfare maximizing appropriation choices. Things should be different when the impact of the disclosure requirement is taken into account. Turning to Case 1(ii) we will compare the innovator’s strategies as derived in Proposition 4.2 with the welfare maximizing appropriation mechanism. We find that patenting could be welfare enhancing in some cases—subject to the extent of the disclosure effect—but interestingly in the relevant cases the innovator never has an incentive to actually patent. Proposition 4.8. Whenever the disclosure requirement has an impact (Proposition 4.2) and licensing is no option, the innovator will (i)

prefer secrecy for all N s ≤ 3. (a) (b) (c)

For N s = 1 secrecy maximizes social welfare only if N p = 3 firms entered with a patent. For N s = 2 patenting would be welfare enhancing for N p ≥ 4 whenever the protective effect is . moderate (β < β˜N p ) For N s = 3 patenting would be welfare enhancing only if N p = 4 and β < 0.68.

4.6 Welfare Considerations

(ii)

119

prefer to patent for all N s > 3 if and only if patent breadth exceeds a critical threshold β > βˆN s , N p . Else the innovator will prefer secrecy. Patenting would be welfare enhancing for a sufficiently strong disclosure effect and β < β˜N s , N p . As β˜N s , N p < βˆN s , N p the innovator’s strategy choice is never welfare maximizing.

This result is due to the opposing effects of patenting which influence the protection decision of the innovator and the welfare effects of a patent in a contrary way. The protective effect of a patent is perceived as a positive effect by the innovator since potential competitors are detained from entering the protected product space. From a welfare perspective this effect is a negative effect, as the exclusive right to market the protected innovation attenuates the competition in the respective market. Understanding a patent as a contract, the disclosure requirement linked to a patent should account for the negative effect that patent protection has on economic welfare. Thus, from a welfare perspective, the disclosure effect is a positive effect as it enforces the market entry of competitors by simplifying their research, avoiding duplicative research efforts. The innovator perceives the required disclosure negatively, as it intensifies the competition he faces. As stated in Proposition 4.8, the parameter constellation where the protective effect outweighs the disclosure requirement so that the innovator patents never coincides with the constellation where the welfare enhancing effect of knowledge disclosure countervails the constraining effect a patent has on competition. Naturally this conclusion is altered by the possibility of licensing. The welfare analysis of the innovator’s appropriation strategies if licensing is an option (Case 2) can be summarized in the following proposition. Proposition 4.9. Licensing is always welfare maximizing. With a license, the positive effect that a patent has on social welfare, namely the required disclosure, is effective while the negative protective effect of patenting is neutralized since the licensees can freely choose their locations in the market. This leaves us to analyze the innovator’s actual licensing behavior. In Section 4.5 we found that it depends on the innovator’s initial situation without the option to license: Either he initially acts as a monopolist, N = 1, or he prefers secrecy without licensing or he prefers to patent without licensing. From Proposition 4.4 we know that an innovator acting as monopolist will only patent and license his innovation if the reservation price is sufficiently low. If we interpret the reservation price as the consumers’ appreciation of the old product, we can say that the propensity to license is higher, the less important the old technology becomes. Whenever the old product is relatively important compared to the innovation, the demand in the new market is so small that it cannot be profitable for the innovator to patent and license the innovation, thereby inviting a competitor to enter the formerly monopolistic market. Thus in the case that market entry costs are so high

120

4 The Decision to Patent with Horizontal Product Differentiation

that the innovator can initially act as monopolist, the propensity to license depends on the reservation price, a parameter which cannot be influenced by policy measures. If we look at a constellation with lower market entry costs, so that the innovator initially shares the market with competitors, Propositions 4.5 and 4.6 state that he will license his patent whenever patent protection is not too high.

4.7 Concluding Remarks In this chapter our aim was to provide a framework in which the decision of an innovator between a patent and secrecy could be analyzed taking into account the possibility of inventing around by competitors as well as considering a varying impact of the disclosure requirement. To do this we introduced the decision to patent into an oligopolistic setting with horizontally differentiated products. In this setting we defined the technological lead of an innovator as the height of the fixed costs of market entry which are decisive for the number of firms that are able to enter the market for the innovative product. Opposing the approach with vertically differentiated products presented in Chapter 2, in the case with horizontal differentiation it is assumed that if secrecy is chosen by the innovator, there are no spillover effects while with a patent the innovator’s lead does not vanish completely. Instead, the disclosure requirement’s impact is modeled as a more or less extensive decrease of initial market entry costs. Thus by patenting the innovator (possibly) faces a reduction of profits due to more competitors entering the market. A patent’s scope in this setting is defined as patent breadth and is decisive for the strategy space of competitors in the sense that they can only enter the market within the non-protected product space. Table 4.2 Summary of the Theoretical Results Concerning the Decision to Patent

ptp

impact discl. req.

MEC

pat. breadth

crit. pat. breadth

α↓

fs ↑

β↑

β crit ↑

–

–

+

–

MEC = market entry costs ptp = propensity to patent

4.7 Concluding Remarks

121

The central parameters of our analysis of the propensity to patent in a setting with horizontally differentiated products were the impact of the disclosure requirement, α, the initial market entry cost, fs , and the intensity of patent protection, patent breadth β. We found that while the impact of the disclosure requirement as well as the market entry costs have a negative effect on the propensity to patent, patent breadth has a positive effect. These results are straightforward: The impact of the disclosure requirement defines the negative effect patenting has from the viewpoint of the inventor. The higher it is, the more firms will be able to enter the market due to the mandatory disclosure of information which results in decreasing market entry costs. Thus an increase of the disclosure requirement’s impact will lead to a reduction of the propensity to patent. Initial market entry costs form a natural barrier to entry: whenever they are high, secrecy as an appropriation mechanism is quite attractive and patent protection is quite unnecessary. If initial market entry costs increase this effect becomes more prominent and the propensity to patent decreases. Regarding the protective effect of a patent, which in this setting is defined by a patent’s breadth, our theoretical model proposes that the stronger patent protection is, the more attractive patenting is for the inventor. A further important result is the influence of the critical threshold of patent breadth, β crit , on the propensity to patent. The height of this threshold is driven by the initial market structure, i.e. how many firms operate in the market with secrecy, N s . We found that a patent only has a restricting effect on the innovator’s competitors, i.e. a positive protective effect, whenever patent breadth exceeds the critical threshold β crit . Thus, when the critical threshold increases (due to a decreasing number of firms operating in the market with secrecy), the range in which a patent is restrictive becomes narrower and thus the propensity to patent decreases. Regarding social welfare we find that—opposing our results in Chapter 2—licensing is always welfare maximizing. Thus no matter whether the disclosure requirement has an impact or not, the licensing of a patented innovation always is the profit maximizing strategy. This is due to the fact that the innovator will offer a license to as many firms as would operate in the market without a license, i.e. while the positive effect of patenting on social welfare—the mandatory disclosure of information—is effective, the negative protective effect is neutralized as licensees can freely locate in the market. Some specific disadvantages of the analysis of the patenting decision in the setting with horizontally differentiated products shall be mentioned. Although this approach allows for a varying impact of the disclosure requirement, now a spillover effect is neglected. Accounting for unintended spillover would result in the following specification of market entry costs fp = (1 − λ)αf˜s . Recall from Footnote 11 that the critical threshold decisive for the impact of the disclosure effect is given by αN ≡ fN +1 /f¯N . If spillover are introduced and generally reduce market entry costs so that we

122

4 The Decision to Patent with Horizontal Product Differentiation

have fN (λ) = (1 − λ)fN ∀ N , the decisive threshold αN is not altered as ∂αN (λ)/∂λ = 0. Consequently, the extension of the model to include unintended spillover of information has no impact on the theoretical results. A further specific drawback to the setting with horizontal differentiation is the assumption that an outside option is only relevant when the innovator acts as a monopolist. Naturally, instead of restricting the price of the outside option in a manner that leads to the desired effect, it would be preferable to derive this mechanism endogenously. However, this would additionally complicate the analysis while it is questionable whether substantial insights or changes to our results could be obtained. In the following chapter we empirically test several hypotheses which summarize our theoretical results concerning the decision to patent with horizontally differentiated products.

Chapter 5

An Empirical Investigation of the Decision to Patent with Horizontal Product Differentiation

For our empirical analysis of the case with horizontally differentiated products we use the same data as in the case with vertically differentiated goods. Nevertheless we implement the differing model assumptions by defining the data sample properly. The empirical analysis proceeds as follows: After summarizing the theoretical results in multiple hypotheses (Section 5.1) the data sample and the implementation of the theoretical parameters in the data are described (Section 5.2). The results of the empirical estimations are presented in Section 5.3. Section 5.4 concludes. The empirical estimations presented in this chapter in large parts follow Zaby and Heger (2009).

5.1 Hypotheses and Their Empirical Implementation In the following section we derive hypotheses from the results of the theoretical analysis concerning the propensity to patent with horizontally differentiated products (see Chapter 4). To examine the consequences of the possibility of inventing around and the impact of the disclosure requirement we introduced the patenting decision into a model with horizontally differentiated goods, the well-known circular city model. In this setting the extent of market entry costs is the decisive factor for the resulting market structure: the lower the fixed costs of market entry are, the more firms are able to enter the market. As we assume that the mandatory disclosure of information can be used by competitors in their attempts to invent around the patent, patenting reduces market entry costs and thus facilitates market entry. Our first hypothesis stems from this basic mechanism. Hypothesis 5.1 The propensity to patent increases when market entry costs decrease. When the initial market entry costs are high, they form an effective barrier to entry. The innovator may thus choose not to patent as then he would face 123

124

5 Empirical Analysis of the Model with Horizontal Product Differentiation

the drawback from the disclosure of information without profiting from the protective effect. If market entry costs decrease, i.e. more firms are able to enter, patenting becomes profitable as it protects at least part of the product space from the entry of rivals. Consequently the propensity to patent increases when the fixed costs of market entry decrease. Recall from the theoretical model that the critical threshold for a restrictive patent is β crit = 2/N s . Whenever a patent is not restrictive it has no protective effect and is thus not profitable for the innovator. If the disclosure requirement has no impact, which means that the number of competitors will not increase by patenting, every restrictive patent solely has a positive protective effect and the innovator will choose to patent. As ∂β crit /∂N s < 0, the critical threshold for patent breadth decreases as the number of firms in the market rises. This enlarges the range in which a patent is restrictive and consequently the propensity to patent increases. These results can be condensed to the following hypothesis. Hypothesis 5.2 Whenever the disclosure requirement has no impact, the propensity to patent rises with the number of firms operating in the market. From Table 1.1, we know that due to the impact of the disclosure requirement by patenting market entry costs decrease to fp ≡ αfs . Thus the change of market entry costs by patenting can be defined as Δf ≡ (1 − α)fs . The innovator’s profits with a patent are higher, the lower the change of market entry costs, Δf , as then less firms are able to enter the market due to the impact of the disclosure requirement. Hence, the decision to patent is crucially influenced by the strength of the disclosure effect. Market entry costs with a patent (fp ) and with secrecy (fs ) drive this result as follows: On the one hand a rise of fs results in a higher entry barrier so that patenting becomes obsolete and consequently the propensity to patent decreases. On the other hand the lower the reduction of market entry costs due to patenting, i.e. the higher fp , the lower is the impact of the disclosure requirement so that patenting becomes more profitable and the propensity to patent rises. Thus, we come to the following hypothesis which corresponds to Corollary 4.1 of our theoretical model: Hypothesis 5.3 Whenever the disclosure requirement has an impact, the propensity to patent decreases with the strength of the disclosure effect. As stated in Hypotheses 5.2 and 5.3, the decision to patent is mainly driven by patent breadth (protective effect) and the impact of the disclosure requirement (disclosure effect). The patenting propensity substantially varies subject to the intensity of the disclosure effect. We find that if the disclosure requirement has no impact (Proposition 4.1), the patenting decision solely depends on the protective effect, i.e. the propensity to patent increases with the intensity of patent protection, β. Further we find that if the disclosure requirement has an impact, the patenting decision depends on the number of firms operating in the market as well as on the extent of patent protection

5.1 Hypotheses and Their Empirical Implementation

125

(Proposition 4.2). We translate these theoretical results into the following empirical equation: P = β0 + β1 N ∗ RE + β2 fs + β3 fs ∗ RE + β4 N + β5 RE + Controls +  , where P denotes the patenting decision, N the number of firms operating in the market (initial market structure), RE reflects the easiness of substitutability as a proxy for the impact of the disclosure requirement and fs are the cost of market entry with secrecy.1 As elaborated earlier, due to ∂β crit /∂N s < 0 a change in N is an adequate measure for variations of the critical threshold of patent breadth. If the disclosure effect is low since substitutability is difficult, the driving force behind the decision to patent is the critical threshold of the intensity of patent protection, β crit . The more firms enter, the lower this threshold will be, and thus the higher is the propensity to patent. Hence, following our theoretical results, we expect a positive effect of N on the propensity to patent. To capture the distinction between the cases the disclosure requirement has an impact and the disclosure requirement has no impact, we include the interaction terms N ∗ RE and fs ∗ RE. Whenever the dummy variable RE indicating the easiness of substitutability takes the value 0, the disclosure requirement has no impact and thus the interaction terms vanish and only the sole effects of N and fs prevail. Whenever the disclosure requirement has an impact, RE = 1, the interaction terms additionally influence the sole effects and the overall effect is given by the sum of both effects.2 To capture market entry costs (fs ) we use the firms’ assessment of the threat of market entry by new competitors. Whenever firms see their market position strongly threatened by market entry, we conjecture that market entry costs are low. According to our theoretical model the single effect of fs should be negative: as market entry costs with secrecy rise, the barrier to entry increases so that the usefulness of a patent diminishes, resulting in a decrease of the propensity to patent. However, the interaction term with the easiness of substitutability, fs ∗ RE, which reflects the market entry costs of competitors accounting for an impact of the disclosure requirement, should have a positive effect on patenting.

1

Note that the empirical translation of the impact of the disclosure requirement is equivalent to our definition of the easiness of reverse engineering in the above section. In order to illustrate this fact we use the same notation. 2 Note that this computation of an overall effect is only feasible if the marginal effects of both variables are significantly distinct from each other.

126

5 Empirical Analysis of the Model with Horizontal Product Differentiation

5.2 Sample and Variable Definition In this section we test our theoretical model reflecting the patenting behavior in a market with horizontally differentiated products. A central assumption to the theoretical analysis is that the successful inventor commercializes his invention immediately, thereby opening a new market. To implement this in empirical terms, we restrict our data to firms which indicate that their innovation activities resulted in the establishment of new markets. As before we only include innovating firms. In the restricted data set we have 45% of firms indicating that they applied for a patent in the considered time period. As stated earlier a variable reflecting the easiness of substitutability is used as a proxy for the impact of the disclosure requirement, RE. Descriptive statistics reveal that nearly 70% of firms find that their competitive environment is characterized by easy to substitute products. The theoretical model finds a critical threshold for patent breadth indicating whether a patent has a restricting effect or not. This critical threshold decreases, the more firms operate in the market in the absence of a patent. Naturally it is not straightforward to implement the actual number of firms operating in a market empirically. Nevertheless the MIP provides a categorical variable displaying the ranges of the number of competitors as perceived by a firm.3 We thus use a dummy variable large number of firms which indicates that a respondent firm has more than 15 competitors. In our data set this is the case for 16% of all firms. In default of a corresponding measure in MIP 2005, we refer to a firm’s perception on whether its market position is threatened by the entry of new rivals as a proxy for initial market entry costs, fs . We argument that whenever a firm perceives its market position as strongly threatened by market entry, initial market entry costs, the initial barrier to entry, are low, this is found relevant by 10% of firms. As described above we include the interaction terms firms * rev. eng. and MEC * rev. eng. Descriptive statistics show that the first, which captures the change in the number of firms due to the impact of the disclosure requirement, is relevant for 12% of all firms while the latter, which reflects the perceived market entry costs if substitutability plays an important role, is relevant for 8% of firms. Consistent to the empirical test of the patenting decision in vertically differentiated markets in the preceding section we include firm size, human capital, customer power, the geographical markets EU and non-EU, cooperation and east as control variables. For definitions refer to Chapter 3, for descriptive statistics see Table 5.1. In order to capture the fact that the market may be characterized by additional market entry barriers other than the one considered as explanatory 3

The ranges are defined as follows: no competitors, 1 to 5 competitors, 6 to 15 competitors and more than 15 competitors.

5.3 Empirical Results

127

Table 5.1 Descriptive Statistics for the Patenting Decision Estimation with Horizontally Differentiated Products Mean Std. Dev. Min Max patent

0.442

0.497

0

1

market entry costs

0.105

0.306

0

1

large number of firms 0.158

0.365

0

1

reverse engineering

0.687

0.464

0

1

MEC * rev. eng.

0.084

0.278

0

1

firms * rev. eng.

0.120

0.326

0

1

log(employees)

4.305

1.673

0

9.077

human capital

0.243

0.255

0.000 1.000

R&D intensity

0.065

0.273

0.000 6.427

capital intensity

0.109

0.272

0.000 4.554

EU

0.584

0.493

0

1

non EU

0.409

0.492

0

1

customer power

0.300

0.458

0

1

cooperation

0.368

0.483

0

1

east

0.321

0.467

0

1

variable for initial market entry costs, fs , we control for capital intensity defined as tangible assets per employee and for R&D intensity defined as expenditures for in-house R&D activities per sales.

5.3 Empirical Results To test the influence of the protective effect as well as the impact of the disclosure requirement on the patenting decision we estimate a probit model and calculate marginal effects evaluated at the sample means. The marginal effects of the interaction terms are calculated according to Cornelißen and Sonderhof (2009). Results are presented in Table 5.2.

128

5 Empirical Analysis of the Model with Horizontal Product Differentiation

According to our first Hypothesis 5.1, a decrease of market entry costs should result in a higher probability to patent, i.e. if a high threat of entry is perceived, the propensity to patent should increase. Recall that the interaction term of market entry costs with the easiness of substitutability, M EC ∗ RE reflects the market entry costs of competitors if the innovator patented and thus accounts for the impact of the disclosure requirement. To capture the entire effect of market entry costs—with and without patenting— we evaluate the sole effect and the effect combined with the easiness of substitutability. We find a negative marginal effect concerning the sole effect of market entry costs and a positive effect of the interaction term. As the latter effect is significantly higher than the sole effect, the overall effect of market entry costs is positive and is thus in line with Hypothesis 5.1. Hypothesis 5.2 derived from the theoretical model states that whenever the disclosure requirement has no impact, the propensity to patent rises with the number of firms operating in the market. As we find a non-significant effect of the number of firms, we are not able to confirm the hypothesis. Obviously, in the absence of easy substitutability an increase in the number of firms, i.e. a decrease in the critical threshold of patent intensity, has no impact on the patenting decision. This can be due to the fact that the lack of substitutability serves as a natural entry barrier perceived as sufficiently high protection thus making patenting obsolete. Hypothesis 5.3 regards the case in which the disclosure requirement has an impact which following our empirical implementation translates into the fact that substitutability is easy (RE = 1). According to the theoretical model, the disclosure effect affects the propensity to patent in two interdependent ways: (i) by affecting market entry costs and (ii) by thereby affecting the number of entering firms. At the same time the sole effect of disclosure has no impact on the patenting behavior (iii). We test this hypothesis looking at these three effects: (i) the interaction of easy substitutability with market entry costs to document the impact of the disclosure requirement on market entry costs, (ii) the interaction of easy substitutability with the number of firms in a market which reflects the effect of the disclosure requirement on the number of entering firms and finally (iii) the single effect of the disclosure requirement.4 As conjectured we find a positive effect of the interaction term MEC * rev. eng. showing that in the case of easy substitutability decreasing market entry costs increase the probability of patenting. The second interaction term firms * rev. eng. revealing the effect of the number of entering firms in the presence of easy substitutability turns out to be negative, which is in line with the proposed effect. Furthermore, as we proposed, the sole effect of easy substitutability is insignificant.

4 Note that the single effect of easy substitutability has to be interpreted as the disclosure effect when neither the dummy variable MEC nor the dummy variable large number of firms takes unit value.

5.3 Empirical Results

129

Table 5.2 Results of the Patenting Decision Estimation with Horizontally Differentiated Products Marginal Effect Standard Error reverse engineering

0.002

0.044

market entry costs

-0.142**

0.062

-0.056

0.058

MEC * rev. eng.

0.305***

0.106

firms * rev. eng.

-0.329**

0.143

log(employees)

0.112***

0.017

human capital

0.246**

0.109

R&D intensity

1.405***

0.303

capital intensity

-0.185

0.147

EU

0.070

0.049

non EU

0.082*

0.048

customer power

-0.059

0.044

cooperation

0.234***

0.044

east

-0.105**

0.043

large number of firms

industry dummies

included

Log likelihood McFadden’s adjusted

-372.83 R2

0.346

χ2 (all)

395.00***

χ2 (ind)

62.59***

Number of observations

831

*** (**, *) indicate significance of 1 % (5 %, 10 %) respectively. This table depicts marginal effects of a probit estimation regarding the determinants of the patenting decision. Marginal effects are calculated at the sample means and those of the interaction terms are obtained according to Cornelißen and Sonderhof (2009). Standard errors are calculated with the delta method. χ2 (all) displays a test on the joint significance of all variables. χ2 (ind) displays a test on the joint significance of the industry dummies. For a definition of the industry dummies refer to Table B.1.

130

5 Empirical Analysis of the Model with Horizontal Product Differentiation

As in Chapter 3 where we empirically investigated the patenting decision in vertically differentiated markets we find the same significant effects for firm size, R&D intensity, geographical markets EU and non-EU and east. Additionally, we confirm a significant positive impact of human capital, i.e. a higher share of highly qualified employees increases firms probability to apply for patents.

5.4 Concluding Remarks This chapter intended to empirically test the theoretical results and predictions obtained in Chapter 4 of this book. Several hypotheses summarizing the theoretical results concerning the propensity to patent with horizontally differentiated products thereby formed the basis of our empirical examination. From our theoretical analysis of the propensity to patent in a market with horizontally differentiated products we deduced three hypotheses. The respective empirical results are summarized in Table 5.3. The first, Hypothesis 5.1, concerns a basic mechanism of the preference circle model: if market entry costs decrease, more firms enter the market. To mitigate this effect, the innovator can patent as this forms an alternative barrier to entry. Thus the hypothesis states that the propensity to patent increases when market entry costs decrease. However, patenting has the drawback of mandatory disclosure which could in turn outweigh the positive protective effect. Our empirical estimation looks at the interdependency of both aspects as we consider the sole effect of market entry costs as well as the interaction of the impact of the disclosure requirement with market entry costs. We find an overall positive effect and can thus confirm the hypothesis. Table 5.3 Hypotheses tested for the Case with Horizontally Differentiated Products Hypothesis description

estimation result

5.1

the ptp increases when market entry costs decrease

confirmed

5.2

if the discl. req. has no impact, the ptp increases with the number of firms

not confirmed

5.3

if the discl. req. has an impact, the ptp confirmed decreases with the strength of the disclosure effect ptp = propensity to patent discl. req. = disclosure requirement

5.4 Concluding Remarks

131

The following hypotheses distinguish the case that the disclosure requirement has an impact, i.e. more firms are able to enter due to a patent, and the case that the disclosure requirement has no impact, i.e. patenting does not change the number of entering firms. If it has no impact, Hypothesis 5.2 suggests that the propensity to patent decreases with the number of firms operating in the market. This finding cannot be confirmed: possibly the lack of substitutability forms a barrier to entry sufficiently high to make patenting obsolete. If the disclosure requirement has an impact, Hypothesis 5.3 proposes that the probability to patent decreases with the strength of the disclosure effect. From the theoretical model we know that this effect is twofold as the disclosure effect influences market entry costs and thereby also affects the number of entering firms. The empirical estimation finds both effects significantly influencing the propensity to patent in the proposed manner: the interaction term of market entry costs and reverse engineering has a positive effect while the interaction term of the number of firms and reverse engineering has a negative effect. Overall, concerning the propensity to patent in markets with horizontally differentiated products, we find that patents can serve the innovator as an additional barrier to entry when the initial fixed costs of market entry decrease. Furthermore the empirical findings propose that the strength of the disclosure effect is in fact decisive for the innovator’s patenting decision.

Chapter 6

Summary and Discussion

The main focus of the present book was to investigate the driving forces behind the patenting decision of a successful inventor taking into account the effects of mandatory disclosure. To achieve this the effects of a patent were divided into two parts, a protective and a disclosure effect. By allowing for an immediate impact of the disclosure requirement we moved away from the common assumption that the disclosure requirement has an impact on the inventor’s profits only after a patent expires. Instead, we accounted for the fact that the disclosure requirement affects the patentee from the moment he decides to patent as he loses (part of) his technological lead immediately. Prior to the theoretical analysis we provided some insights on the development of modern patent systems and their major characteristics. Especially the disclosure requirement, research exemptions, a patent’s scope and the required inventive step were considered. Further, the economic literature concerning the propensity to patent was analyzed and classified according to the respective implementation (or lack of implementation) of the disclosure requirement. After a brief introduction to the new theoretical approach presented in this book and an overview of the empirical literature regarding the propensity to patent, we set off with the analysis of the decision to patent. Chapters 2 and 4 of the book covered the theoretical analysis of the decision to patent. To keep the analysis tractable, we separately considered cumulative innovations in a setting with vertically differentiated products (Chapter 2) and stand-alone innovations in a setting with horizontally differentiated products (Chapter 4). This distinction has several advantages. Introducing the decision to patent into a dynamic model of vertical product differentiation gives us the opportunity to take the time advantage of a successful inventor into account. We are able to investigate his strategic decision between relying on his headstart, i.e. keeping the invention secret, as a means to protect his intellectual property, or choosing to patent his invention, thereby losing his lead and (possibly) enforcing an advanced entry of his competitor. Moreover the analysis allowes us to introduce a spillover effect reflecting the unintended

133

134

6 Summary and Discussion

spillover of information in the case that an innovation is kept secret. Introducing the decision to patent into a model of horizontally differentiated products then provided the possibility to analyze a varying impact of the disclosure requirement: Contingent on the fact that the innovator patents, the fixed costs of market entry for his competitors decrease to a given extent. Depending on the initial market structure this decrease may induce more firms to enter the market, i.e. the disclosure requirement has an impact, or the number of firms operating in the market remains unchanged, i.e. the disclosure requirement has no impact. After comparing the alternative appropriation strategies patent or secrecy we introduced the additional strategy to patent and license an innovation in order to analyze possible changes to our findings regarding the propensity to patent. We concluded both theoretical chapters with a welfare analysis of the inventor’s patenting behavior. The central assumptions of the alternative approaches are summarized in Table 6.1. Table 6.1 Central Assumptions of the Theoretical Models Assumption

vertical differentiation horizontal differentiation

market structure

duopoly

oligopoly

technological lead

time advantage

higher market entry costs for competitors

spillover effect (secrecy)

0≤λ≤1

λ=0

disclosure requirement α = 0, temporary (patent) monopoly shortened patent scope

0 ≤ α ≤ 1, reduction of market entry costs

patent height, φ patent breadth, β restriction when to enter restriction where to enter

In general, both theoretical models suffer from an incomplete implementation of the restrictions concerning patent law. While—opposing most theoretical models—the impact of the disclosure requirement is properly accounted for, other characteristics of the patent system are disregarded, e.g. patenting costs, patent duration, timing of disclosure and patent grant or the required inventive step. Including patenting costs which increase over the duration of the patent would naturally turn secrecy into a more attractive appropriation mechanism compared to patenting, so that the propensity to patent should decrease. However, our general qualitative findings would not change, as we will briefly analyze in the following. Subject to the increasing patent renewal costs minor patents could have a shorter duration. This implicates that in the model setting with vertical differentiation where time plays a decisive role, the patent term could end before the competitor has accomplished to

6 Summary and Discussion

135

introduce a non-infringing follow-up innovation. Nevertheless, as the patentee would anticipate this, his strategic decision not to renew a patent will balance the effects of renewing the patent against the advanced market entry of a competitor in order to maximize his profits. According to European patent law a patent application is published 18 months after the priority filing, irrespective of the fact whether it has already been granted or not. Our theoretical approaches implicitly assume that the publication, i.e. the mandatory disclosure, takes place at the same time as the filing of the patent. In the setting with horizontal differentiation one could argument that this time gap between filing and disclosure is enclosed in the fixed costs of market entry, as its actual effect is that the headstart of the innovator increases. In the model with vertical differentiation the time advantage of the inventor is extended by the retarded disclosure, thus his initial headstart would rise resulting in a decreasing propensity to patent. The implementation of the necessary inventive step for an innovation to be applicable for patent protection would lead to a cutoff of our results for low values of the technological lead. Including this patentability requirement would lead to a critical threshold for the technological lead defining whether an innovation is patentable. As according to patent law minor technological advances are not patentable, all innovations embodying advances that lie below the critical threshold would be kept secret. A—non continuous—reversed u-shaped relationship between the technological lead and the overall patent effect would result: small advances are not patentable so secrecy prevails, intermediate advances are patentable and the innovator profits from patenting while large advantages are patentable but the innovator rather chooses secrecy due to the disclosure requirement. The introduction of the possibility to license the innovation in both settings is accomplished in a very simplified manner as we abstract away from alternative methods of licensing, i.e. auctioning or payment of a royalty per unit, by only including a fixed fee license. This is due to the fact that we do not attempt to provide a thorough analysis of the propensity to license but aim at gaining some insights on how the possibility to license influences the propensity to patent. Furthermore we assume that the innovator possesses the complete bargaining power so that his competitors face a take-it-or-leave-it offer. Relaxing this assumption would lead to a weakening of our results: as the innovator’s bargaining power decreases licensing would become less profitable as the share of profits he could collect from his licensees would decline. Finally, we should point out that our analysis completely disregards the stochastic nature of innovations and thus also disregards possible effects of parameter changes on the original incentive to invest in R&D. Without abstracting away from this fact the presented analysis would not have been tractable.

136

6 Summary and Discussion

Our main findings can be summarized as follows. The propensity to patent increases (i)

when reverse engineering becomes easier, i.e. the spillover parameter λ increases, and thus secrecy becomes a weaker appropriation mechanism,

(ii)

when the intensity of patent protection, patent height, φ, or patent breadth, β, increases,

(iii)

when licensing becomes an option,

and the propensity to patent decreases (iv)

when the impact of the disclosure requirement increases (α decreases) or

(v)

when the technological lead γ of the inventor increases.

From a welfare perspective these effects are reversed: On the one hand, the intensity of patent protection mitigates competition so that increasing the scope of a patent results in higher prices and (possibly) less diversification. On the other hand, the impact of mandatory disclosure influences social welfare positively, as it enhances the diffusion of knowledge and thus facilitates future inventions. Interestingly we find that the innovator’s patenting behavior is never welfare maximizing in the sense that for the parameter values where a patent would be welfare enhancing, the innovator chooses not to patent. If licensing is possible, the alternative to patent and license is the first best option from a welfare point of view if patent protection is very strong. Regarding the main focus of our theoretical analysis, i.e. the impact of the disclosure requirement on the decision to patent, we can conclude that the implications of mandatory disclosure of information are crucial for the patenting decision of a successful inventor. Furthermore we find that even if the disclosure requirement has no impact, not every invention (innovation) is patented. The reason behind this is that other barriers to entry, e.g. hard-toachieve reverse engineering or high market entry costs, may provide sufficient protection for the inventor. Both theoretical approaches were accompanied by an empirical investigation of the theoretical results. Using data from the Mannheim Innovation Panel (MIP) of the year 2005, we were able to test several hypotheses deduced

6 Summary and Discussion

137

from our theoretical results. The empirical analysis of the case with vertically differentiated products was undertaken with two estimations, one regarding the decision to patent and the other concerning the threat of entry, i.e. the timing of market entry of the competitor. By this the empirical investigation covered the decisive stages of the underlying game theoretic approach: On the first stage of the game the inventor decides whether to patent or not and on the second stage of the game firms strategically determine their timing of market entry. The empirical investigation of the case with horizontally differentiated products consisted of one estimation focussing on the probability to patent. Our central theoretical findings and the corresponding hypotheses are summarized in Table 6.2. Table 6.2 Summary of the Theoretical and Empirical Results Concerning the Decision to Patent techn. lead

spillover

pat. height

MEC

pat. breadth

discl. req.

γ↑

λ↑

φ↑

fs ↑

β crit ↑

α↓

ptp

–

+

+

–

–

–

Hyp.

3.1

3.2

3.4

5.1

5.2

5.3

(not conf.)

(conf.)

(conf.)

(conf.) (not conf.)

(conf.)

MEC = market entry costs ptp = propensity to patent Hyp. = Hypothesis conf. = confirmed

We find that our empirical results support the theoretical findings that two of the considered factors impose a positive influence on the propensity to patent. These are the extent of the spillover effect, λ, and one of the parameters describing the intensity of patent protection, patent height φ.1 An increase in this parameter strengthens the protective effect of a patent, ceteris paribus making the appropriation strategy patent more attractive. Hypothesis 3.4 refers to the fact that the intensity of patent protection in the case with vertical product differentiation has a negative impact on the threat of market entry. Consequently an increase of patent height ceteris paribus has a positive effect on the propensity to patent as by patenting the threat of

1

Note that the relationship between the spillover parameter λ and the propensity to patent is also referred to by Hypothesis 3.3 which could not be confirmed empirically. The reasoning behind this is that this hypothesis intended to lay out the mechanism behind Hypothesis 3.2 and does not refer to the direct relationship between the spillover effect and the probability to patent.

138

6 Summary and Discussion

market entry can be mitigated. Note that patent breadth empirically could only be taken into account in form of the critical threshold β crit which is decisive for the protective effect of a patent. A patent only has a protective effect which possibly outweighs the negative disclosure effect when patent breadth exceeds this critical threshold. Thus the propensity to patent should decrease as the parameter range in which a patent is protective decreases, i.e. β crit , increases. The parameters describing the headstart of the inventor should have a positive effect on the propensity to patent. An increase of the lead-time advantage γ or of the headstart embodied in market entry costs for competitors, fs , sustains the disclosure effect of a patent, ceteris paribus making patenting less attractive. Naturally, this is also the case for the impact of the disclosure requirement, α, which by definition imposes an increase of the disclosure effect. While we can confirm these relationships for market entry costs, fs , and the impact of the disclosure requirement, α, the effect of the lead-time advantage γ on the propensity to patent is not supported by our empirical findings. Thus our empirical investigation of the theoretical results comes to the conclusion that the hypothesis regarding the central result of the theoretical analysis with vertically differentiated products, Hypothesis 3.1, cannot be confirmed. Nevertheless our empirical results offer a quite interesting insight on how the result stated in Hypothesis 3.1—the higher the technological lead of the inventor, the lower is his propensity to patent—can be brought in line with economic intuition: what we can confirm empirically is the proposition of our theoretical model that an increase of the spillover effect yields a higher propensity to patent (Corollary 2.1, Hypothesis 3.2). Recall the underlying mechanism: an increase of the spillover effect reduces the technological lead of the innovator and by this the propensity to patent increases. This is exactly the same interrelationship between the technological lead and the propensity to patent which is proposed by Hypothesis 3.2. Thus our theoretical result concerning the impact of the technological lead on the propensity to patent is actually validated to some extent—namely the proposed negative interdependency only holds in the case that the spillover effect is high. Interpreting the spillover parameter as a measure reflecting the easiness of reverse engineering, we can conclude that there is a negative influence of the technological lead on the propensity to patent in markets where reverse engineering is easy-toachieve, i.e. spillover effects are high. One aspect which is not considered in the empirical investigation—due to the lack of adequate data—is the possibility to license a patented invention. Introducing the alternative to patent and license an invention substantially influences the propensity to patent. In the theoretical approach concerning vertical product differentiation we find that licensing increases the critical threshold decisive for the patenting decision and consequently the propensity to patent increases. In the case with horizontally differentiated products we

6 Summary and Discussion

139

find that the innovator will possibly choose to license and patent his innovation even if he formerly acts as a monopolist. Further, if he shares the market with competitors, he will patent and license whenever patent breadth is not too high. To summarize, it should be pointed out that licensing has a major impact on the propensity to patent and should always be taken into account when investigating this issue. Another central conclusion we draw is that the actual outcome of policy changes regarding the central parameters of a patent system is hardly possible to predict. Regarding our theoretical analysis we find that the parameters influencing the propensity to patent influence social welfare in a contrary way: On the one hand, while the protective effect increases the advantageousness of a patent in the eyes of the inventor, it diminishes social welfare by mitigating competition between firms. On the other hand, the impact of the disclosure effect, which has a detrimental effect on patenting for an innovative firm, enhances social welfare by imposing knowledge diffusion. Our welfare analysis allows for only few general conclusions. For both modeling approaches we find that licensing can be welfare enhancing. This is due to the fact that the positive effect that patenting has on social welfare, i.e. the diffusion of knowledge due to mandatory disclosure, is effective while the negative effect of constraining competition, i.e. the protective effect, is neutralized. Additionally our welfare analysis allows us to conclude that extending the scope of patent protection has a negative effect on social welfare. Overall we find that the patenting behavior of the inventor is rarely welfare maximizing. In the case with horizontal differentiation the appropriation strategies secrecy or license are welfare maximizing so that whenever the innovator solely patents without selling licenses to competing firms, social welfare is reduced. Thus policy attempts should yield at improving the incentives to license. Speaking in terms of the theoretical model this would implicate that patent breadth should be moderate (see Proposition 4.6). In the case with vertical differentiation we even find that the patenting behavior of the inventor always leads to a suboptimal choice concerning social welfare. Nevertheless, introducing licensing may have a welfare enhancing effect and as a patentee always has the incentive to sell a license to his competitor, the promotion of licensing is a possible alley for policy attempts. However, concluding we can state that policy attempts which attempt to improve the patent system to enhance social welfare should be undertaken with great care, as they could possibly lead to an unintended decline of patent applications. We will illustrate this issue referring to the legal differences regarding the implementation of a statutory research exemption.2

2

See Section 1.1.2 for a definition of research exemptions.

140

6 Summary and Discussion

A research exemption to patent protection allows firms to use patented information for research purposes without infringing the rights of the patentee. While in Europe such an exemption is part of statutory patent law, in some countries, i.e. the U.S. and Australia, such confinements of a patentee’s rights do not exist. Yet it is vividly argumented for and against the introduction of research exemptions (Australian Government (2009), Hagelin (2005)). The results obtained in the preceding analyzes provide some insights on this issue and can contribute to the discussion. First of all recall that one of the main arguments justifying the existence of a patent system is that it promotes the diffusion of knowledge. De facto the absence of a research exemption undermines this justification, as the prohibition to use the information disclosed in a patent application inhibits the dissemination of information thereby decelerating technological progress. The consequence is a so-called look-but-don’t-touch rule (Hagelin (2005)) which results in a random impact of the disclosure requirement: if the information embodied in a patent application is susceptible of purely mental manipulation, the use of the patented information to develop a non-infringing substitute product is an act which does not infringe the patent. If the information contained in the patent application can only be fully understood through physical manipulation, the use of the patented information to develop a non-infringing substitute product is an infringement of the patentee’s rights (Hagelin (2005), pp. 14). Obviously the latter case is equivalent to an expansion of the patent’s duration: as competitors will only be allowed to actually use patented knowledge after a patent expires, their date of entry with a substitute product is postponed into the future.3 Speaking in terms of our theoretical investigation in the absence of a research exemption the disclosure requirement has an insignificant effect.4 Thus the situation is that “[...] the patent owner could stop a researcher’s activities if the researcher created a copy of the invention on his own and experimented with that copy. [...] [T]his right of the patent owner runs directly contrary to the avowed purpose of the patent law: the encouragement of the useful arts and science” (Bruzzone (1993), pp. 53). The introduction of a statutory research exemption would result in an increasing impact of the disclosure effect. As our analysis shows, this will (possibly) lead to a decreasing propensity to patent. Let us take a closer look at the implications of such a policy change. In the model with vertically differentiated products the inventor will always patent in the absence of a disclosure effect. The enforcement of a research exemption would lead to an increasing impact of the disclosure requirement 3

The discussion of research exemptions in the U.S. mainly concerns the pharmaceutical industry where a research exemption would allow producers of generic drugs to go through mandatory admission procedures or clinical trials before the patent term ends, enforcing their immediate market entry after the patent on the branded drug expires. 4 In theoretical terms this translates into the condition that α = 0 and/or α > αN .

6 Summary and Discussion

141

so that the propensity to patent decreases as now the patenting decision is contingent on the tradeoff between the protective and the disclosure effect. Concerning the impact of the policy change on social welfare we have to distinguish two cases: (i) patent height is high so that secrecy is welfare maximizing and (ii) patent height is low so that a patent is welfare maximizing.5 Recall that in the latter case the inventor never patents. In Case (i) the implementation of a research exemption would be welfare enhancing as the increasing impact of the disclosure effect would lead to a diminishing propensity to patent—the welfare maximizing strategy secrecy would thus be chosen more frequently. In Case (ii) the policy change would have no effect on social welfare: As the inventor even refrains from patenting in the absence of an experimental use exemption for very low values of patent height, the introduction of a research exemption—which makes patenting even less attractive—would further strengthen the advantageousness of the appropriation strategy “secrecy”. These findings weakly support the arguments for the implementation of a research exemption, though it might be that the policy change has no effect at all. Let us proceed with the case of horizontally differentiated products. For this model setting we found that in the absence of a research exemption (a) secrecy will prevail whenever patent breadth is small and (b) patenting will prevail whenever patent breadth is high.6 Recall that secrecy and licensing are the welfare maximizing appropriation strategies. Consequently, the implementation of a research exemption inducing a rising impact of the disclosure requirement in Case (a) leads to a positive effect on social welfare as the impact of mandatory disclosure ceteris paribus increases the propensity to keep an innovation secret. In Case (b) a research exemption would likewise enhance social welfare as the propensity to patent is ceteris paribus reduced.7 These findings support the arguments for the introduction of a research exemption. Overall we come to the conclusion that the statutory implementation of a research exemption could be ineffective or could have positive welfare effects regarding cumulative innovations, while it would have a welfare enhancing effect for imitative innovations. This illustration of the complexity of the effects of a policy change support our initial statement that a prediction of the overall effects of a policy 5

The actual condition for patent height is (i) φ ≥ φWF and (ii) φ < φWF , see Equation (2.30). 6 The actual critical conditions for patent breadth can be found in Proposition 4.1. 7 Technically speaking for Case (a) we move from Proposition 4.1 (i) always secrecy and 4.1 (ii) partly secrecy to Proposition 4.2 (i) and 4.2 (ii) with β below the critical threshold so that secrecy always prevails. Thus the propensity to choose secrecy rises. In Case (b) we move from Proposition 4.1 (iii) always patent to Proposition 4.2 (i) always secrecy and 4.2 (ii) with β above the critical threshold so that a patent always prevails. Thus the propensity to patent rises.

142

6 Summary and Discussion

change or the deduction of policy implications from our theoretical investigation should be undertaken with great care. In the end we identified the driving forces behind the propensity to patent as those factors influencing the contrary effects of patenting, the protective effect and the disclosure effect. Although our welfare analysis is naturally only rudimental due to the partial analyzes we conducted, we can nevertheless conclude that the welfare effects of a patent system are not consistently positive.

Appendix A

Proofs of Propositions, Lemmata and Corollaries in Chapter 2

Proof of Lemma 2.1: Using t = ql , the intersection point for the non-inventor can be derived by equating his alternative profits, Fj (qjI ) = Lj (qjI ). Rearranging terms yields qjI =

e−rγ Ah − Al . erAm (e−rγ − e−1 )

(A.1)

Analogously the intersection point for the inventor can be derived as qiI =

Ah − e−rγ Al . erAm (1 − e−1−rγ )

(A.2)

  Clearly qiI γ=0 = qjI γ=0 . As obviously ∂qiI /∂γ < 0 it would be true that qiI < qjI for γ > 0 if ∂qjI /∂γ > 0 holds. Then, if both firms follow the strategy adopt first (σu2 = ql , u = i, j) the non-inventor reaches his intersection point first and thus always loses the preemption race. To determine the sign of ∂qjI /∂γ > 0, we need to take a closer look. Carrying out the differentiation we get ∂qjI Ah − eAl = −rγ . ∂γ e Am (e − erγ )2

(A.3)

This derivative is positive as long as Ah − eAl > 0 holds. Resubstituting Ah = (2b − a)2 /9 and Al = (b − 2a)2 /9 and setting a/b = c we get (c − 2)2 − e(1 − 2c)2 > 0. This function is positive for c ∈ ] − 0.1529, 0.8490 [. Consequently the derivative ∂qjI /∂γ is always positive as due to the assumption b > 2a > 0 the domain of c is c ∈ ]0, 0.5[. 

143

144

A Appendix to Chapter 2

Proof of Lemma 2.2: From Lemma 2.1 we know that Lu and Fu , u = i, j have exactly one intersection point. First suppose that two situations are possible for both firms: (a) quI < qu∗ and (b) quI ≥ qu∗ , u = i, j. In situation (a) the dominant strategy for firm u is adopt first (σu2 = ql ) since, as ∂Fu /∂q < 0 and ∂Lu /∂q > 0 ∀ q < qu∗ , it is always true that Lu (q) > Fu (q) ∀ q > quI . In situation (b) the dominant strategy for u is wait (σu2 = qh ) since, as both curves have only one intersection point, quI , and limq→0 Fu (q) = ∞, it is always true ∗ that Fu (q) > Lu (q) ∀ q < quI . By inserting qjI and qh, j from equations (A.1) and (2.14) into inequality (a) we get a critical condition for the non-inventor’s adoption decision,   Ah 1 ≡ γˆ . (A.4) γ < ln e − r Am If and only if γˆ > 0 both strategies, adopt first and wait, exist for the noninventor. Rearranging γˆ > 0 yields a critical condition for consumer diversity1 3√ a >2− e−1. b 2

(A.5)

Whenever γ < γˆ the non-inventor’s dominant strategy is adopt first since qjI < ql,∗ j holds. For γ ≥ γˆ the intersection point is to the right of the profit maximizing quality ql,∗ j and thus the non-inventor’s dominant strategy is wait. The case is different for the inventor: Inserting qiI and ql,∗ i from equations (A.2) and (2.13) into inequality (a) and rearranging terms yields the critical condition γ > ln[e − 49 (2 − ab )2 ]/(−r). Due to condition (A.5), the right hand side of this inequality is always negative so that inequality (a) is fulfilled for all γ ≥ 0. Consequently the inventor’s dominant strategy always is adopt first. 

Proof of Lemma 2.3: We get tcrit by solving Fj (tcrit ) = Lj (t∗l, j ) as tcrit =

1 r

    Al Am 1 − ln . (e − eγr ) + Ah Am (1 − e1−γr )

(A.6)

Our aim is to prove that a critical γˆ ˆ exists for which tcrit ≤ t∗l, i ∀ γ ≤ γˆˆ crit ∗ and t > tl, i ∀ γ > γˆ ˆ holds. If a function Ω = tcrit − t∗l, i is monotonically

1

Note that this condition corresponds to the preemption-condition for symmetric firms as stated by Dutta et al (1995).

A Appendix to Chapter 2

145

increasing in γ and has negative (positive) values for low (high) γ’s then one critical γ for which Ω = 0 must exist. Solving ∂Ω/∂γ > 0 for c yields c>

 1/2 1 1 (e − eγr )(−1 + e1+γr )2 − . 2 3 e(1 + e2 + e2γr − 4e1+γr + e2+2γr )

(A.7)

By numerical simulations we can show that this condition is always met whenever the market coverage condition for a preemption equilibrium with ql = ql,∗ j −  as stated in Footnote 8 is fulfilled. This leaves us to analyze the functional values for a high (low) γ. As we analyze the situation where the non-inventor chooses the strategy wait (σj2 = qh ) we consider the region γ ≥ γˆ . Then Ω(ˆ γ ) must be the minimum of the function Ω. Inserting γ = γˆ we get Ω(ˆ γ) =

Al e(A2h − 2Ah Am e + A2m (e2 − 1)) . Ah Am (Am + Ah e − Am e2 )r

(A.8)

The denominator of this function is negative for −0.3 < c < 4.3, its nominator is positive for 0.03 < c < 3.97. As the considered domain for consumer diversity is c ∈ [0.2384, 0.5 [ (see Footnotes 5, 7 and 8), the function indeed is negative for a low value of γ, Ω(ˆ γ ) < 0. This leaves us to show that Ω(γ) > 0 for some γ > γˆ . As we assumed that γ < 1/r let us check the arbitrarily chosen functional value of γ = 3/(4r). We get  Ω

3 4r

 =−

  4(1 − 2c)2 (e5/2 − e) 1 9(e − e3/4 ) ln − . 4(c − 2)2 9r(e3/4 − e − e5/2 + e11/4 ) r

This expression is positive for all c ≥ 0.24 which completes our proof.

(A.9) 

Proof of Proposition 2.1: (i) preemption equilibrium—From Lemmata 2.1 and 2.2 we know that if γ < γˆ both firms engage in a race for being the first and that the inventor will always win this preemption race. Thus in equilibrium the inventor markets the quality ql = qjI whereas the non-inventor optimally differentiates as stated in Equation (2.10) and adopts the quality qh = qjI + 1/r. (ii) maturation equilibrium—From Lemma 2.2 we know that in the case γ ≥ γˆ the non-inventor waits to be the second adopter. In this case the inventor is able to reach his profit maximizing quality level ql = ql,∗ i and the non-inventor optimally differentiates by choosing qh = ql,∗ i + 1/r. 

146

A Appendix to Chapter 2

Proof of Proposition 2.2: As a patent protects a certain quality range it enables the inventor to choose a higher quality level than with secrecy, φ > qiS . As ∂Li /∂q > 0 ∀ q < ql,∗ i , the inventor will always profit from this protective effect of a patent. With a weakly protective patent, φ < ql,∗ i , the inventor will adopt the quality that corresponds to the height of the patent qiP = φ. With a strongly protective, ∗ P ∗ φ ≥ ql,∗ i , or delaying, φ > qh, j , patent he will adopt the quality qi = ql, i since this maximizes his profits. The non-inventor maximizes his profits by optimally differentiating. This is possible for weakly and strongly protective patents. If the protectional degree of a patent is very high (delaying patent) the entry of the non-inventor is postponed into the future. As ∂Fj (q)/∂q < 0 he will enter as soon as he can reach a quality level that lies outside the protected range, qjP = φ + .  Proof of Proposition 2.3:2 If the patent effect ΔP is monotonically decreasing in γ and takes positive as well as negative values, then there must exist exactly one critical value γ˘ which is decisive for the  inventor’s patenting  decision.  First note that ΔP γ=0 > 0 since Li (qiP )γ=0 > Li (qiS )γ=0 due to qiP > qiS and ∂Li (·)/∂q > 0 ∀ q < ql,∗ i . We thus know that the patent effect, ΔP , can  take positive values. Next let us look at dLi (qiS )γ>0 /dγ > 0. Differentiating we get    dLi (·)γ>0 ∂Li (·)γ>0 ∂Li (·)γ>0 ∂q S i = + . (A.10) dγ ∂γ ∂γ ∂qiS It is easy to show that the first term on the right hand side of (A.10) is greater than zero. The same is true for the second term since ∂Li (·)γ>0 /∂qiS ∀ qiS < ql,∗ i and ∂qiS /∂γ > 0 ∀ qiS = qjI (see the proof of Lemma 2.1). Then the  total differential dLi γ>0 /dγ is positive and consequently the patent effect is  monotonically decreasing in γ as ∂Li (qiP )γ=0 /∂γ = 0. This leaves us to show that ΔP can take negative values. For γ = γˆˆ a maturation equilibrium will result with qiS = ql,∗ i (see Proposition 2.1). In this case a patent is needless for the inventor, as he is able to reach his profit maximizing quality with secrecy. Thus the patent effect should be negative. To begin with, presume a strongly protective patent. Then   (A.11) lim ΔP = Li (ql,∗ i )γ=0 − Li (ql,∗ i )γ=γˆˆ < 0 ˆ γ→γ ˆ

For expository reasons we carry out parts of this proof for qiS = qjI . Following equal ∗ − . arguments all the same can be shown for qiS = ql, j

2

A Appendix to Chapter 2

147

 since we know from (A.10) that dLi (·)γ>0 /dγ > 0 as long as ∂qiS /∂γ > 0 which is the case for qiS = ql,∗ i . This is all the same true if patent height decreases, ql,∗ i > φ = qiP , as this leads to a decrease of the first term on the  right hand side of Equation (A.11) due to ∂Li (qiP )γ=0 /∂φ > 0. By this we know that the patent effect, ΔP , can take positive as well as negative values. Thus, due to the fact that ΔP is monotonically decreasing in γ there must  exist one single critical value γ˘ .

Proof of Corollary 2.2: (i) protective patents—With weakly protective patents the inventor will adopt the quality that corresponds to the height of the patent qiP = φ since this maximizes his profits. From Equation (2.17) it is easy to derive ∂ΔP /∂φφ 0. Consequently an increase of patent height increases the l, i

propensity to patent. For strongly protective patents the propensity to patent remains unchanged by a further increase of patent height, since  the inventor will always choose qiP = ql,∗ i for all φ ≥ ql,∗ i so that ∂ΔP /∂φφ> q∗ = 0. l, i

(ii) delaying patents—In this case a patent delays the adoption date of the ∗ non-inventor due to φ > qh, j . Then the adoption date of the non-inventor is P qj = φ +  while the inventor’s adoption date is not influenced by an increase of patent height beyond ql,∗ i . From Equation (2.17) we can derive ∂ΔP /∂qjP > 0. Consequently the inventor’s propensity to patent rises if patent height ∗  increases beyond qh, j. Proof of Lemma 2.6: If secrecy prevails the non-inventor realizes s

Fjs (qis , qjs ) = e−1−r(qi +γ)

πh . r

If the inventor patented and offered a license the non-inventor could realize ∗

∗ −1−rql, i Fjl (ql,∗ i , qh, j) = e

πh . r

∗ Comparing the alternative profits we find that Fjs (qis , qjs ) > Fjl (ql,∗ i , qh, j) ∗ s ∗ whenever ql, i −qi > γ. From the Proof of Lemma 2.3 we know that ql, i −qis = γ − Γ with Γ ≡ ln[e − 49 (2 − ab )2 ]/(−r). Due to condition (A.5) Γ is always negative so that ql,∗ i − qis > γ and consequently the non-inventor has no ∗ incentive to buy a license, Fjs (qis , qjs ) > Fjl (ql,∗ i , qh,  j ).

148

A Appendix to Chapter 2

Proof of Proposition 2.6: (i)

(ii)

weakly and strongly protective patents—It is easy to show that ql,∗ i > φWF holds. Consequently for a strongly protective patent the patent effect on social welfare is negative, ΔWF P, strong < 0. This leaves us to check whether the inventor will actually choose to patent if patent height fulfills the critical condition. Assuming that patent protection is weak so we have qiP = φ it must be that the overall patent effect ΔP (see Equation (2.17)) for a patent of height φ = φWF is positive to assure that patenting occurs for patent heights where it is welfare enhancing. Inserting qiP = φWF and qis = qjI into Equation (2.17), we find that ΔP (φWF ) < 0 for all values of γ. This means that if patent height is low enough for a patent to be welfare enhancing, the protective effect of the patent is too small to outweigh the disclosure effect and consequently the inventor refrains from patenting. P s delaying patents—As ΔWF P, strong < 0 we know that WFstrong < WF . P P From Lemma 2.7 we can deduce that WFdelay < WFstrong so it must s be that WFP  delay < WF .

Proof of Proposition 2.7: According to our analysis in Section 2.6.3, social welfare with licensing corresponds to social welfare with a strongly protective patent. Compared to the alternative secrecy, licensing is thus never welfare enhancing, WFl < WFs . But since social welfare increases as the intensity of patent protection deP creases we have WFP delay < WFstrong , meaning that licensing is welfare enl hancing whenever patent protection is very strong, WFP  delay < WF .

Appendix B

Definition of Industry Dummies

Table B.1 Definition of Industry Dummies ind NACE code

description

1

1, 15, 17, 18, 19

agriculture, food, textile, leather

2

10, 14, 23, 40, 41

mining, coke, fuel, electricity

3

20, 21, 36, 37, 90

wood, paper, publishing, printing, furniture, recycling, sewage

4

24, 25, 26

chemicals and pharmaceuticals, plastics, non-metallic mineral products, glass

5

27, 28

metals

6

29, 34, 350, 351, 352, 354, 355 machinery, motor vehicles without aerospace

7

30, 31, 32

office machinery, electrical machinery, radio television communication

8

33, 353

medical, precision and optical instruments, aerospace

9

64, 72

telecommunication, post and communication, computer services

10

73

research & development

11

74

business activities

Industry category 11 is the reference category and is not included in regressions.

149

Appendix C

Proofs of Propositions and Lemmata in Chapter 4

Table C.1 Critical Thresholds of Market Entry Costs for N ∈ [1, 6] N

p πi, Np

1

4v 3



v 3

fs, N s fs >

1 8

fp, N p fP >

1 8

2

1 8

1 8

1 8

3

β(4−2β−β 2 )2 32(3−2β)2

1 27

β(4−β)2 (2−β)(1−β) 32(3−2β)2

4

β 32

1 64

(1−β) 32

5

β(20+14β+11β 2 )2 2×64 (3+2β)2

1 125

(1−β)(8+4β−3β 2 )2 2×63 (3+2β)2

6

β(2+3β+3β 2 )2 8(7+9β)2

1 216

(1−β)(3+2β−3β 2 )2 16(7+9β)2

Proof of Lemma 4.1: ˆk, k+1 < 0 Consumer migration takes place whenever xˆk, k+1 < 0. Solving x 2  p p as critical condition for consumer for Δpp ≡ pk − pk+1 we get Δpp > 1−β n−1 migration. Obviously the critical threshold on the right hand side decreases 151

152

C Appendix to Chapter 4

with the number of firms entering, n, and with the breadth of the patent, β. Inserting the equilibrium prices for any number of firms N > 3 and solving for β, the critical condition for asymmetric prices translates into a critical threshcme old of patent breadth. We find that consumers migrate whenever β > βN . Proof of Lemma 4.2: First let us show that firm k’s demand is smallest for high ppk and low ppk+1 . ˆk, i + xˆk, k+1 . From equations (4.8) and (4.10) we get x ˆk, i We have Dkp = x and x ˆk, k+1 . Now, inserting the price reaction functions ppi from Equation (4.13) and ppk+1 from Equation (4.15) and assuming that due to its negligible impact on k’s pricing decision, ppk+2 can be treated as a constant, we have ∂Dkp /∂ppk < 0. To analyze the influence of firm k + 1’ s pricing decision we substitute ppi and ppk (see Equation (4.14)) in Dkp and get ∂Dkp /∂ppk+1 > 0. Thus we have that Dkp reaches its lowest values for high ppk and low ppk+1 . Next we need to show that in the case that ppk+1 reaches its minimum and ppk reaches its maximum firm k’ s demand is still positive. This corresponds to the cases where ppk+1 = 0 and ppk = ppk, 4 as ∂ppk, N /∂N < 0. Inserting n = 3, ppk+1 = 0, ppk, 4 = (1 − β)β/4 and ppi, 4 = β/8 and solving Dkp > 0 for β we get √ the critical condition β > 1/4(−3 + 17) ≈ 0.27. Since the patent needs to be restrictive to have an impact, for n = 3 it must be that β > 1/2 so that  the critical condition for β is always fulfilled.

Proof of Lemma 4.3: Differentiating the patentee’s profit function πi,p 3 = ppi, 3 Di,p 3 we have ∂ppi, 3 p ∂Di,p 3 ∂πi,p 3 = ppi, 3 + D . ∂β ∂β ∂β i, 3

(C.1)

Differentiating the patentee’s demand, Di,p 3 , see Equation (4.9) with respect to β using p ∂ppi, 3 1 ∂pk, 3 β = + (C.2) ∂β 2 ∂β 4 and inserting ppk, 3 from Equation (4.20), simplifying yields 1 − 3β + β 2 ∂Dp = ∂β 2(3 − 2β) which is negative for any restrictive patent, as then 2/3 < β < 1 holds. Thus the patentee’s demand decreases with patent breadth.

C Appendix to Chapter 4

153

Now let us turn to the patentee’s price choice. Obviously the derivative of his optimal price, see Equation (C.2), with respect to β is positive whenever ∂ppk, 3 ∂β

β >− . 2

It is easy to show that for 2/3 < β < 1 the derivative ∂ppk, 3 /∂β (from Equation (4.20)) fulfills this condition whenever β < β o with β o ≡ (−3 + √ 105)/8. Thus, as patent breadth rises the patentee will increase his price until the critical threshold β o is reached. After this point a further increase will lead to a price reduction as the negative influence of the decreasing prices  of the border firms, ∂ppk, 3 /∂β, becomes dominant.1 Proof of Proposition 4.1: (i)

¯ the profit funcDue to model assumptions we have that for β ≤ 2/N tions in the respective cases patent or secrecy coincide, πi,p N¯ = πi,s N¯ , in which case the innovator prefers secrecy.

(ii)

Further it can be shown for all πi,p N p with N p > 3 that ∂πi,p N p /∂β > 0. Since πi,s N s is independent of β, it must then be that πi,p N¯ > ¯ . For N p = 3 solving π p − π s > 0 for β yields πi,s N¯ ∀ β > 2/N i, 3 i, 3 β > 0.915.

(iii)

is always fulfilled As obviously πi,s N¯ > πi,s N¯ +1 , then πi,p N¯ > πi,s N+1 ¯  and the innovator prefers to patent.

Proof of Proposition 4.2: (i)

In the cases N s < 3 the profits of the innovator are the same with secrecy and with a patent, see equations (4.4) and (4.6). It is easy to show that πi, 1 > πi, 2 holds within the domain of v (see Footnote 5). Thus if πi, 2 > πi,p N p holds for N p > 2, it is never profitable to patent for N s < 3. Obviously πi, 2 > πi,p 3 for all β. This leaves us to show that πi,p 3 > πi,p N p with N p > 3. Using pp and Dp from equations (4.6) and (4.9) it is easy to show that ∂πi,p N p /∂ppk < 0 generally holds. Knowing that ∂ppk /∂N p < 0 we can conclude that ∂πip /∂N p < 0. Consequently

1 Note that a dominant price effect only occurs in the case N p = 3 as then prices under a restrictive patent are higher than in all cases N p > 3. Consequently, as in the limit for β → 1 all prices tend to zero, the downward slope of the price function ∂ppk, N p /∂β is highest for N p = 3 so that the patentee’s neighbors are affected relatively stronger than in the cases N p > 3.

154

C Appendix to Chapter 4

πi,p 3 > πi,p N p must hold so that a patent is never profitable for N s < 3. For N s = 3 we need to show that πi,s 3 > πi,p N p for N p > 3. In the limit β → ∞ all patent profits tend to 1/32. We know that ∂πi,p N p /∂β > 0 with N p > 3 so that 1/32 is the maximum value patent profits can reach. Since πi,s 3 > 1/32 the innovator will always prefer secrecy. (ii)

In the limit β → 0 all patent profits tend to zero and for β → ∞ all patent profits tend to 1/32. As ∂πi,p N p /∂β > 0 ∀ N p > 3 and πi, N s < 1/32 for N s > 4 all patent and secrecy profit functions must have exactly one intersection point whenever N p < N s and N p, s > 3.  We get βˆN s , N p by solving πi,s N s = πi,p N p for β.

Proof of Proposition 4.3:  Solving πi,p np N p →∞ > πi,s N s with πis = 1/(N s )3 (see Equation (4.4)) for √ β yields the critical threshold β > 2 3 4/N s . Note that the right hand side is greater than unity whenever N s ≤ 3. Since β ∈ ]0, 1[, the inequality can  never be fulfilled for N s ≤ 3 and thus the innovator chooses secrecy.

Proof of Proposition 4.5: The innovator will choose to license whenever πi,L N L > πi,s N s . Inserting πi,L N L (Equation (4.27)) and πi,s N s (Equation (4.4)) it is easy algebra to show that a license is always profitable for the innovator if he sells a number of licenses that corresponds to the number of firms operating in the market with secrecy, nL = N s − 1. 

Proof of Proposition 4.6: (i)

We know from Proposition 4.2 that ∂πi,p N p /∂N p < 0. Consequently, if πi,L 5 > πi,p N p holds for N p = 3 it must also hold for N p > 3. Inserting πi,p 3 from Equation (4.21) it is easy to show that πi,L 5 > πi,p 3 is always fulfilled if β < 1.31.

(ii)

From Lemma 4.4 we know that we have N L = N p so it suffices to look at N L ≥ 6. For the case N p ≥ 6 we have limβ→∞ πi,p N p = 1/32 and limβ→0 πi,p N p = 0. It is easy to show that πi,L 6 < 1/32 and due

C Appendix to Chapter 4

155

to ∂πi,L N L /∂N L < 0 the same must hold for N L > 6. As additionally ∂πi,p N p /∂β > 0 and ∂πi,L N L /∂β = 0 there must exist exactly one intersection point of πi,p N p and πi,L N L for every N p = N L with N L ≥ 6 crit and N p ≥ 6. Consequently we have πi,L N¯ > πi,p N¯ ∀ β < βN  ¯ .

Proof of Proposition 4.7: Solving WFs3 − WFp3 > 0 (see equations (4.28) and (4.31)) for v we get 2 +21924β 3 −13392β 4 +3357β 5 v > v crit ≡ −1152+8880β−19520β . It is easy to show 1728β(−3+2β)2 crit = 0.121 at β = 0.578. As the domain of that v crit has a local maximum vmax the reservation price by assumption is 5/16 ≤ v < 3/4 the reservation price always exceeds the maximum of the critical threshold so that social welfare in the case N p = 3 is greater with secrecy than with a patent. 

Proof of Proposition 4.8: We only consider restrictive patents so that β > 2/N . (ia)

For N s = 1 social welfare amounts to WFM . Comparing WFM to WFpN p with N p > 1 it is easy to show that for ∗ ∗ ∗

(ib)

For N s = 2 social welfare amounts to WFs2 . Comparing WFs2 to WFpN p with N p = 3 it is easy to show that WFs2 > WFp3 . For N p > 3 WFpN p > WFs2 holds if ∗ ∗ ∗ ∗

(ic)

N p = 2 patenting yields a higher social welfare N p = 3 secrecy yields a higher social welfare N p ≥ 4 patenting yields a higher social welfare.

Np Np Np Np

= 4 ∧ β < 0.853 = 5 ∧ β < 0.660 = 6 ∧ β < 0.834 → ∞ ∧ β < 0.830

For N s = 3 social welfare amounts to WFs3 . Comparing WFs3 to WFpN p with N p > 3 it is easy to show that WFpN p > WFs3 holds if ∗ ∗ ∗ ∗

Np Np Np Np

= 4 ∧ β < 0.680 = 5 ∀ β > 2/5 = 6 ∧ β < 0.645 → ∞ ∧ β < 0.632

156

C Appendix to Chapter 4

(ii)

For N s > 3 social welfare amounts to WFsN s . Comparing WFs3 to WFpN p with N p > 4 it is easy to show that WFpN p > WFsN s holds in the following cases: (a)

(b)

(c)

Ns • • • Ns • • Ns •

=4 N p = 5: WFp5 < WFs4 ∀ β N p = 6: ∧ β < β˜4, 6 = 0.538 N p → ∞ ∧ β < β˜4, ∞ = 0.523 =5 N p = 6: ∧ β < β˜5, 6 = 0.456 N p → ∞ ∧ β < β˜5, ∞ = 0.450 =6 N p → ∞ ∧ β < β˜6, ∞ = 0.399

From Proposition 4.2 we know that the innovator will patent whenever β > βˆN s , N p . For the relevant cases the innovator will patent if (a)

(b)

(c)

Ns • • Ns • • Ns •

=4 N p = 6, β > βˆ4, 6 = 0.707 N p → ∞, β > βˆ4, ∞ = 0.794 =5 N p = 6, β > βˆ5, 6 = 0.480 N p → ∞, β > βˆ5, ∞ = 0.635 =6 N p → ∞, β > βˆ6, ∞ = 0.530

Obviously we have β˜N p < βˆN s , N p in all considered cases, so that the innovator will never choose to patent in the domain of β where a  patent would be welfare enhancing.

Proof of Proposition 4.9: From Equation (4.28) we know that WFs = 12−1 N 2 + v. Let us distinguish the cases (i) initially secrecy prevails and (ii) initially a patent prevails. We set off with Case (i). Whenever the disclosure requirement has no impact so that N s = N L licensing has no effect on economic welfare. If the disclosure requirement has an impact, N s < N L , using WFL = WFs we get ∂WFL /∂N > 0 meaning that licensing is welfare enhancing whenever the number of firms operating in the market increases. Now let us turn to Case (ii). Necessarily we have N L = N p . Due to the fact that licensees can freely locate on the circle the protective effect of a patent diminishes due to licensing. Comparing WFp (N p ) with WFL (N p ) we

C Appendix to Chapter 4

157

find (see Proposition 4.7) that licensing is the dominant strategy from a welfare perspective. 

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