THREE ESSAYS ON THE ECONOMICS OF AGRICULTURAL BIOTECHNOLOGY

DISSERTATION

Presented in Partial Fulfillment of the Requirements for

the Degree Doctor of Philosophy in the Graduate

School of The Ohio State University

By

Denis A. Nadolnyak, M.A.

* * * * *

The Ohio State University 2003

Dissertation Committee: Approved by Professor Ian M. Sheldon, Adviser

Professor Mario J. Miranda ______Adviser Professor Barry K. Goodwin Department of AEDE

ABSTRACT

This dissertation consists of three essays on the economics of agricultural biotechnology.

In the first essay, A Model of Diffusion of Genetically Modified Crop Technology in

Concentrated Agricultural Processing Markets - The Case of Soybeans, a dynamic model

of diffusion of a genetically modified (GM) crop technology is developed and simulated

using the U.S. soybean market data. The model accounts for factors specific to

agricultural markets, such as oligopsony power of crop processors, grower

characteristics, and identity preservation requirements. Simulation results show how

these factors affect the magnitude and distribution of the potential gains from adopting genetically modified crops. In particular, market power of crop processors decreases the equilibrium adoption levels and prolongs the diffusion period. Producer uncertainty and perception of the risks associated with planting GM crops increases equilibrium adoption levels but lengthens the diffusion period, thus making the welfare implications of such a situation ambiguous. Producer heterogeneity with respect to new crop profitability has different effects on the dynamics of the diffusion process, depending on the average profitability and other distribution parameters. The general conclusion is that, if GM crops are safe for human consumption and do not harm the environment, market power of the processors diminishes total surplus generated by the GM innovation.

ii The second essay is called Valuation of International Patent Rights for

Agricultural Biotechnology. In it, the choices that biotechnology companies make about

marketing different genetically modified (GM) crops in different countries with highly

uncertain returns are modeled as a real option problem of the entry decision solved at a

micro-level by individual firms. The model is aggregated in order to reflect the

heterogeneity of different genetic events, as well as different markets, in terms of their

(potential) profitability. The solution to the model produces distributions of entry

probabilities that are determined by the functional forms, and parameter values, that

reflect different market environments and, thus, govern the evolution of stochastic returns

from marketing. These proportions are then compared to the actual data on incidences of biotech firms entering foreign markets with different GM crops, and conclusions about the distribution of their patent values, evolution of returns, and efficiency of local intellectual property rights protection are drawn.

In the third essay, Patent Policy Analysis for the Case of Agricultural

Biotechnological Innovations, certain peculiarities of the process of development of agricultural biotechnological innovations are considered, in particular the distinction between an R&D race for a gene (genetic event) discovery and subsequent competition for developing the discovery’s marketable applications in the form of genetically modified crops. A formal model is specified and analyzed with regard to how different patent protection policies affect firms’ R&D strategies and social surplus from innovations. It is found that inclusive scope patent protection unambiguously encourages more R&D and faster innovation diffusion than the additional scope protection, which, in turn, is superior to length protection (which speaks in favor of U.S. patenting practices as

iii compared to those of the European Union). Introduction of licensing into the model either preserves or reverses the ranking of protection regimes depending on the nature of licensing contracts.

iv

Dedicated to my wife

v ACKNOWLEDGMENTS

I wish to thank my adviser, Ian Sheldon, for intellectual support, encouragement, and enthusiasm which made this thesis possible, and for his patience in correcting my articles.

I thank Mario Miranda for stimulating discussions of the issues pertaining to the second essay and for seriously helping me with the Matlab code for model solution.

I am grateful to Barry Goodwin for discussing with me various aspects of my work and for encouragement.

This research was supported in part by a grant from the National Research

Initiative. I thank Ian Sheldon for his crucial assistance in this respect.

I also thank my wife, Dr. Hartarska, for the motivation she provided me with and for the time and effort she spent making sure I was properly focused on my research.

vi VITA

September 11, 1971 …………………….Born – Nikolaev, Ukraine

1993……………. …………………………B.A. in Shipbuilding Engineering (second major Economics) Ukrainian State Maritime Technical University

1997………………. ……………………..M.A. in Economics (Honors) University of Essex, UK/Central European University

1998………………………………………...Graduate Teaching and Research Associate, The Ohio State University

PRESENTATIONS AND PUBLICATIONS

1. Nadolnyak, D.A., and Sheldon I. M. A model of diffusion of genetically modified crop technology in concentrated agricultural processing markets. Working paper presented at the 10th EAAE Congress on Exploring Diversity in the European Agri-Food System in Zaragoza, Spain, August 28-31, 2002.

2. Nadolnyak, D.A., and Sheldon I. M. A Model of Development of Agricultural Biotechnological Innovations. Working paper presented at the Annual Meeting of the American Agricultural Economics Association in Los Angeles, July 28-31, 2002.

3. Nadolnyak, D.A., and Sheldon I. M. Effect of Different Patent Protection Regimes on the Efficiency of Research in Agricultural Biotechnology. Presentation at the Agricultural Economics Seminar, Department of Agricultural, Environmental, and Development Economics, The Ohio State University, May 2002.

4. Nadolnyak, D.A., and Sheldon I. M. Simulating the Effects of Adoption of Genetically Modified Soybeans in the U.S. Paper presented at the Annual Meeting of the American Agricultural Economics Association in Chicago, August 5-8, 2001.

vii 5. Nadolnyak, D.A., and Sheldon I. M. Modeling Distributional Effects of Adoption of Genetically Modified Soybeans in the U.S. Paper presented at the Hawaii Conference on Business, Honolulu, June 14-17, 2001.

6. Nadolnyak, D.A. Adoption of GM Crops and Imperfections of Agricultural Markets. Presentation at an Agricultural Economics Seminar, Department of Agricultural, Environmental, and Development Economics, The Ohio State University, May 2001.

7. Nadolnyak, D.A. Oligopsony in Crop Processing Markets and Adoption of GMOs in Agriculture. Presentation at the Agricultural Economics Seminar, Department of Agricultural, Environmental, and Development Economics, The Ohio State University, February 2001.

8. Gonzalez-Vega, C., Graham, D.H., Nadolnyak, D.A., Hartarska, V.M., and Safavian, M. (1999) Financial Experience and Attitudes Towards Regulation of Micro and Small Enterprises in Russia: Preliminary Survey Results from Samara, Occasional Paper, The Ohio State University, September, 1999 (also presented at the FINCA workshop in Samara, Russia).

9. Nadolnyak, D.A. and Hartarska, V.M. (1999) Review of the Legal and Regulatory World for Private Entrepreneurs in Russia, Occasional Paper, The Ohio State University, Rural Finance Program, September, 1999.

FIELDS OF STUDY

Major Field: Agricultural, Environmental, and Development Economics

viii TABLE OF CONTENTS

Page

Abstract.…………………………………………………………………………………..ii

Dedication………………………………………………………………………………....v

Acknowledgements……………………………………………………………………….vi

Vita………………………………………………………………………………………vii

List of Tables……………………………………………………………………………..ix

List of Figures…………………………………………………………………………….x

Essays:

1. Essay 1. A Model of Diffusion of Genetically Modified Crop Technology in Concentrated Agricultural Processing Markets - The Case of Soybeans…………………………………………………1 1.1. Introduction………………………………………………………………….2 1.2. The Mechanism of Diffusion…………………………………….…………..4 1.3. The Processors’ Game……………………………………………………....11 1.4. Calibration…………………………………………………………………..18 1.5. Simulation Results……………………………………………………….….20 1.6. Summary of the Results.………………………………………………….....31

2. Essay 2. Valuation of International Patent Rights for Agricultural Biotechnology: A Real Options Approach………………………………………………………..33 2.1. Introduction………………………………………………………………….34 2.2. Description of the Model…………………………………………………....38 2.3. Data Description and Analysis………………………………………………43 2.4. Simulation Results…………………………………………………………..52 2.5. Conclusions……………………………………………………………….....60

vi Page

3. Essay 3. Patent Policy Analysis for the Case of Agricultural Biotechnological Innovations……………………………………..62 3.1. Introduction………………………………………………………………...63 3.2. Gene Discovery R&D Race………………………………………………..66 3.3. Application Development and Introduction Stage…………………………70 3.4. Base Case…………………………………………………………………..72 3.4.1. Scope Patent Protection………………………………………….72 3.4.2. Length Patent Protection…………………………………………84 3.5. Extensions………………………………………………………………….89 3.5.1. Heterogeneity of Applications……………………………………89 3.5.2. Licensing………………………………………………………….90 3.6. Conclusions…………………………………………………………………98

Appendix A. technical solution of the dynamic oligopsony game in the first essay….………………………………………………………………102

Appendix B. derivations of the formulae used in the third essay………………………107

List of References….…………………………………………………………………..115

vi LIST OF TABLES

Table Page

1.1. Stationary (Long-Run) Equilibrium Price, Quantity, and Gross Processing Margins with Varying Number of Firms…………………21 1.2. Changes in the Stationary Values in Response to an Increase in the Number of Oligopsonists…………………………………….22 1.3. Stationary (Post-Diffusion, Long-Run) Values…………………………………25 1.4. Changes in the Stationary Values in Response to an Increase in the Producer Uncertainty…………………………………………25 1.5. Model’s Sensitivity to an Increase in Producer Heterogeneity with Respect to Profitability of GM soybeans…………..…………………..28 1.6. Model’s sensitivity to increase in discount rate r……………………………….30

2.1. Worldwide GM Crop Approval Data…………………………………………....47

3.1. Sensitivity of s to the Discount rate……………………………………………..78

ix LIST OF FIGURES

Figure Page 1.1. Soybean Marketing Chain…………………………………………………………3 1.2. Gradual Supply Adjustment…………………………………………………….....11 1.3. Costs of Identity Preservation……………………………………………………..16 1.4. Diffusion and the Number of Crop Processors……………………………………23 1.5. Diffusion Dynamics and Producer Uncertainty……………………………………26 1.6. Diffusion Dynamics and Producer Heterogeneity…………………………………29 1.7. Diffusion Dynamics and the Discount Rate……………………………………….31

2.1. Worldwide Frequency of GM Crop Approvals……………………………………49 2.2. Worldwide Frequency of Approvals without the First-Year Approvals in the US and Canada………………………………………50 2.3. Frequency of GM Crop Approvals in Industrialized and Developing Countries………………………………………………………….51 2.4. Optimal Entry Policy……………………………………………………………….53 2.5. Sample simulation results………………………………………………………...... 55 2.6. Change in δ – the rate of depreciation of the returns………………………………57 2.7. Sensitivity to θ ……………………………………………………………………..59

3.1. Structure of the Process of Agricultural Biotechnological Innovations……………64 3.2. The Assumed R&D “Cost” Function……………………………………………....68 3.3. Innovator Payoff and Welfare as Functions of Inclusive Scope Protection………..75 3.4. Innovator Payoff under Additional Scope Protection……………………………....79 3.5. Welfare under Additional Scope Protection………………………………………..82 3.6. Social Welfare under Inclusive and Additional Scope Protection………………....84 3.7. The Effects of Licensing under Inclusive Scope Protection……………………….92 x ESSAY 1

A MODEL OF DIFFUSION OF GENETICALLY MODIFIED CROP TECHNOLOGY IN CONCENTRATED AGRICULTURAL PROCESSING MARKETS - THE CASE OF SOYBEANS

ABSTRACT

In this essay, a dynamic model of diffusion of a genetically modified (GM) crop technology is developed and simulated using the U.S. soybean market data. The model accounts for factors specific to agricultural markets, such as oligopsony power of crop processors, grower characteristics, and identity preservation requirements. Simulation results show how these factors affect the magnitude and distribution of the potential gains from adopting genetically modified crops. In particular, market power of crop processors decreases the equilibrium adoption levels and prolongs the diffusion period. Producer uncertainty and perception of the risks associated with planting GM crops increases equilibrium adoption levels but lengthens the diffusion period, thus making the welfare implications of such a situation ambiguous. Producer heterogeneity with respect to new crop profitability has different effects on the dynamics of the diffusion process, depending on the average profitability and other distribution parameters. The general conclusion is that, if GM crops are safe for human consumption and do not harm the environment, market power of the processors diminishes total surplus generated by the GM innovation.

1

1.1. INTRODUCTION

Application of biotechnology in agriculture is expected to provide significant consumer and producer benefits, the magnitude and distribution of which depend critically on the structure of the markets via which the innovation effects are realized, as well as on the behavior of the market participants. In this paper, a dynamic model of diffusion of a supply-push genetically modified (GM) crop technology is developed and the model’s simulation results are presented. For calibration purposes, the structure and database of the U.S. soybean complex are used.1 The novelty of the model is in explicitly accounting for the possibility of oligopsony power (otherwise called ‘buyer power’) and strategic interaction of the companies in the crop processing sector, the reality of which is a growing concern in many agricultural markets in the U.S. The model also incorporates such important determinants of the diffusion process as the crop growers’ heterogeneity and their path dependent adoption behavior, as well as the identity preservation and segregation requirements. As the soybean market structure and the nature of GM soybeans are typical for many agricultural markets, the results in this paper are applicable to the diffusion of other GM crops. GM (Roundup Ready) soybeans were designed to be resistant to glyphosate - a powerful herbicide that has a side-effect of severely damaging traditional (non-GM) soybeans. This improvement classifies GM soybeans as a supply-push, or process, innovation that saves on the growers’ production and management costs. In the last twenty years, the soybean processing industry, to which soybean growers sell most of their output, has become significantly more concentrated than most other U.S. food processing industries (Larson, 1998). At present, the four largest processing firms own about 80 percent of the industry’s total capacity. There are also indications of an increasing real value of the soybean processing, or crush, margin as compared to the breakeven level in crushing (Shaub et al., 1988; Soya and Oilseed Bluebook, 2000). Soybean growers, however, are small and numerous and, therefore, are

1 The terms GM soybeans and GM crop are, therefore, used interchangeably throughout the paper. 2 likely to be competitive. These stylized facts are indicative of potential oligopsony power that the processing firms may be able to exercise in the raw soybean markets. In order to analyze how market power in processing may impact diffusion of a new technology such as GM soybeans, a vertical market structure is assumed where competitive growers sell soybeans to a concentrated processing sector that handles and processes soybeans via crushing them into soy-oil and soy-meal, which are subsequently sold to food manufacturers and the livestock sector:

Adopters: Soybean Growers (competitive)

soybeans

Processing Industry: Processing Companies (oligopsony) (handle soybeans and produce meal an oil)

soyoil soymeal

Cattle Growers Food processors

Figure 1.1. Soybean Marketing Chain

The processing firms react to introduction of the GM soybeans that save on growers’ costs by making their strategic output and pricing decisions subject to the adoption behavior and other characteristics of soybean growers, to each other’s responses, and to the demands for “pure” (non-GM) and GM soybean products. 3 We find that a more competitive processing industry facilitates the diffusion of a GM crop, which benefits both growers and consumers. Finite adjustment speed of the GM crop supply, which is introduced in order to model certain (path-dependent) adoption behavior of the crop growers, impedes the diffusion process but benefits agricultural producers in the long run. Producer heterogeneity with respect to profitability of GM soybeans is also an important determinant of the diffusion process, as higher heterogeneity results in lower adoption levels and a higher price of the GM crop. Producer heterogeneity also affects the speed of GM crop diffusion: if the eventual adoption is going to be partial, higher heterogeneity is likely to speed up the diffusion process, but might lower the present value (PV) of the social surplus. High discount rates shorten the adoption period and increase the total surplus, together with the GM soybean output and price. In section 1, we discuss the mechanism of adoption of agricultural innovation by the growers. In section 2, we provide a short review of the literature on dynamic oligopoly and lay out the model of GM soybean adoption. Calibration data are presented in section 3. In section 4, we discuss the results.

1.2. THE MECHANISM OF DIFFUSION. There are a number of theories of innovation diffusion, each offering an explanation of the fact that it always takes time for a new technology or product to become widespread. A good applied review of these theories and factors affecting GM crop diffusion can be found in Fernandez-Cornejo and McBride (2002). In modeling crop (soybean) growers’ adoption behavior, we accommodate two approaches to innovation diffusion that have been most successful from an empirical standpoint: the probit and epidemic approaches. The probit, or partial equilibrium, approach is based on the fact that potential adopters are heterogeneous in profitability of the new technology (Stoneman, 1983). Innovation diffusion is gradual (adoptions occur at different times) because of the assumption that the price of the innovation is decreasing exogenously due to accumulation of experience,

4 improvements on the supplier side and, possibly, an increase in demand as more customers become aware of the benefits of a new technology. According to the standard probit model, a firm i with a vector of characteristics zi and profitability gain (cost reduction) of h(zi) from the new technology will adopt at time t if the present value of adopting is greater than the current price of the innovation/innovative input: e h(zi ) / r ≥ pt . Assuming that there is an expectation about the future price, pt +1, changes

e the decision rule into h(zi ) ≥ rpt + ( pt − pt+1) (Stoneman, 1987). We alter this approach by recognizing that, first, adoption of GM crops is reversible and, second, that it is the changes in the GM crop (farm output) price rather than the seed or chemical inputs that affect the growers’ adoption decisions. Most importantly, we endogenize these crop price movements by making them a result of a oligopsonistic game that the crop processors play with the producers. An oligopsonistic processing industry is endogenized in the game-theoretic framework due to strategic behavior of the crop processing companies2. The reasons for the growers’ heterogeneity in profitability of a new GM crop depend on the nature of the genetic modification. In this respect, the most important soybean grower characteristics are: - The level of weed infestation. GM soybeans provide cost savings to the growers because of their resistance to glyphosate – a potent herbicide that harms traditional soybean varieties. Weed infestation is a more urgent issue in the southern soybean growing regions than in the Midwest and in the North; - The level of farm income, as it affects growers’ acceptance of the risks associated with the GM crops, such as adverse environmental effects or changes in consumer acceptance of GM foods. Related producer characteristics are farm size, diversification, storage capacities, and other factors that affect a farm's financial stability;

2 In agricultural markets, it is the output price of the GM crop that changes due to “buyer power” – the oligopsony reacts to the shock of introduction of a new GM crop by strategically adjusting its prices and purchasing volumes. In a dynamic model, this adjustment is gradual. For tractability, we assume the producer input (seed) price is constant (or changes exogenously), at least during the adoption period, which is equivalent to a long patent protection regime. Considering the dynamics of a vertical monopoly- oligopsony situation with an intermediate stage of competitive production is another challenging task. 5 - Producers’ risk-aversion and perception of the riskiness of a GM crop – something that usually depends on education; - The extent to which producers’ contractual relations with buyers or suppliers restrict their production choices. Depending on the contractual arrangements, producers might be more or less willing to take the risk and plant a GM crop. Assuming that growers are more heterogeneous with respect to profitability of a GM crop than its traditional counterpart, and that the two distributions are uncorrelated, the supply of the GM crop will be more inelastic than that of the traditional crop, with a (small) portion of it lying below the traditional crop supply curve. Letting superscripts G and N define the GM and traditional (non-GM) crop respectively, the long-run supplies can be defined as:

N N N N G G G G G N G N w t = a + b Qt and w t = a + b Qt , with b > b and a < a , (1) where w is the crop price and Q is the quantity purchased from the producers. The drawback of the otherwise theoretically plausible and empirically robust probit approach is that it does not explicitly incorporate producers’ behavior with regard to uncertainty and learning associated with the new technology, particularly from the producer’s point of view. As both uncertainty and its mitigation via learning, or accumulation of experience, are important determinants of GM crop producers’ adoption behavior, it is reasonable to introduce the epidemic approach to innovation diffusion, otherwise also called the “logit” approach because of the conventional simplifying assumption that innovation diffusion is governed by a logistic function (Griliches, 1957, Mansfield, 1961). The cornerstone of the “epidemic” reasoning as applied to the economics of innovation is that delayed adoption (otherwise sometimes called “backwardness” or “retardation”) reflects uncertainty that firms attach to future profit streams, which, in turn, arises from the rate at which firms learn from existing users’ experience. Thus, the epidemic approach explains the dynamics of innovation diffusion by assuming that potential adopters lack knowledge about the profitability of a new technology or product and by emphasizing the importance of learning about it as information becomes more widespread as adoption levels rise over time. Under reasonably simple settings, and considering the fact that agricultural producers are likely

6 to form their expectations based on past adoption levels, i.e., exhibit adaptive expectations, current adoption can be specified as dependent on past adoption levels and negatively related to uncertainty, or lack of knowledge, about the profitability of new technology. Faster adoption speed and higher adoption levels in the past imply better information and less uncertainty about a new GM crop. It is thus not only the current demand for it, but also past production/diffusion levels, that affect producer planting decisions. Due to the specific nature of agricultural markets, the epidemic (logit) approach has been particularly applicable in the research on diffusion of agricultural innovations. It was first used in explaining adoption patterns of hybrid corn in the US (Griliches, 1957). Subsequent works on adoption behavior of agricultural producers focused on a modified version of the epidemic approach, the so-called effective information hypothesis (Fischer, Arnold, and Gibbs, 1996), under which the quantity and quality of relevant information about a new technology that is available to potential adopters determines adoption levels. This uncertainty is mitigated over time via learning, which can be from a neighbor or from own experience (Foster and Rosenzweig, 1995), from increasing quality, or “nearness”, of information (Fischer, Arnold, and Gibbs, 1996), from reduction in the information “noise” as adoption becomes more and more widespread, or simply from profitability in the past year via popularity weighting (Ellison and Fudenberg, 1993). Recently, Marra, Hubbel, and Carlson (2001) found that the most important factors in the American farmers’ decisions to adopt Bt cotton were on-farm experience and current county and state adoption and yield levels, which stresses the importance of information “nearness” and reduction in the “noise” as the innovation becomes more widespread.3 In compliance with the “epidemic”, or effective information, reasoning, GM crop (soybean) adoption decisions in this essay are assumed to be influenced not only by current demand for them but also by the growers’ observations of recent GM crop prices and adoption levels. This path dependency, or lagged adoption, has important implications for the dynamics of the process, particularly in imperfectly competitive markets for raw agricultural commodities, by creating incentives for oligopsonistic

3 These findings also under-stress the importance of seemingly rich and useful information supplied by the interested and potentially partial parties like the seed producers or chemical manufacturers. 7 processors to preempt each other by “investing” in expansion of the GM crop acreage as current (purchasing) prices have more than an immediate impact on adoption: they also affect future adoption decisions. The overwhelming majority of GM crops differ from conventional ones in that they save on producers’ costs, i.e., it is the expected cost savings that make producers switch from conventional to the GM crop varieties. However, these cost reductions are mainly weed and pest management related, which makes them hard to estimate, both for economists and for producers themselves (for a good review of the empirical research on the subject, see Shoemaker et al., 2001). As we argue above, adoption, therefore, depends not on the actual cost savings, but on their perception by the producers, which largely depends on the information from (experience of) those who have already adopted the crop. This information can be approximated by the past adoption levels and by the speed of diffusion in the past.4 Technically, the expected cost of growing the GM crop can be defined as a function of not only the current production volume (planted area), but also of aggregate past production levels:5

G G G G E[ct ] = c(Qt , f (Qt− )) , where f (Qt− ) represents past production levels. + − Assume, as Ryder and Heal (1973) did with consumption utility, that the past production levels that enter the cost are exponentially weighted:

t G −st sτ f (Q t− ) = se e Q dτ , i.e., higher recent adoption levels mean more good news ∫ τ 0 about the technology and thus make the producers expect higher cost savings.

4 This is consistent with the hypothesis of information “nearness” and the related concept of information “noisiness” that we mentioned before. It is important to note that the actual cost savings remain higher than the perceived ones during the diffusion process due to the finite speed of dissemination of the relevant information. This gap, however, is narrowing over time as adoption levels rise and more veritable information becomes available from both formal and informal sources. 5 This is similar to the family of utility functions that depend on not only on the current but also on the past consumption. One of the interesting applications of this specification is their use in explaining the incidence of revolutions (Davies, 1962). A period of high consumption builds up high customary or expected consumption levels, and a sharp decline in income, though it may be to the levels that are historically high, produces a sharp fall in satisfaction and causes social unrest. However, the reasoning behind our formulation is different: while past consumption of a good usually matters for its current desirability because of habit formation, past production levels reflect the volume and quality of currently available information relevant to making current production decisions. 8 The expected cost function can be structured in the following way:  t  E(c ) = A + Q a + b(s e −s(t−τ )Q dτ ) . t t  ∫ τ   0  In this otherwise trivial cost function, only the integral term on the right is unusual: the expected costs are inversely related to the speed of adoption in the past (particularly in the most recent past). Using the integration by parts rule and assuming

Q0=0:  t  E(c ) = A + Q a + b(Q − e−s(t−τ )Q&dτ ) . t t  t ∫ τ   0  The higher the recent increases in the adoption levels, the more beneficial is the perception of the new technology, and therefore the lower the expected cost of growing a new crop. Parameter s reflects the importance of learning from other producer experience and of the crop “reputation” effects reflected in its past adoption levels: 0 ≤ s < ∞ . Note that, when s = ∞ , the past adoption levels do not matter, and the short- and long-run supplies are equal.

The marginal cost,

∂E(c ) t t = a + 2b(se−st esτ Q dτ ) , ∫ τ ∂Qt 0 can be identified (through a trivial profit maximization problem by a competitive producer) with the right hand side (RHS) of the inverse crop supply function:

t t wG = a + b(s e−s(t−τ )Q dτ ) = a + b(Q − e−s(t−τ )Q&dτ ) . (2) t ∫ τ t ∫ τ 0 0

Differentiating the supply function gives the rate of change in the price:

t wG − a w&G = bs(Q − s e−s(t−τ )Q dτ ) = bs(Q − t ) , t t ∫ τ t 0 b

G G G G G G w&t = s(a + b Qt − wt ) = s(wLR (Qt ) − wt ) . (3)

9 This is equivalent to an equation of motion for a dynamic problem: the price changes according both to the quantity supplied and the last period price that represents the “carryover” effect or simply conservative or cautious producer behavior. It should be mentioned that the derivation of expression (3) above is but one of several ways to obtain it. For example, the same expression can be obtained for discrete time specification:

G G G G wt = swLR (Qt ) + (1− s)wt−1 = s(a + bQt ) + (1− s)wt−1 , s=[0,1];

t t G i i t G wt = as∑∑(1− s) + bQt−i (1− s) + (1− s) w0 converges to wLR (Qt ) as t → ∞ , and i==0 i 0

G G G G ∆wt = wt − wt−1 = s(a + bQt − wt−1) .

However, we set the problem in continuous time in order to preserve differentiability and provide a neater analytical solution. A few words are in order about the exact nature of the sticky prices logic in our model. The application of sticky prices is specific here, as it reflects producer behavioral peculiarities, which are different from the motivation behind sticky consumer prices. Our structure reflects what one could call slow realization of cost savings. At the moment of introduction of a GM crop, its production is zero, and producers do not possess full information about the cost benefits from it, i.e., they know the crop’s traits and other characteristics, but do not have quite enough information about the private benefits from it. Therefore, they take the price of the conventional counterpart of the GM crop as a yardstick for the price of the GM harvest. Those who have planted it eventually save on management and other costs, but their initial expectation was different (there was not enough information) and they might have sold the crop before they even planted it. The eventual selling price of the first GM crop is thus smaller than the original price of the conventional crop, but higher than the price given by the long-term supply function under the assumptions of full information and complete certainty. In other words, the short-run GM crop supply is flatter than the long-run one. It is only in this (and similar) situation that the price stickiness makes sense. Figure 1.2 provides an illustration.

10 This setup is justified by recent empirical research on adoption of GM crops that suggests that path dependent, lagged, or bandwagon-like, behavior of crop growers with respect to adoption of agricultural biotechnological innovations is an important force behind the diffusion process (Fischer, Arnold, and Gibbs, 1996). The traditional crop supply, however, is not assumed to be lagged or path dependent. In contrast to the GM crop, the traditional crop is assumed to exhibit instantaneous adjustment due to the absence of the influences discussed above.

G w0

G w1 G w2 G w3 G wT

G G wLR (Q1 )

G G G G Q1 Q2 Q3 Q

Figure 1.2. Gradual Supply Adjustment

1.3. THE PROCESSORS’ GAME (Strategic Behavior) The crop processing industry is assumed to consist of n identical firms that purchase both GM and traditional crop varieties, process them, and sell the processed products to consumers. In the case of soybeans, the processed products are soyoil and soymeal that are sold mainly to food manufacturers and to livestock growers. The processors are risk-averse (because of their diverse activities) and know the growers’

11 adoption behavior. Because there are only a few crop processors, their industry is assumed to be an oligopsony, in which firms behave in a non-cooperative Cournot-Nash fashion.6 The industry is assumed to be a stable Nash equilibrium up to the moment when a GM crop is introduced (soybeans in our example). From that moment, the crop becomes differentiated and firms start adjusting to the new situation7. From the discussion of the growers’ adoption behavior, it follows that the process of adoption of a GM crop is state dependent and the appropriate state is the GM crop price8. The processors are assumed to set the volumes of input purchases. When the processing industry is an oligopsony and the supply adjustment of producers is less than instantaneous, incentives for strategic pricing behavior exist. This strategic behavior of processing companies, together with the supply and demand conditions, determines the path of GM crop adoption.

Profit maximization A processing firm i maximizes the present value (PV) of its profits from processing both traditional and GM crops:

∞ J = e−rt π G +π N − c IP (ρ G ) dt , (4) i ∫ {it it it } 0 the instantaneous profits being:

G G G N G G G π it = pt (Qt ,Qt )Qit − wt Qit , (5)

N N G N N N G N N π it = pt (Qt ,Qt )Qit − wt (Qt ,Qt )Qit , (6) where Q’s denote quantities of raw soybeans purchased and p’s and w’s are processing output and input prices respectively. cIP denotes the costs of identity preservation

6 The empirical justification of this assumption is questionable. While early studies found confirmation of the fact that concentrated industries in the U.S. indeed behaved in a Cournot-Nash fashion (Gollop and Roberts, 1979), the results of more recent research are more controversial, ranging from explicit rejection of the Nash behavioral hypothesis (Slade, 1995) to recognizing that tests based on the conduct parameter method simply lack power and, therefore, cannot be presented as evidence of a certain behavioral pattern (Corts, 1999). 7 We do not explicitly account for arbitrage in the crop futures market, assuming instead that growers do not take full advantage of hedging or that the processors also have market power there. This prevents (perfect) arbitrage and thus does not violate the model’s oligopsonistic setup. 8 There is a voluminous literature on price discovery, particularly in agricultural markets. The general opinion is that the prices efficiently reflect the supply and demand conditions. 12 function whose argument ρ G is the share of the GM crop9. Superscripts G and N refer to the GM and traditional (non-GM) crops. The profits are approximated by the so-called gross processing margins - differences between the processing output and crop input values. This approximation is justified by the fact that crop-processing technologies have fixed coefficients, which is particularly true for soybeans.

GM crop supply The dynamics of GM crop diffusion is governed by equation (3), which describes the state-dependent GM input price according to the reasoning about the diffusion process described in Section 2:

G G G G w&t = s(w (Q t ) − wt ) . (3) It is assumed that the initial price of the GM crop, as perceived by producers, is equal to the current non-GM crop’s price, which reflects a high level of demand uncertainty associated with the advantages of a completely new product.10 For every G processing firm i, the GM crop price wt represents a state variable, and the volumes of G N crop purchases, Qit and Qit , represent the firm’s controls/choice variables. G G G G G wt (Qt )=a +b Qt is the long-run path independent supply equation and s is the supply adjustment parameter which is a function of all the exogenous factors influencing adoption behavior11. Below, as GM soybeans are the crop whose diffusion is chosen as a modeling example, some details of the model’s specification are provided that correspond to the realities of the soybean market and processing in the U.S.

9 The infinite horizon assumption is justified by the fact that it implies maximizing the value of the firm. 10 Generally, the initial GM price can be equal to or less than the price of the traditional variety (as herbicide-tolerant and pest-resistant crops are (strictly) inferior to the non-GM crops from the final N consumer point of view). Setting it to w0 does not change the results. 11 Technically, s here is the speed at which the price converges to its level on the long-run supply equation. This speed is finite because adoption decisions are made on the basis of relevant information the availability of which increases with adoption. 13 Substitution possibilities and output variations. Let us consider the possibilities of agricultural producers switching to/from other crops in response to soybean price changes. If we treat the environment outside soybean production as static, an increase in the area planted with soybeans should be anticipated in response to reduction in their production costs due to introduction of the GM variety. But, accounting for the fact that all the major soybean “competitor” crops to which the growers can switch (corn in particular) are undergoing similar genetic modifications and that, together with the fact that the structure of markets for corn, rapeseed, canola, sunflower, and other crops are similar to that of soybeans12, it is more realistic to assume that no substantial increase in soybean acreage will take place in response to soybean profitability changes. Thus, rather than assuming numerous substitution possibilities or considering the soybean industry independent of the rest of the agriculture, we resort to an assumption of constant area planted with soybeans. This assumption in no way interferes with the intents and purposes of the essay; it simply implies that total soybean output remains constant after GM soybean introduction, as GM soybeans do not exhibit higher yields (Lin, 2000): T N G Q =Qt +Qt . (7) Soybean producers thus have a choice of switching from traditional to GM inputs. The N price of traditional soybeans, wt , which does not exhibit any path dependency, is defined as

N N N N N N T G 13 wt = a + b Qit = a + b (Qi − Qit ) . (8)

Processing output demands. For analytical convenience, the demands for GM and non- GM outputs are specified as linear functions of the weighted sums of meal and oil demands, the weights being technological coefficients of oil and meal production:

G G G G pt = α + β Q t , (9)

12 Similar GM varieties have been introduced, the structures of the seed and crop processing industries are almost the same, and the end uses of the processed products are also similar. 13 N G wt is assumed not to depend on wt because the cross-price effect is already captured by the effect Qt N has on Qt . 14 p N = α N + β N Q N = α N + β N (QT − Q G ) . (10) t t t Cost of identity preservation. The identity preservation requirements (IPR), which come at a cost, are consumer demand (or consumer concern) related, and appear with the introduction of GM soybeans. The inclusion of the costs of identity preservation is not crucial in this diffusion model, as the evidence of obligatory segregation of crops in the U.S. is scant at best. However, voluntary segregation has been encouraged by premiums that processors and elevators sometimes pay for non-GM crops14. Little is known about the structure of the identity preservation (IP) costs, except that they are significant and non-linear (see, for example, Lin, 2000, and Bullock, Desquilbet, and Nitsi, 2000). The argument is two-fold. On the one hand, the more GM crop is grown in comparison to traditional varieties, the more expensive IP compliance is. On the other hand, smaller share of traditional soybean output also implies lower IP costs because there are fewer non-GM shipments to inspect and it is easier to segregate them from GM soybeans. The cost of identity preservation consists of the cost of checking non-GM soybeans/oil/meal for the presence of GMOs (inspection cost CI) and the cost of cleaning storage or processing facilities before using them for traditional (non-GM) varieties after storing or processing GM soybeans there. The inspection costs are linear in the quantity of non-GM soybeans. The cleaning costs are a non-linear function of the share of non-GM produce, typical elevator and crushing plant size, and of the efficiency of elevator and processing facilities’ management. Obviously, production management efforts are directed towards specializing production and storage facilities in either traditional or GM inputs, but, given the assumption of imperfect (less than perfect) management, the costs of cleaning will depend on the frequency of a production facility’s switching from GM to non-GM crop. Technically, letting N define the number of shipments of non-GM soybeans to an elevator and/or processing facility over a certain period of time, the aggregate cost of facility cleaning is:

N c G Csegregation = c ∑ j Pr( j ρ ) , j=1

14 The recent USDA adoption report emphasizes the requirement to segregate GM exports to EU and Japan. 15 where cc is the cost of a one-time cleaning and Pr(j|ρG) is the conditional probability that a shipment of non-GM soybeans is received j times after receiving shipment(s) of GM varieties conditional on the share of the GM crop grown, ρG=QG/QT. It can be shown that, with uniform distribution of arrivals of non-GM shipments, the cleaning cost CS is an inverted parabola skewed to the right the height of which depends on the management efficiency. Figure 1.3 below provides an illustration. The most consistent way to specify the costs of segregation is

S G G 2 T G C = µ(ρt − ρt )Qt , where ρ is the share of non-GM and GM produce, and µ is a coefficient reflecting facility management efficiency and the actual cost of one-time cleaning. The total cost of identity preservation for firm i is thus:

IP I S I N G G 2 N G Cit = Cit + Cit = cit Qit + µ(ρit − ρit )(Qit + Qit ) . (11)

$ CS CI

MAX 0 N N (# of shipments)

Figure 1.3. Costs of Identity Preservation (Cs – costs of segregation, CI – costs of inspection)

Dynamic oligopsony The two most common structures of non-cooperative dynamic oligopoly games are those of open- and closed-loop (feedback). Under the open-loop structure, the agent’s information set consists of calendar time and the initial state vector. Each firm chooses a

16 sequence (trajectory) of controls, which is a function of time and the initial state only, which is similar to a commitment. In other words, each firm maximizes its stream of profits given the initial condition and an assumed path of its rivals given a behavioral assumption (Nash-Cournot in this case). The equilibrium then is a Nash equilibrium in open-loop strategies. Under the assumption of open-loop behavior, the stationary (steady state) values are equal to their static analogues. The feedback structure is richer than that of open-loop because, in the former, the agent’s information set consists of calendar time and value of the current state vector. Under this structure, firms can respond to surprises caused by random shocks and are made more “aware” of the possibility of rivals’ defection. The equilibrium thus is a set of decision rules rather than a set of trajectories and it is subgame perfect but not unique (inter alia, it can regress to punishment and trigger strategies). The shortcoming of the feedback setup is the game becomes quite difficult to solve for more than two firms. Despite the differences in construction, the outcomes under the two setups are essentially similar. In certain cases, open-loop models generate the same outcomes as those of closed-loop and it has been shown that the differences in comparative statics with respect to the steady states, as well as in comparative dynamics, are only cardinal and not ordinal (Karp and Perloff, 1993, Maskin and Tirole, 1988). In particular, feedback models always lead to more competitive behavior than open-loop models, which is the result of a more pronounced preemptive incentive. In this paper, for reasons of analytical tractability, the GM crop diffusion model is solved under the open-loop structure. By definition, the solution to the open-loop oligopsony game with Nash-Cournot behavior is determined by the simultaneous solution to n profit maximization problems:

∞ max J = e −rt {}π G + π N − c IP (ρ) dt , i ∈(1,n) , (12) G N i ∫ t t it Q it ,Q it 0 subject to the single GM crop supply equation (3):

G G G G w&t = s(w (Q t ) − wt ), (3)

G w 0 , and the transversality condition. It is easy to show that, because the Hamiltonian for each firm is strictly concave in the control, and the firms are identical, the equilibrium at 17 G G any point of time is symmetric (Fershtman and Kamien, 1987). Thus,Qit = Q jt ∀ i ≠ j ,

N T G T G and Qit = Qt /n − Qit = Qit − Qit ∀ i. The assumption of constant proportions of traditional and GM soybeans for each firm can be justified by the fact that each processing company has plants and elevators in every soybean growing state and therefore complete specialization in GM or traditional varieties is unlikely. The solution to this problem is described in Appendix A.1.

1.4. CALIBRATION In order to simulate the process of diffusion of GM soybeans and to show its dynamic properties, the model is calibrated with annual data from the U.S. The recent data are obtained from public sources (Soya and Oilseed Bluebook, 2000). Below are the values of the parameters used in the simulation.

Soybean supply: N - Soybeans used for crushing prior to adoption: Q0 = 43.5 million metric tons; N - Traditional (non-GM) soybean price: w0 = $241 per metric ton; - Area planted: L = 28 million hectares; - Yield (same for both traditional and GM varieties): y = 2.62 MT/hectare; - Producer’s cost saving from planting GM in comparison to the traditional variety: ∆π = $20/hectare or $7.63/MT (Moschini, Lapan, and Sobolevsky, 2000); - elasticity of planting area with respect to price: ϕ = 1.2. This measure is rather arbitrary because of the fact that the existing soybean and oilseed models (FAPRI, SWOPSIM, and AGLINK) arguably underestimate soybean elasticities assigning them values ranging from .22 to .6 (Moschini et al., 2000). The coefficients that emerge from these numbers are: ∂wN 1 wN b N = = = 4.617 , a N = wN − b N Q N = 40 , and aG = a N − ∆π = 32.37 . ∂Q N ϕ Q N For the reasons discussed above, we assume bG = 1.1 and bN =4.84.

18 IP costs: According to various estimates, the inspection costs related to the IP requirements range from $0.18 to $0.54 a bushel (Lin, 2000). We, therefore, set cI =$1.5/MT. µ, the management efficiency parameter, is assumed to be equal to 30.

Demand for crushing products: For clarity, we have assumed constant prices of outputs. This may be more realistic considering the competition that US crushers face in world markets. But, even if the industry is facing a residual demand in the output markets, the possibilities for exercising market power in the output markets are miniscule in comparison to those in the soybean input market. The following coefficients have been used: - The transformation coefficients for meal and oil are: γM = 0.79 and γO = 0.21.

- The meal price is the average price in the 1990’s: pM = $219/MT. We assume that the price of meal from GM soybeans remains the same.

- The oil price is the average price in the 1990’s: pM = $590/MT. We assume that the prices after the introduction differ from this level by 5% for oil from traditional beans and –10% for oil from GM produce. The output prices in our model are weighted meal and oil prices:

G O G M N O N M p = γ pO + γ pM = 283, and p = γ pO + γ pM = 301

The initial value for the GM soybean price, wo, is assumed to be the current non- GM crop price. This is not a strong assumption for two reasons. First, it is natural to view a first-time introduced crop that only holds a promise of higher profitability as equivalent to its traditional counterpart. According to our hypothesis, the GM price should start to decline as the cost savings become apparent. (Appendix A.2. contains an explanation of the mechanics of a positive crop expansion that is simultaneous with the declining crop price. This mechanism is very important for our model setup.) Second, the purpose of this simulation is to try to describe, rather than forecast, the process of agricultural biotechnological innovation. Different starting values for the state variable do not change the mechanics of it.

19

1.5. SIMULATION RESULTS Due to the poor analytical tractability of the model’s comparative dynamics analysis, numerical simulation is used to examine the model’s sensitivity to various factors and to and draw conclusions. In particular, it is of interest to examine how the model’s parameters affect the diffusion dynamics and equilibrium prices and outputs of GM and traditional soybeans, as well as the magnitude and distribution of gains realized due to the innovation adoption. The software used for the simulation is MATLAB. Below, the results of a sensitivity analysis are presented with respect to the number of firms in the processing market, growers’ adoption behavior, growers’ heterogeneity with respect to profitability of GM soybeans, and the discount factor. These results are by no means exhaustive, but we believe that we cover important determinants of the diffusion process of biotechnological innovations.

Number of processing firms in the raw soybean market. Interesting results are obtained by varying the number of soybean processing firms which, in the model, reflects processor oligopsony power. A more competitive market (having more firms) leads to greater realization of the producer cost savings that GM soybeans offer, which implies a higher long run equilibrium share of GM soybeans with a correspondingly lower share of non-GM soybeans. A more competitive processing industry also “extracts” less of the surplus from producers (slows down the proverbial technological treadmill), which is indicated by a higher equilibrium price of GM soybeans. In general, a more competitive processing sector means that processors garner a lower share of the cost savings from the GM technology, while grower and consumer surpluses are larger. Market characteristics approach competitive levels as the number of firms increase. Tables 1.1 and 1.2 below provide an illustration.

20

Number of processing firms 1 2 3 10 100 GM soybean price ($/ton) 134 165 180 207 220 Traditional soybean price ($/ton) 144 114 102.4 74.7 65.4 GM soybean output (mill. tons) 21 27.5 30 36 38 Traditional soybean output (mill. tons) 22.5 16 13.5 7.5 5.5 Aggregate processing margin (mill. $) 6375 5913 5465 4216 3401 * s=0.5

Table 1.1.: Stationary (Long-Run) Equilibrium Price, Quantity, and Gross Processing Margins with Varying Number of Firms

The number of processing firms also affects the dynamics of diffusion. The length of the adoption process, defined as the time it takes prices and quantities to come arbitrarily close to their stationary values, is negatively correlated with the number of processors. In compliance with the general results of dynamic oligopoly theory with Nash-Cournot behavior, firms in a more competitive market expand their purchases of GM soybeans faster because of the incentive to pre-empt rivals by seizing a market share before they do. With fewer processors, however, it is rational to first start buying only the cheapest GM soybeans from those growers who enjoy the highest cost savings from the new technology and then to gradually expand GM soybean purchases, keeping prices low because of the slow GM soybean supply response. Figure 1.4 provides an illustration of the dynamics of the process. It is clear that the long-run (post-diffusion) values comply with static oligopsony theory: greater market power leads to underproduction (in our case, underproduction of the more cost efficient commodity of the two – the GM crop) and to more favorable prices for those with that power (in our case, the lower price of GM soybeans).

21 Share of GM soybeans ↑ Total surplus ↑ Share of non-GM soybeans ↓ Grower surplus ↑ Price of GM soybeans ↑ Consumer surplus ↑ Price of traditional soybeans ↓ Processor surplus ↓ Adoption time ↓

Table 1.2: Changes in the Stationary Values in Response to an Increase in the Number of Oligopsonists (Processing Firms).

The dynamics of the adoption process also has an intuitive appeal: the GM crop’s price decline since the crop’s introduction is much sharper under oligopsony in processing because an oligopsonist targets much lower adoption levels at a lower price. Appendix A.2. explains the mechanics of GM crop expansion when its price decreases from its original levels. It is shown that GM output will expand only if the rate of decrease in its price is below a certain critical level and, if this condition holds, the rate of GM output expansion is negatively related to the first derivative of the rate of the price change. Thus, the GM output increase is lower when the price drops too quickly. Alternatively, slow increase in GM crop purchases by the oligopsonist leads to a sharper price decline (which is the reason why it buys less than a more competitive industry). When the industry is more competitive, there is a pre-emptive incentive for every firm to “invest” in expansion of the GM crop, which leads to faster and higher diffusion levels and a slower decline in the GM crop price, and higher post-diffusion adoption levels.

22

Figure 1.4. Diffusion and the Number of Crop Processors

23 Needless to say, GM crop expansion is gradual (even in the case of monopsony) because of the application of the “epidemic” or information efficiency diffusion hypothesis in modeling the producers adoption behavior. The higher the parameter s that reflects the importance of past adoption levels in making a decision to pant the GM crop (higher s actually means less importance and vice versa), the more gradual is the downward GM crop price adjustment associated with the crop diffusion. This is true for any given number of processing firms. In the feedback version of the model, the results discussed above would be similar, but with the stationary values reflecting more competitive behavior. The intuition behind this is that the initial GM soybean price being below its long-run value encourages the rivals’ purchases of the GM crop (which is identical to the argument that capacity building encourages investment in standard models). Under the feedback assumptions, there are stronger incentives to “invest” in GM soybean acreage expansion now rather than later as a means of preempting the rivals’ expansion into the GM market.

Growers’ adoption behavior. As discussed in Section 2, growers’ adoption behavior is summarized by the parameter s, which represents the speed of GM soybean supply adjustment, reflecting producer perception of uncertainty about the crop’s acceptance and prices, importance of past and current adoption rates and levels for price expectation, and availability and speed of dissemination of information affecting planting decisions. The simulation results indicate that slow supply adjustment of the GM crop leads to a higher long-run share and price of GM soybeans, but has the opposite effect on non- GM soybeans. Slow supply adjustment (low s), however, is also associated with serious delays in the adoption process, which makes the welfare effects ambiguous (see Tables 1.3 and 1.4 and Figure 1.5). The lagged adoption behavior of the growers appears to be an imperfect substitute for their market, or bargaining, power vis-à-vis the crop processors. The uncertainty associated with future demand for GM crops and slow dissemination of relevant information prevents producers from reacting competitively, or quickly, enough to the

24 incentives from processors. For crop processors, it is rational to expand GM purchases more slowly when the supply price does not adjust instantaneously. The slower the adjustment speed, the longer it takes to reach the desired diffusion levels. In the post- adoption period, this is reflected by the fact that the post-diffusion (long-run) GM soybean output and price are higher when the speed of supply adjustment is low. One of the intuitive explanations for this is that, when upstream producers, though competitive, are relatively slow adopters, the oligopsonistic processing industry downstream has to provide higher incentives to adopt in the form of higher input prices. Though diffusion is slow, the eventual adoption levels will be higher. s 0.1 0.35 0.5 0.75 0.9 1 GM soybean price ($/ton) 207 191 188 186 186.5 185 Traditional soybean price ($/ton) 74.7 88.5 90.8 93.1 94 95 GM soybean output (mill. tons) 36 33 32.5 32 31.8 31.6 Traditional soybean output (mill. tons) 7.5 10.5 11 11.5 11.7 11.9 Aggregate processing margin (mill. $) 4225 5037 5226 5203 5230 5250

Table 1.3. Stationary (Post-Diffusion, Long-Run) Values (n=4)

Share of GM soybeans ↑ Total surplus χ

Share of non-GM soybeans ↓ Grower surplus χ

Price of GM soybeans ↑ Consumer surplus χ

Price of non-GM soybeans ↓ Processor surplus ↓ Adoption time ↑↑

Table 1.4. Changes in the Stationary Values in Response to an Increase in the Producer Uncertainty (decrease in s) 25

NOTE: the 3-D diagrams above do not show the long run values due to the small time scale.

Figure 1.5. Diffusion Dynamics and Producer Uncertainty 26 Simulation results suggest that, in the long run, growers benefit from their GM adoption behavior and that finite supply adjustment hurts both the oligopsonistic processors and consumers. However, the benefit to growers comes at the cost of delayed adoption, which may well offset it. Depending on parameter values, particularly the relation between the time discount rate and the supply adjustment speed, slow GM soybean supply adjustment may or may not result in greater net PV of consumer and producer surplus. Here, one should probably mention the significance of fast adoption from the perspective of the international competitiveness of the U.S. The reason is the international “spillovers” of agricultural innovations, in particular of biotechnologies. Biotechnology innovations may be adapted to different environments much faster than other agricultural innovations, for which location-specificity typically plays an important role (Moschini, Lapan, and Sobolevsky, 2000). Besides, biotechnology innovations are generated within multinational firms that are ideally positioned for worldwide marketing. While the sales of new technologies to countries that export competitive products increase the profitability of a multinational, they also undermine U.S. competitiveness in export markets for the final products. In case of soybeans, higher GM technology adoption rates abroad increase cost efficiency of other major world soybean producers, thus undermining the U.S. competitiveness in the international soybean market.

Level of growers’ heterogeneity with respect to cost savings from the GM crop. The heterogeneity of crop growers, modeled under the probit approach, is an important parameter as it affects the dynamics and equilibrium values of the adoption process. Different levels of heterogeneity can be modeled by pivoting the GM crop supply curve around the point where it intersects the non-GM crop supply curve (this preserves the mean of the additional, GM factor related, producer heterogeneity and can be expressed in terms of elasticities). Intuitively, the first adopters from a more heterogeneous producer population will have lower production cost and thus will adopt faster and accept a lower price. Partial adoption will occur even if an innovation would not be viable with a more homogeneous

27 population. Thus, heterogeneity facilitates the initial stage of the diffusion process. However, as adoption reaches producers with average and below average profitability, it slows down considerably. If the long-run equilibrium adoption levels do not reach the average adopter, higher producer heterogeneity facilitates diffusion. However, if the equilibrium levels imply adoption by the below average producers, the long-run equilibrium adoption levels may be lower and the price higher. The model suggests that, the more heterogeneous growers are with respect to GM crop profitability, the lower will be the equilibrium GM crop output and the higher its relative price, the lower the aggregate processor profits, and the faster the adoption process. This confirms the intuitive result above and also accounts for the fact that, given the real world parameter values used in the model, long-run adoption levels (those targeted by profit-maximizing processors) reach far beyond the average adopter. While the fast initial diffusion speed makes up for a slowdown later on, the equilibrium adoption levels are lower, and the non-discriminating price that has to be paid for the crop is higher. Table 1.5 and Figure 1.6 below illustrate these results.

Share of GM soybeans ↓ Total surplus χ

Share of non-GM soybeans ↑ Total producer surplus χ

Price of GM soybeans ↑ Consumer surplus ↓ Price of non-GM soybeans ↑ Processor surplus ↓ Adoption time ↓

Table 1.5. Model’s Sensitivity to an Increase in Producer Heterogeneity with Respect to Profitability of GM soybeans

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Figure 1.6. Diffusion Dynamics and Producer Heterogeneity 29 While the welfare implications of adopters’ heterogeneity are parameter sensitive and therefore ambiguous, it is clear that the way a biotech innovation improves a crop affects the dynamics and equilibrium levels of (and hence the gains from) the diffusion process. According to the simulation results, heterogeneity of potential adopters with respect to a particular innovation is an important economic consideration at the stage of innovation design.

Discount rate. Clearly, the discount rate (r) also affects both the speed of convergence and the stationary values. In compliance with the general dynamic oligopoly (oligopsony) theory, the simulation results show that the higher the discount rate, the shorter the diffusion period, and the higher the steady state GM output and price. The welfare effects, however, are parameter sensitive and, therefore, ambiguous. Table 1.6 and Figure 1.7 below illustrate.

Share of GM soybeans ↑ Total surplus χ

Share of non-GM soybeans ↓ Total producer surplus χ

Price of GM soybeans ↑ Consumer surplus χ

Price of non-GM soybeans ↓ Processor surplus χ

Adoption time ↑

Table 1.6. Model’s sensitivity to increase in discount rate r

30

Figure 1.7. Diffusion Dynamics and the Discount Rate

1.6. SUMMARY OF THE RESULTS In this essay, a model of adoption and diffusion of a genetically modified (GM) crop technology is developed. We focus on certain important aspects of the adoption process: it is specified as a dynamic Nash oligopsony game, in which oligopsonistic crop processing companies that purchase crops from farmers make their strategic production decisions taking into account the GM crop characteristics, adoption behavior of crop growers, and identity preservation requirements. Numerical simulation of GM soybean diffusion in the U.S. is used for sensitivity analysis.

The simulation results show that competition in agricultural markets facilitates the process of a supply-push biotechnological innovation and increases adoption levels. On the other hand, oligopsonistic behavior of crop processors slows the diffusion process while maintaining higher levels of traditional soybean production, thereby reducing aggregate welfare gains from the innovation.

31 Slow speed of GM crop supply adjustment, which is shown to reflect adoption behavior of the crop growers, impedes the diffusion process but benefits agricultural producers in the long run. Welfare results, however, are ambiguous as there is a tradeoff between more plausible long-run equilibrium outcomes and protracted diffusion. Slow diffusion may also hurt U.S. international competitiveness. Higher producer heterogeneity with respect to profitability of the innovation results in lower equilibrium adoption levels and higher price of the GM crop. Higher levels of producer heterogeneity also speed up the diffusion process but, depending on the way heterogeneity is modeled, do not necessarily increase aggregate surplus. It is certain that heterogeneity of potential adopters with respect to profitability of a particular innovation should be an important economic consideration at the stage of innovation design. Higher discount rates shorten the adoption period and increase equilibrium GM soybean output and price, as well as the total surplus.

32 ESSAY 2

VALUATION OF INTERNATIONAL PATENT RIGHTS FOR AGRICULTURAL BIOTECHNOLOGY: A REAL OPTIONS APPROACH

ABSTRACT

Uncertainty of returns from marketing is an extremely important factor affecting the diffusion of a wide range of genetically modified (GM) crops worldwide. Biotechnology companies face complicated choices in making decisions about whether to enter agricultural markets in different countries with their agricultural products. In this paper, these choices are modeled as a real option problem of the entry decision solved at a micro-level by individual firms. The model is aggregated in order to reflect the heterogeneity of different genetic events, as well as different markets, in terms of their (potential) profitability. The solution to the model produces distributions of entry probabilities that are determined by the functional forms, and parameter values, that reflect different market environments and, thus, govern the evolution of stochastic returns from marketing. These proportions are then compared to the actual data on incidences of biotech firms entering foreign markets with different GM crops, and conclusions about the distribution of their patent values, evolution of returns, and efficiency of local intellectual property rights protection are drawn.

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2.1. INTRODUCTION Genetically modified (GM) crops can be marketed in many countries. The biotech companies that hold stocks of patented genetically modified crops (genetic events) face the choice of entering these markets. Entering a particular market brings a flow of uncertain revenues (not necessarily positive), but is also associated with substantial entry costs. The costs of entry involve building the storage and retail capacities, getting approval and possibly local patent protection, and obtaining producer acceptance and establishing customer loyalty via developing public relations and conducting advertising campaigns. Thus, before entering a particular foreign market, owners of the rights to GM crops must weigh the costs and benefits of such a decision. This involves not only comparing the entry costs with the expected present value (PV) of the future returns, but also accounting for the option value of not entering the market, which should be significant given the uncertainties associated with bioengineered products. Not entering a market at any particular time gives a firm the benefit of waiting until new information arrives, i.e., new benefits or hazards of a GM crop may be discovered, consumer acceptance may change, or a more viable GM crop may appear. The firm can then revise the expected values of costs and returns and thus make a more informed decision. The option value of delaying entry into particular markets is by no means negligible. The future safety and profitability of GM crops is highly uncertain - consider the largely inconclusive empirical research on the profitability of Roundup-Ready soybeans and Bt corn in the US, not to mention the more controversial and less widespread genetic modifications introduced elsewhere, like those of rice or papaya (see, for example, Shoemaker et al., 2001). As is well known, an option value increases in both the volatility of the (returns from) underlying asset and time to expiration15. When the uncertainty of returns is significant and a firm believes that bits of information that will clarify the situation are to arrive in the near future, the option value of not entering a

15 However, the option value can never be greater than the value of the underlying asset. For a through review of real options theory, see Trigeorgis, 1999. 34 particular market presently may be large enough to cover the expected present returns from entering a market. This situation bears a striking resemblance to an American call option on a dividend paying stock or asset.16 Exercising the option, effectively making a purchase, means acquisition of the stream of stochastic future returns, but giving up the opportunity not to exercise it. Not exercising the option implies giving up the current dividends but preserving the option value. Entering a market is equivalent to exercising an option because it implies commitment in the form of the sunk costs of entry, i.e., getting regulatory approvals, obtaining customer and producer loyalty, establishing production capacities or licensing to local seed companies, etc., which is equivalent to the exercise price, and becoming entitled to a stream of returns from marketing. An alternative way to specify the model would be to introduce compound options in the form of an additional option to abandon a market if it turns out to be unprofitable. For now, we do not explicitly consider the abandonment option in order to keep things less complicated and also because the precedents of pulling out of GM seed markets are rare and the costs of abandonment are unclear17. In the model presented in this essay, we assume that the biotech companies will enter a particular market only if the expected discounted value of future net returns conditional on the information currently at their disposal is greater than the value of the option to delay marketing the product. An optimal sequential policy for the agent has the form of an optimal entry rule that determines whether to enter a market at time t depending on the information currently available, i.e., whether to incur the entry costs and secure a stream of uncertain returns. If the decision not to enter is taken, the agent is getting a net current profit of zero but keeps the option to wait until the next period, when new information becomes available that will refine the expectation of the future returns. At the aggregate level, the proportion of the products that enter a foreign market at any age t is the proportion that satisfies the entry criteria at this age but did not satisfy them at t-1. The entry proportion at each age is a function of the value of the model’s parameter

16 In the realm of real options, it is analogous to an option to defer investment. 17 An additional complication of pulling out of a GM seed market is effectively giving up the property rights on the crop there: once a crop has been “diffused” but the market is abandoned, producers would be free to re-plant the GM seeds if it is privately profitable. 35 vector, which consists mainly of the coefficients of the distribution functions that describe the heterogeneity of the initial product values and their evolution over time. The data provide the actual proportions of products that enter foreign markets. Loosely speaking, the problem is to determine the optimal entry rule and find values of the model’s parameters that make the entry proportions implied (generated) by the model as close as possible to the actually observed ones. Formally, we are looking to specify a discrete stochastic model of optimal entry, call it optimal commitment, in order to derive the implications of this model for aggregate behavior and to estimate the model’s parameters using aggregate data on how many GM crops enter foreign markets each year. So far, the best approximation we have found for this has been the GM crop approval data that contains the dates of different genetic events of particular crops being approved for environmental safety, food, feed, and marketing in different countries. While this may not be the best indicator of entering a foreign market, these are the most complete and detailed data we have found so far. Our hypothesis is that, assuming that costs of entering a particular foreign market are approximately the same for a certain class of GM crops, or proportional to the market size, the timing and frequency of their approvals indicate their relative values and, therefore, the distribution of these values. Generally speaking, the sooner the crop enters a market after it is patented, the more valuable it is. The distribution of incidences of entry, together with economically justifiable assumptions about the distribution and evolution of stochastic returns from marketing, defines the distribution of relative values of different genetic events (GM crops). It should be noted that, without some “anchor” value, it is impossible to get ordinal patent/GM crop values, but knowing their distribution, i.e., relative values, can also be of value. While this does not answer all the questions, these results help identify the proportion of the patents that actually cover the R&D expenses of biotech companies and shed light on the profitability of GM crops in different world regions. The difference between this model and other R&D models is that it does not require information that is unavailable in the majority of cases. In addition, instead of deriving the results from making assumptions about the R&D production and cost functions, the model makes assumptions about the stochastic returns from marketing

36 the R&D products, i.e., the processes that generate them. The correctness of these assumptions can be verified by comparing the samples generated by the model to the actual data. Besides, the model does not treat mere patent counts as indicators of R&D profitability – something that has been the “Achilles’ heel” of the R&D literature. If compared to a simple NPV rule of entering a foreign market, other things being equal, the real option model would predict relatively late entry into different markets, particularly in the early stages of product lives when information is scarce. Later on, however, the real option model would predict a higher proportion of entries, particularly as patents approach their expiration dates. In the analysis of patent values, discrete choice optimal stochastic control models have only been used in the analysis of optimal patent renewal data and applied to the countries where obligatory patent renewal rules exist, i.e., Germany, France, and the Norway.18 Under the patent renewal rule mechanism, a patentee has to pay an annual renewal fee in order to keep the patent in force. Knowledge of the renewal fee schedules and having very extensive aggregate data on all patent cohorts (by year of patenting) in a country makes the task of evaluating the distribution and average magnitude of patent values quite accomplishable. In particular, the simulations performed by Pakes (1986) showed a very close fit to the actual aggregate data on French and German patent renewal behavior and highlighted the differences between the two countries, i.e., patent offices’ claim approval behavior and the intensity with which the inventors explore the marketability of their products. Similar models have also been used in dealing with other issues, such as job matching, sequential binary choice models for birth sequences of married women, etc. It should be mentioned that, though discrete optimal stochastic control techniques have a wide range of applications and provide rich interpretation of data, they share one common disadvantage. Both the estimation technique and the simulation/estimation results heavily depend on the details of the stochastic specification and, because of the complexity of the estimation problem, it is difficult to determine the robustness of the conclusions to the stochastic assumptions chosen. The only way to

18 See Pakes (1986), Schankerman (1986), Lanjouw, Pakes, and Putnam (1998), and Pakes and Schankerman (1984). 37 offset this shortcoming is to be very careful and informed in the model’s construction, so that the specifications are as close to economic reality as possible.

2.2. DESCRIPTION OF THE MODEL The model that we use employs the Markov assumption, namely it assumes that the distribution of the next period’s return conditional on current information depends only on current returns and the parameters of the problem. The model is essentially a search model: each year the firms that hold patents on GM crops gather information about their economic viability in different countries, or world regions, and explore the ways in which these crops can benefit producers and/or consumers. Three outcomes of this search are possible: one is that this search does not provide any new information; another is that the crops can never be profitably exploited, and yet another one is that information is uncovered indicating that the returns will increase in subsequent years. The conditional distribution of outcomes, should they occur, is non-stationary over time, which allows for the possibility that patent holders explore the most promising alternatives first. In addition, we assume that patent protection is finite, i.e., that there is a statutory limit to patent lives, so that the model has a finite horizon. Given these assumptions, it is possible to obtain an explicit solution for the optimal entry rule as a function of the parameters of the Markov process and the age of the patent, which should simplify estimation of the real-life aggregate data. On the other hand, the model presents some difficulties with respect to calculation of aggregate entry probabilities. To allow for heterogeneity, we assume that there is a distribution of initial returns among patents, which is modified over time as agents uncover more profitable ways of exploiting their patented ideas. The distribution of returns at each age does not have an analytic form and, therefore, neither do the entry probabilities. (Pakes uses a simulated frequency approach). Below is a formal description of the discrete choice optimal stochastic control model of market entry. A biotech firm has N patents on GM crops, genetic events of particular crops. There are many firms, but this is irrelevant to the model, as it is not about competition.

38 Each crop is protected by a patent of length L, the patent can be broader than just one event, in which case several crops are protected by the same patent. The firm is deciding whether to enter a new market with each of the products, possibly a market in a foreign country. The returns from marketing in this country (rt) evolve according to a stochastic process, and entering the market requires a considerable one-time sunk cost, C, which is related to capacity building, getting approvals, customer loyalty, producer acceptance, etc. One can assume that the entry cost is declining due to the gradual lowering of the regulatory barriers and increasing consumer and producer acceptance. The situation is very similar to an American call option: the firm has an option to “buy” marketing its new product in a foreign country at the price of the sunk entry cost

(Ct). The option’s maturity is L, and the time to expiration is L-t. The value of the option to enter the foreign market with stochastic returns at any particular time t is,     L−t   V (t) = max βE[V (t +1) | Ω ], _E β i r | Ω − C . (1) 1 424 434 t ∑ t+i t  t   i=0   do _ not _ enter _ at _ t 1 424 4 434 4   enter _ at _ t  The first term in the brackets is effectively the option value: it shows what the firm gets if it decides not to enter the foreign market, i.e. the discounted value of the patent in the next period.19 The second term is what the firm gets if it decides to exercise the option at t and enters the foreign market. In this case, it gets a PV of the flow of per period returns until the patent’s expiration, rt+i (i = 0, L -t) conditional on the current information, Ωt , 20 minus the sunk entry costs, Ct. Given the distributional assumptions about the returns are specified, equation (1) can be solved recursively for two variables: cutoff values rt and proportions of products entering the market π t . For each t, there exists a unique return (cutoff value), rt , such that the option is exercised (entry occurs) if the actual current return rt> rt . Alternatively, the option is not exercised if rt < rt . Knowing the cutoff values ( rt ’s as functions of the

19 Note that the option value is non-negative, even the future returns turn out to be negative. 20 A possible extension is to introduce another option – an abandonment option of exiting the market after entering if the returns are really bad, but this would complicate the analysis. 39 distributional parameters and t) permits calculation of the shares of patented products, call them different GM crops, π t ’s, that will be marketed at each t. Given the availability of empirical data on the number of GM crops that enter markets in different countries over several years, the simulation results can be compared to the actual proportions in several ways and conclusions drawn. Below we suggest the distributional assumptions of the model and try to justify them on empirical grounds. - When the invention is made, i.e., the option is born, we have a known initial

returns distribution. The initial returns (r1) are lognormally distributed with a

mean of µ and variance σ R :

log(r1) ~ η(µ,σ R ) . (2) This distribution is properly skewed, which reflects the fact that the bulk of the innovations, genetic events, are not as profitable as the few that lie on the far right.

- The evolution of the returns is a Markov process. The information set Ωt thus

consists of the current return, rt, and the current time, t. The conditional

distribution of rt+1 is:

 0 with _ probability _ exp(−θrt ) rt+1 =  (3) max{δrt ,z} with _ probability _1− exp(−θrt ) where the density of z:

−1 qt (z) = σ t exp(−(γ + z) /σ t ) ,

t−1 and σ t = φ σ , for t=1,…, L-1. In addition, δ ≤1 and φ ≤ 1. This process has the following economic interpretation. At each age, patent holders, biotech firms, gather information on and explore ways of improving their crops’ marketability and safety in order to increase profits. Three outcomes of this process are possible: 1) It is found that the crop can never be profitably exploited, which is something

quite common among GM crops. This event occurs with probability exp(−θrt ) - 40 note that it occurs with smaller probability the larger are the current (estimated)

returns from marketing the product, rt . In this case, the product never enters the

market (technically, 0 is an absorbing state, as exp(−θrt | rt = 0) =1) and a single realization of zero return is an absorbing state. The option value on this product is zero as well. 2) No new information is discovered, this search does not provide any new information, in which case the current returns decay at the rate of δ ≤1, which can be attributed to obsolescence due to the arrival of better substitutes, e.g., consider the number of patented herbicide resistant versions of soybeans and cotton. In this case, entry is not likely, but a decrease in the entry costs may still trigger it. 3) Information is uncovered indicating that the returns will differ from the returns expected before the new information became available, e.g., the environmental safety concerns have been raised or lowered, intellectual property rights (IPR) protection has been improved or worsened, or the producers have recognized or rejected the convenience of growing a crop. The new return depends on the precise realization of z, which is specified as a random variable with a two parameter exponential distribution. z is greater than zero with probability

exp(−γ /σ t ) (new information does not necessarily indicate positive returns – consider the Taco Bell Bt corn incident) and density that declines at a constant

rate σ t thereafter. φ ≤ 0 allows for the possibility that the probability of the returns will increase declines over time, or for the possibility that the patentees lay their hands on the most relevant and important information first.

The stochastic process above generates the distribution of r2, r3, ... from the original distribution of r1 (defined by the parameters µ and σ R ) and the parameters (θ,γ ,σ ,δ ,φ) . A solution for the optimal entry problem is a sequence of cutoff return values for

L every period that determine the entry decision, {rt }t=1 , as a function of the parameters of

41 the model. The distribution of the initial returns, the stochastic process generating the subsequent returns, and the entry rule defined by the sequence of cutoff values determine the unconditional distribution of returns at each age that depends only on the parameters of the model:

1− F(r,t) = Pr[]rt ≥ r,rt−1 ≥ rt−1,...,r2 ≥ r2 ,r1 ≥ r1 . The proportion of GM patent holders who enter at age t is the proportion with current returns above rt , but with the previous period returns below rt−1 , which can be written as

π t = F(rt ,t) − F(rt−1,t −1) .

π t thus also depends only on the vector of the parameters of the model (i.e., by w= (µ,σ R ,θ,γ ,σ ,δ ,φ) ). With these definitions, the likelihood of a particular value of the parameter vector conditional on the actual (observed) data is, l(w) = ∑∑n( j,t)log(π ( j,t, w)) , jt where n(j,t) denotes the number of approvals of patents granted at time j and t years after patenting. The distributional specifications for the stochastic returns are by no means final – these were chosen as the most economically and empirically justifiable given the industry facts we have at the moment. Different distributional specifications are certainly possible, including continuous ones, and should be favored if they are considered to reflect the actual situation in the GM crop markets better. One suggestion would be to make the entry costs stochastic but with a declining mean. We would like to point out once more that the distributional specifications for the stochastic returns and this evolution are essential for this model, and probably are even more important than the parameter values. The reason is that it is these specifications, together with the parameter values, that give rise to particular patterns of entry that should be compared to their real life counterparts, so in effect one must test the validity of the functional forms as well as their parameters. The need to be as flexible as possible in the distributional assumptions also explains why the model is solved numerically. 42 This model can be solved recursively using numerical methods. The simplest way to proceed is to generate the population of the initial returns and their evolution over time, using either repeated Monte Carlo sampling or, better, Gaussian quadrature nodes. Then, the program should solve the problem recursively, starting at the terminal (patent expiration) date, for whether entry is optimal for a given current realization of r.21 The

L solution is a sequence of cutoff values, {rt }t=1 , that specify whether a firm should enter given it gets a return rt, i.e., enter if rt ≥ rt and do not if otherwise. This sequence then

L determines the entry proportions for each age, {π (t)}t=1 , all being dependent on the parameters, and functional specifications, only. The maximum likelihood estimation of the parameter vector w from the actual entry data is more computationally burdensome, as it requires the use of nested fixed point estimation. However, Matlab routines for similar problems are available and would require but a few adjustments to be suited to this particular problem.

2.3. DATA DESCRIPTION AND ANALYSIS In searching for data that would most adequately reflect the decisions of biotech companies entering foreign and domestic markets with particular patented genetic events (GM crops), we did not find any sources that would provide the exact identifiable market entry dates. In fact, an entry into a market is not a one-time event, as it takes time to establish capacities, contract retailers, get approvals, and otherwise prepare the ground. However, there might be certain events that are likely to indicate that the entry commitment has been made, i.e., the option has been exercised.

21 If this problem is to have a real real options setup, contingent claims analysis, there is a potential issue of finding the right twin security, i.e., with perfectly correlated returns, that would be used to determine the required rate of return. This rate of return is then used to derive the so-called adjusted risk-neutral probabilities, defined as p=[(1+r)-d]/(u-d) in the real options literature, that allow expected values to be discounted at the risk-free rate. This eliminates the common mistake of comparing projects with flexibility to the “naked” projects that allow for no flexibility. In the absence of such a twin security, one can derive the required rate of return by assuming that risk of entering a particular market is a function of average market risks. Otherwise, one must use actual probabilities of future returns, and problem becomes more like a decision tree analysis (DTA), which is basically equivalent to the real options but leads to overestimation of the option value.

43 One such event is getting a GM crop approved for production and/or consumption in a certain country. The particular significance of an approval comes from the fact that we are dealing with genetically engineered food and feed, the approval of which implies long and expensive scrutiny. Had the subject of an approval been less controversial, the whole procedure would be of much less significance, but GM crops have been considered unsafe for consumption and unpredictably dangerous to the environment for enough to warrant special attention. There is significant evidence that suggests that the process of approval of GM crops and/or food in any particular country is both costly and lengthy, perhaps, with the exception of the US and particularly Canada. It usually takes up to several years to get a crop (event) approved, and the approval process demands constant attention and injection of resources on behalf of the applicant. It is hard to imagine that dealing with other aspects of entry can take that long. Thus, while an approval date can certainly be a noisy indicator of entry date, we assume that this particular event is coincidental with entry. The data set that we use comes from a Canadian non-profit initiative called Essential Biosafety, which is currently funded primarily by the Monsanto company. The purpose of the initiative is to provide an “information resource and educational tool to meet the needs of scientists, regulatory personnel, policy makers, and others interested in the environmental and food safety of GM plants”. The Essential Biosafety webpage gives access to a comprehensive, veritable, and constantly updated GM crop database that contains precisely the newest and quite detailed information on all the existing events, i.e., traits infused into/imposed on certain crops via genetic modification. In particular, the database provides data on the approval of all these events in different countries. Unfortunately, these data do not contain any other economic indicators, which probably is symptomatic of the general lack thereof. A cursory examination of the data on GM crops that have been developed so far reveals that, to date, 78 events of 17 crops have been patented. The most widely “genetically altered” crops are:

44 - Corn (maize): 22 events, 9 of which provide resistance to the European Corn borer, 19 provide resistance to various herbicides, and one is resistant to the corn root worm, some events actually produce combined pest and herbicide resistance. - Argentine canola: 15 events, 12 of which are herbicide tolerant, and the rest have modified seed fatty acid content and male sterility. - Soybeans: 7 events altogether, 5 of which have herbicide tolerance, and 2 have modified seed fatty acid content. - Cotton: 7 events, 3 of which provide pest resistance, and 5 herbicide resistance. The rest of the GM crops include carnations (3), chicory (1), flax/linseed (1), melons (1), papayas (1), polish canola (2), potatoes (4), rice (2), squash (2), sugar beet (2), tobacco (1), tomatoes (6), and wheat (1).22 The main crop developers are Aventis Cropscience, Du Pont, Monsanto, Syngenta Seeds, Pioneer Hi-Bred International Inc., and Astra-Zeneca. The approval time-span encompasses the period from 1994 to 2002. Unfortunately, the database does not contain the patenting dates, so we gathered the dates of patenting from elsewhere. In cases where the patenting dates were not available, we assumed them to be coincidental with the date of the first approval, which always happened in the US, so there is a high chance that the approval and patenting indeed happened at the same time. It should be mentioned that there are different types of approval listed in the data set: environmental, food, feed, and marketing. Unfortunately, marketing approval was granted only to a negligible fraction of events, and there is no detailed explanation of what these different types of approval actually mean. We thus assume that an event has been approved if it has received both environmental and food and/or feed approvals. Ideally, we would like to have data rich enough to define a pattern of entry for every country and, most importantly, for every patent cohort, i.e., a group of patents granted at the same time. However, though currently there exist as many 78 approved events, their approvals are so scattered among countries and across time that no proper econometric analysis is possible.23 We thus resort to using descriptive statistics of the worldwide and

22 It is probably indicative the prevailing herbicide tolerant trait is that of glyphosate tolerance – something pioneered and proven popular by the Roundup Ready soybeans has been attempted in many other plants. 23 The overwhelming majority of approvals still happen in the US and Canada. 45 regional approval data, which by assumption identifies entry, and, for now, consider frequencies of approvals rather than their proportions. Table 2.1 contains the number of approvals by country and by time measured by the number of years since the event’s patenting.24 Clearly, the US and Canada have a great lead in the number of approvals, which should be attributed mainly to the fact that all the common obstacles to GM crop introduction are much less severe there.25 In particular, the entry costs there are likely to be very small in comparison to the expected returns. Regulatory approval is likely to take less time and resources, and respect for intellectual property rights on patented innovations is much more pronounced in these countries, i.e., there is virtually no uncontrolled diffusion by illegal replanting of GM seeds. In addition, consumer attitudes are more accommodating, and producers are more receptive to agricultural innovations. But, most importantly, there is much less uncertainty/risk associated with the future returns from marketing the GM crops, and, therefore, the value of the option to defer entry is not as large as elsewhere, hence the early approval. On the other hand, it is precisely the ease of approval that might make the data on countries like US and Canada less meaningful in the context of our model in the sense that approval there is less likely to imply entry. These concerns aside, the entry proportions approximated by the national approval data give rise to some interesting observations. Figure 2.1 shows the frequency of approvals worldwide plotted against the number of years between patenting and approval of an event. This time reflects how long a patentee waited after he effectively acquired an option to enter a (foreign) market before exercising it, i.e., the time the option was held before it was exercised. Clearly, there is a downward trend in the approval frequency, indicating that most of the events, genetic modifications of crops, occur soon after patenting. However, the figure does not indicate immediate approval and market entry.26 The approvals happening

24 The economic rationale behind our reasoning justifies measuring approval/entry dates only by the time since patenting and not by the calendar time. 25 We were surprised to see the only GM trait of papaya (nutrient enhancement) being approved for environment and consumption only in the US and Canada and nowhere else. 26 While getting an approval might not necessarily mean entry, an entry into a market definitely implies an approval, i.e., an approval is a necessary condition for entry. 46 some time after an opportunity to enter appears is indicative of a positive option value of this opportunity, a call-like option to defer investment. In other words, there is uncertainty in the markets for GM crops, and therefore any flexibility in decision making presents economic agents with a non-negative option value (the right but not the obligation) and makes many of them wait for new information to arrive in order to be able to estimate the expected returns more precisely and make better decisions.

Approval date (years after patenting) 0 1 2 3 4 5 6 7 8 COUNTRY Argentina 23 11 7 Australia 1 113363 1 120 Brazil 1 1 Canada 16 18 11 4 3 1 53 China 1 1 Czech Republic 1 1 European Union 153 9 Japan 2 10 15 2 2 1 2 34 Korea 3 3 Mexico 21 3 Netherlands 2 2 Philippines 1 1 Russia 1 1 South Africa 11 1 3 Switzerland 2 1 3 United Kingdom 0 United States 33 14 5 2 1 55 Uruguay 1 1 TOTAL 52 45 47 18 11 9 11 4 1 198

Table 2.1. Worldwide GM Crop Approval Data

47

Generally speaking, had there been no uncertainty, agents would make a decision either to enter immediately or never to enter. Another consistency with the real options approach shows up in the fact that, though the frequency of approvals declines with the patent age, which can be attributed to declining returns due to substitution and other obsolescence effects and because of declining entry costs, the decline is significantly less steep (more gradual) at later ages. This is because, as the patents’ time to expiration declines, so does the option value, which provides an additional incentive to enter. While we do not have exact information on the length of patents that protect these genetic events (many are patented in different countries), it is very likely to be comparable with the time span in Figure 2.1. The downward trend in the approval frequency is much less noticeable in the early ages of patent lives. As a matter of fact, approvals peak again around the patent age of 2, which most probably accounts for many patent holders being willing to defer immediate entry. Note that there is no universal, unaccounted for, or exogenous influences - the frequencies show approvals at the same patent age, not at the same calendar time. Our observations can be refined in two ways: 1) by eliminating the US and Canadian approvals from the sample as they are less likely to indicate entry because of the relatively trouble-free approval. Figure 2.2 below shows the predictable result: only the second peak in approvals remains, since which the numbers of approvals decline; 2) by dividing the world into two regions represented by industrialized and developing countries.27 Assuming that the influences within the two regions are similar yet there are significant differences between the two, and that the entry costs are proportionate to the size of the market, such division should highlight the differences in uncertainty and distribution of the returns and thus in the value of the patents between the two regions. Arbitrarily assigning Argentina, Brazil,

27 The word industrialized applies to agriculture as well. 48 China (?), Mexico, Philippines, Russia, South Africa, and Uruguay to the second region and the rest to the first, we get the following trends, presented in Figure 2.3.28

Worldwide Frequency of GM Crop Aprovals 60

50

40

30

20

10

0 012345678 Years after patenting

Figure 2.1. Worldwide Frequency of GM Crop Approvals

It is obvious from the figure that, while in the industrialized countries most of the events get approved soon after patenting, the overwhelming majority of approvals occurs just above the age of 2. On the one hand, this might be indicative of the fact that it takes relatively longer to get a crop approved in the developing countries, which is not a good guess because approval is probably more difficult and lengthy in countries like EU and Japan. On the other, the difference between the approval patterns in the industrialized and developing countries (Figures 2.3) might signify that:

28 Other refinements of the current data are possible, such as adjusting the size of agricultural markets or omitting the less popular crops. 49 1) the volatility of the returns (parameters σ and σ R in the model) is higher in the developing world; 2) the probability of discovering that an event cannot be marketed at all (negatively related to parameter θ in the model) is also higher in the developing world, which results in a high value of the option to defer entry, hence the pattern. 3) the depreciation/obsolescence rate of introduced genetic events (parameters δ and φ in the model) in the industrialized world is higher due to substitution. Again, the difference between the decline in the approval frequency immediately after the peak and closer to patent expiration is more pronounced in the developing world. As we argued above, this reflects a higher option value due to greater uncertainty.

Worldwide Frequency of Approvals without the First-Year Approvals in US and Canada 50

40

30

20

10

0 012345678 Years after Patenting

Figure 2.2. Worldwide Frequency of Approvals without the First-Year Approvals in the US and Canada29

29 For illustrative purposes, the smoothed plots are used. 50 Frequency of GM Crop Approvals in Industrialized Countries 60

50

40

30

20

10

0 012345678 Years after Patenting

Frequency of GM Crop Approvals in Developing Countries 7

6

5

4

3

2

1

0 012345678 Years after Patenting

Figure 2.3. Frequency of GM Crop Approvals in Industrialized and Developing Countries

51 2.4. SIMULATION RESULTS The purpose of simulating the entry process is to verify whether real world entry data can be replicated using real option theory applied to biotechnology patent rights and to examine the sensitivity of the process to the parameter specification. Overall, the simulation results confirm the empirical observations above. Intuitively, uncertainty, or volatility, of future returns implies that the option to enter has a positive value, which results in delayed entry as compared to a deterministic version of the model. The higher is the risk of losing money in the future, the higher the option value at any time. Still, the probability of entry, equivalent to entry frequency in case of multiple firms and markets, should decline over time due to declining option value in comparison to the remaining expected returns, i.e., the option expires together with the patent. The mean of the entry probability distribution should shift to the right in response to an increase in the volatility of the returns from entering, which implies that the option value becomes more significant and entry in the early ages is less likely. Therefore, the entry probability should decline at a lower rate in a more uncertain environment. In other words, entry occurs earlier if the returns are more predictable, as there is less option value to entry deferral to forego.

The model is simulated using the MATLAB software and the Compecon library for MATLAB programs that accompanies a book on Computational Economics by Miranda and Fackler (2002) and provides excellent numeric optimization and function approximation tools. The optimal entry policy is computed by solving the model recursively by comparing the values of entering and not entering, i.e., according to the equation (1). The patent value is a function of the current return and time. The optimal entry policy is a T-vector of the minimal return values that trigger entry at every particular time. After the optimal entry policy is found, a sample of the initial stochastic returns is generated and their evolution is simulated. Using this simulation and the optimal entry policy, i.e., the critical return values, the entry probabilities (proportions) for each patent age are computed, which can be compared to the real world data.

52 The minimal returns that trigger entry are always decreasing with the patent age, which reflects the declining value of the option to defer entry. A typical optimal policy rule looks like one in Figure 2.4.

Figure 2.4. Optimal Entry Policy

Of particular interest are the plots of entry hazard probabilities against the patent age – something that can readily be compared to the empirical data available. The entry hazard rates in the simulation set in discrete time are just probabilities of entry during a certain period given entry has not occurred before. It is assumed that the patent length is ten years, and that after patent expiration the profits are competed away to a zero level. A few sample simulation results are presented in Figure 2.5 below.

53

a) E[r0]=E[z]. Proportion of products that are marketed before patent expiration: 0.70

b) E[r0]

54

c) E[r0]

Figure 2.5. Sample simulation results

The hazard rate of entry is decreasing and convex in the age of the patent due to the finite option life and depreciation of returns. The jump in the first period that sometimes shows in the simulation results is by no means accidental or erroneous. It is related to the separate specification of the distribution of the initial returns and the stochastic process governing their subsequent evolution. It shows the sequence of decision making: immediately after patenting, current profitability of an event (crop trait) is assessed, but ambiguity about the evolution of future returns still remains. If the trait has good profitability potential that has not been perceived initially, the next period realization of the random variable z is likely to be higher than the initial assessment of current returns. Thus, it is the first realization of z, the truly random component of the

55 returns evolution, that the patentees are waiting for. If the distribution of z has a higher mean than the distribution of the original returns, there will be a jump in the entry hazard rate after the first realization of z has been observed, even if the variance of z is higher than that of r0. In the current version of the model, the jump occurs only in the first period, i.e., when z presents itself. It is almost as if the biotechnology companies learn something new about the stochastic process of the returns evolution (the distribution of z), not just the next realization. Introduction of additional random variables affecting the returns evolution in subsequent periods would produce a smoother temporary increase/decrease in the entry hazard rate – something similar to the Figure 2.3, which shows frequency of entering markets in the developing countries. In Figure 2.5a, the means of the distributions of the initial returns and of z are the same; in 2.5b, the mean of z is slightly higher, and the difference is even greater in 2.5c. By the virtue of this argument, the difference between approval patterns in the two world regions can be explained in part by the higher degree of market risk in the developing countries. While the initial assessment of the current returns from marketing in a particular country may have been low (probably a result of underestimation), in the first years of patent life the biotech companies were finding that the average profitability there was higher than expected, which triggered higher entry levels. In the industrialized world, however, the stochastic processes governing the returns evolution were known from the start, and that is why the probability of entry is the highest in the beginning.30 Another illustrative aspect of the model is depreciation of the returns. Clearly, slower depreciation of the returns (higher δ ) increases the value of entry deferral relative to the value of entry and shifts the distribution of entry hazard rates to the right, which is illustrated by the thicker right tail of the distribution. This result is consistent with the observation of the differences between approval proportions in the industrialized and developing countries: patent depreciation in the industrialized countries is higher than in the developing ones, most likely due to the higher rate of arrival of substitutes (consider,for instance, the number of different herbicide tolerant soybean traits approved

30 Alternatively, the initial returns could have been overestimated. 56 in the US and Canada). Figure 2.3 illustrates this difference (similar to the one in Figure 2.6).

High δ (0.9) – slow depreciation

Low δ (0.5) – fast depreciation

Figure 2.6. Change in δ – the rate of depreciation of the returns 57 The (sunk) cost of entry has a similar effect: higher depreciation of entry costs due to an easier approval procedure or establishing retail networks is largely equivalent to lower depreciation of the returns. While there can be a certain momentum in the developing world, it is reasonable to expect the initially high entry costs to decline relatively fast.

The simulation results are quite sensitive to θ , the parameter that affects the probability of the absorbing state of zero returns: the higher is θ , the lower the probability of zero returns. Lower probability of zero returns increases the entry hazard rate almost uniformly. It is effectively equivalent to a reduction in the uncertainty of the returns, which implies a reduction in the value of the option to defer entry (or investment). Other things being equal, reduction in uncertainty increases the probability of entry at any time, particularly in the beginning of the option life, as the patentees are facing “cumulative” uncertainty. Figure 2.7 on the next page illustrates. Again, one can see a correspondence of these results to empirical data. The returns from marketing a GM crop are more likely to turn into zero in a developing country, primarily due to the crop’s fungibility - the farmers re-plant the GM seeds without paying for them (Moschini and Lapan, 1997, Traxler, 1999 and 2003). For example, illegal planting of herbicide tolerant soybeans has been quite widespread in Argentina. Unless intellectual property and patent rights are re-enforced there, the patent holders may consider their profits gone.

58 Low θ (higher probability of zero returns)

High θ (lower probability of zero returns)

Figure 2.7. Sensitivity to θ .

59

2.5. CONCLUSIONS Even with the currently available data, it is possible to make some interesting conclusions by comparing empirical observations to the simulation results obtained from the model described in this paper. The distribution of incidences of market entry is indicative of the heterogeneity of the values of GM crops (i.e., patented genetic events). Roughly speaking, the flatter this distribution, the more heterogeneous the patent values are, and the more uncertain is their profitability. A part of this heterogeneity is attributed to heterogeneous profitability of the crops/events themselves and the other part accounts for the differences in the profitability of the markets where the entries occur. Insufficient volume of the currently available data does not permit separation of these two effects perfectly. However, the differences between the frequencies/proportions of entry in the industrialized and developed countries show that an average value of a GM crop event is lower and heterogeneity of the values, as well as uncertainty of the returns, is higher in the latter. This confirms the well-known facts about poor intellectual property rights enforcement in the developing world, as well as high entry costs there, all of which prevents biotech companies from entering those markets. There has been a lot of controversy about whether GM crops actually benefit the developing countries or harm them in the way the “green revolution” arguably did, but it appears that many of the genetic events can potentially be more beneficial to the developing countries than to the industrialized ones, at least in the short run (in particular the crops with enhanced nutrient content). So far, the data analyzed in the light of the model developed in the paper suggest that biotech companies recoup most of their R&D expenses, and earn most of the profits, from marketing their agricultural products in the industrialized part of the world, despite the sometimes strong consumer and government opposition. While it is hard to determine exactly what proportion of patents accounts for the bulk of the profits from the R&D activities, it appears that most patented genetic events do not generate any significant profits for their developers.31

31 So far, industry facts and adoption volumes suggest that most profits have been earned from selling glyphosate resistant soybeans and Bt corn to farmers. 60 Overall, the sensitivity analysis of the simulation results suggests that the option value of deferring entry, i.e., the option value of patents on crop genetic events, is higher in the developing countries. High volatility of the returns from marketing GM crops makes biotechnology firms delay entry into foreign markets in order to obtain more information on the prospects there. Of course, the higher option value does not compensate for the difference from the value in the industrialized world; it only partially offsets the unfavorable influences present in the developing world. In particular, the results suggest that the probability that marketing a GM crop will bring zero profits, and the volatility of positive returns, are both higher in the developing countries. However, the returns from marketing GM crops in the third world do not decay at as high a rate as in the industrialized countries, possibly due to higher arrival rate of substitutes in the latter – something that also partially offsets the disadvantages of marketing there.

61 ESSAY 3

PATENT POLICY ANALYSIS FOR THE CASE OF AGRICULTURAL BIOTECHNOLOGICAL INNOVATIONS

ABSTRACT

In this essay, certain peculiarities of the process of development of agricultural biotechnological innovations are considered, in particular the distinction between an

R&D race for a gene (genetic event) discovery and subsequent competition for developing the discovery’s marketable applications in the form of genetically modified crops. A formal model is specified and analyzed with regard to how different patent protection policies affect firms’ R&D strategies and social surplus from innovations. It is found that inclusive scope patent protection unambiguously encourages more R&D and faster innovation diffusion than the additional scope protection, which, in turn, is superior to length protection (which speaks in favor of U.S. patenting practices as compared to those of the European Union). Introduction of licensing into the model either preserves or reverses the ranking of protection regimes depending on the nature of licensing contracts.

62

3.1. INTRODUCTION. The Process of Agricultural Biotechnological Innovations The purpose of this essay is to provide some insight into the structure and mechanics of the process of development and appropriation of agricultural biotechnological innovations at the current stage of the industry lifecycle. In particular, we are interested in the issue of how different patent protection regimes affect the outcomes of basic biotechnology R&D and introduction of its applications, genetically modified (GM) crops in agriculture. Despite the fact that biotechnology has been around for a number of years and is an important industry with great potential, considerable ambiguities in the intellectual property rights protection of biotechnological innovations remain, which warrants attention (Brennan, Pray, and Courtmanche 2000, Utterback, 1994, Kalaitzandonakes and Bjornson, 1997, Kalaitzandonakes and Hayenga, 2000a). A stylized structure of the process of agricultural biotechnological innovations is shown in Figure 3.1. (based on Brennan Brennan, Pray, and Courtmanche, 2000, and Harhoff, Regibeau, and Rockett, 2001). The process starts with the first stage, the basic discovery R&D race, during which firms in the industry compete for the discovery of a particular gene. A gene discovery usually implies that the gene and its functions are identified, together with the physical ways of separating the gene and its particular traits and inserting them into a target plant’s DNA. The firms in the industry may be looking for a particular gene at a time, or for a number of genes. This process is characterized by a considerable degree of uncertainty, as R&D processes are of a creative nature, and it is hard to identify what factors or events contribute to the frequency of incidences of successful innovations. The firms’ strategies at this stage are likely to be investments in R&D that “buy” random discovery dates. The investments can be lump-sum or flows, and can vary over time depending on the firms’ strategic considerations. Obviously, R&D investments and the gene discovery date λ depend on the rewards firms expect from it, on the number of firms, the nature of competition, and the R&D “cost” function.

63 End of the application Patenting the diffusion, Tg The process Gene discovery gene at λ + ρ begins date λ

The gene is under patent protection Stage 1. R&D Race for a Gene Discovery

Stage 2. Application Development and Marketing

The gene discoverer is developing The patent granted the gene applications Competitive application monopoly stage development and marketing

time

Figure 3.1. Structure of the Process of Agricultural Biotechnological Innovations

A gene discovery in agricultural biotechnology does not, apart from the gene’s licensing value, imply any immediate gains, as the value of the gene can be realized only through the development of its marketable applications, i.e., GM crops with certain traits, which can be either cost-reducing (herbicide or pesticide resistant) or quality enhancing (enhanced vitamin or nutrient content). It is during the second stage of the process that the value of the discovered gene is determined and shared between the firm that originally discovered it (the leading firm) and the rest of the firms in the industry. The analysis in this essay assumes that the same firms that participate in the gene discovery race are also involved in the application development and introduction, which is a close approximation to reality. During the application development, or diffusion, stage the strategies of the gene discoverer (the leader) and of its rivals differ. As is shown in Sections 3 and 4, under certain patent protection regimes, the leader finds it profitable to wait before patenting the gene, even 64 under the threat of “re-discovery” by a rival and the presence of knowledge spillovers. During this time, defined as ρ in the figure above, the leader takes advantage of being the only one who possesses the new information on the gene by working on its applications, i.e., developing different GM crops that utilize the discovered gene’s functions. The time of patenting the gene is chosen strategically and depends on the length and scope of patent protection, potential profitability of applications, licensing opportunities, and the structure of the industry. Under patent protection, the leader enjoys monopoly status and continues to develop, market, and possibly license GM crops after patenting. However, when the patent expires, the remaining firms in the industry start competing for the remaining applications, which brings profits down to zero. The diffusion of applications stops at time Tg when all possible applications of the gene have been discovered and marketed. In the model, agricultural biotechnological R&D is specified as a two-stage process, with the first stage determining the industry leader and the gene patent holder, and the second determining the payoffs from appropriating the market value of the gene’s applications (GM crops). It is recognized that the two stages are of a different nature, yet are related, as one determines the incentives and intensity of participation in the other. It is also recognized that, in most cases, private payoffs from innovative activity do not coincide with the social benefits from it, as society generally does not care which firms benefit from an innovation or how the benefits are distributed among them. Generally, society benefits from the fastest possible introduction of as many innovations and their applications as possible. In the case of agricultural biotechnology, society would be interested in maximizing the discounted value of all applications associated with a

d −(τ +t ) th particular gene, i.e., max v (1+ r) i , where v is the discounted value of an i ∑1 i i application at the time of its introduction and ti is the time of its market introduction since the gene discovery. After disaggregating the process into two stages, the dual goal becomes minimizing the time it takes to discover a gene and maximizing welfare from the introduction of its applications. It is unfortunate that the best imaginable mechanism for ensuring optimal private R&D and innovation diffusion, simply paying the inventor an amount V* from the federal

65 budget, is rendered infeasible by the lack of information about the R&D “production function” and by the redistribution costs. Instead, governments use a set of policy tools in order to influence the outcomes of innovative R&D activities. Different levels of intellectual property rights protection and antitrust policy are by far the most common ones. Patent protection is guaranteed by patent law and in fact endows the patent holder with limited monopoly power, and antitrust policy is exercised mainly as selective approval of mergers and acquisitions and regulation of entry barriers. Considering the nature of the agricultural biotechnology R&D process, it is of interest to question how these different regulatory policies might affect the outcomes of the patent race and application development stages, and what welfare they result in. Two different models from the literature on economics of innovation are used in the analysis of the effect of these policies on the social surplus from the innovation diffusion. The analysis, while presenting some ambiguities, defines a certain ranking of different patent protection regimes in terms of their social desirability.

3.2. GENE DISCOVERY R&D RACE The process of discovery of a basic innovation always involves uncertainty. However, while there is always a heavy dose of serendipity involved in making any significant scientific breakthrough, particularly in biotechnology, success is also inevitably determined by the amount of money put into it. This, and the non-cooperative nature of R&D efforts pursued by firms working on the same issue, has led to modeling competition in the R&D sector as a tournament game that also resembles a “war of attrition”, where R&D firms continue investing in the research until the discovery is made by one of them. Once this happens, the winner reaps the rewards for being the first to make the discovery, and the rest of the firms drop out of the race, possibly diverting their efforts to other research areas. The literature on competition in the R&D sector, the so-called patent, or R&D, race models, have tried to throw light on the issue of what affects the time it takes an R&D industry to make a discovery. While the intuitively plausible conclusion that greater

66 reward for winning a patent race shortens the time it takes the industry to make a discovery has always been agreed upon, whether more severe competition in the R&D sector has the same effect has been a point of contention. On the one hand, competition should stimulate individual firms’ R&D efforts; on the other, it might also have a discouraging effect and reduce individual firm investment. It is not clear which effect will prevail, and thus how the level of competition affects the time it takes the industry to make a discovery. Out of the voluminous literature on patent (R&D) races, we have chosen Lee and Wilde’s (1980) model, which is a modification of Loury’s (1979) model relating the innovation process to market structure, as the most obvious way to illustrate the mechanics of the process. An R&D industry consists of N identical firms playing a non-cooperative Nash game of racing for a discovery. Assuming that the firms pursue discovering a particular gene with a view to inserting it into agricultural crops in order to enhance their characteristics, implies identifying the gene’s functions and finding a way to separate it. Racing for a single gene can be justified by assuming that the gene is believed to have the greatest potential number of lucrative marketable applications, like the genes responsible for herbicide and pesticide tolerance, which makes non-cooperative pursuit of its discovery more worthwhile than coordinating firms’ efforts and pursuing different discoveries at once. Discovering the gene itself does not result in an immediate payoff to the inventor. The gene itself is not marketable, unless one licenses it, – the inventor can only earn money by selling the gene’s marketable applications, in particular the crops into which the gene has been inserted. The process of inserting the gene into the germplasm also takes time and, as is shown in subsequent sections, the profits from marketing GM seeds are determined not only by the demand for them but also by how many marketable applications this firm can appropriate and when. This, in turn, is determined by the kind of patent protection that is granted to either the basic discovery or its applications and by the industry structure. For now, assume that the first firm that makes the discovery is simply awarded a reward of V. The firms’ strategies are described by a fixed cost investment F and a flow

67 of per period investments xi that continue until one of the firms stumbles upon the discovery. These investments purchase this firm a random discovery dateτ (xi ) that is assumed to be exponentially distributed:

− h ( xi )t pr[τ (xi ) ≤ t] = 1 − e , (3.2.1) which implies that the expected introduction time is,

E[τ (xi )] = 1/ h(xi ) , (3.2.2) where h(xi) is equivalent to a “cost” of R&D and exhibits some initial increasing returns, which determines a long-run industry structure with a finite number of firms (natural oligopoly):

h(x)

~ x x x

Figure 3.2. The R&D “Cost” Function

Defining the date of discovery by firm i’s rivals as τ (xi ) = min{τ j (x j )} and probability of j≠i

ai this happening before time t as Pr(τ i ≤ t) =1− e , where ai = ∑h(x j ) is a constant j≠i instantaneous probability of introduction by the rivals, the expected benefit to a representative firm from investing in the R&D is:

68 ∞  t  Vh E[B] = Pr(τˆ = t) Pr(τ = s)Ve −sr ds dt = , (3.2.3) ∫∫i   00  a + h + r and the expected costs are

∞  t  x E[C] = xe −rs ds Pr(τˆ = t _ or _τ = t)dt + F = + F , (3.2.4) ∫∫  i i 00  a + h + r making the expected profit from participation in the gene discovery R&D race V − x E[π ] = E[B] − E[C] = − F . (3.2.5) a + h + r An analysis of the optimization conditions and comparative statics leads to the following conclusions: - an increase in the number of firms in the industry leads to an earlier discovery date, i.e., dE[τ (N)]/ dN < 0 . - an increase in the number of firms decreases expected profits: dE[πˆ]/ dN < 0 . - given a specific stability condition, the equilibrium individual firm investment increases in the number of firms (size of the industry): dxˆ / dN > 0 . This is the opposite of Loury’s result ( dxˆ / dN < 0), which is a consequence of the difference in investment specification – Loury did not assume a lump-sum investment. Another important and obvious conclusion is that an increase in the reward from the discovery, V, increases individual firm R&D investment and, therefore, results in earlier introduction. This is a very important observation, as the value of V is determined at the gene application development stage of the innovation process. This stage represents an altogether different game which is the main focus of the article. As is shown in subsequent sections, the private payoff V for winning the R&D race depends not only on the profitability of individual applications of the basic discovery, but also on the gene and application patent protection regimes (appropriability), firm behavior and, to some degree, antitrust policy.

69 3.3. APPLICATION DEVELOPMENT AND INTRODUCTION STAGE After the gene discovery, the gene’s potential value has to be appropriated. In agricultural biotechnology, this happens through development and marketing of the gene’s applications, or genetic modifications of agricultural crops engineered by inserting the gene into their DNA, which results in acquisition of a particular useful trait, such as herbicide resistance or enhanced nutrient content. There is much less uncertainty involved in the process of application development, which implies that firms in the industry can more or less precisely estimate the time it takes to develop an application, as well as the total number of applications that can be developed from the newly discovered gene that corresponds to the number of crops whose value can be increased by a trait inflicted by the gene’s insertion. In the model presented below, these facts are accommodated by the following assumptions (some of which are borrowed from Matutes, Regibeau, and Rockett, 1996): - A total of d marketable applications can be developed from the gene, the number d being equivalent to the number of agricultural crops that become more profitable due to acquiring the gene’s trait. - There are N identical competitive firms in the R&D industry, each capable of developing and marketing applications of the basic discovery. - The applications can be developed by a single firm with a fixed speed of one at a time. This reflects the fact that firms have limited resources, which is due to their resource scarcity, market rigidities, and possibly natural limits to the firm’s size. - ρ defines the time between the gene discovery and gene patenting. As we show below, it is sometimes privately optimal for the inventor to wait before patenting in order to use this time to develop more applications that will be covered by the patent. - Before the first application is introduced by the original gene discoverer, i.e., before the gene is patented, the rivals cannot get hold of the information that would enable them to start developing their own applications. We also assume that neither the patent nor already introduced applications contain enough information for the rival R&D firms to develop or reverse engineer other

70 applications. This assumption reflects the realities of genetic research. Alternatively, however, one can assume that the penalties for patent infringement are sufficiently high to discourage rivals from it.

- Tg defines the gene applications diffusion time, the time it takes for all possible gene applications to be developed and introduced. - Markets for applications are assumed to be independent of each other, and marketing of each application yields a flow of per period profits v. - Firms do not work on the same applications, i.e., there is no coordination problem. In the absence of rivalry, the gene discoverer would develop and introduce all the d applications himself, one at a time. With rivalry, the leading firm’s behavior depends on the type and level of the gene’s patent protection provided by patent law. In the absence of any intellectual property rights, as well as under most protection regimes, the leading firm has an incentive to wait for a period of ρ before patenting if the patent covers the ρ applications developed during this time. Doing this allows the inventor to secure more applications for himself, leaving fewer of them to the rivals after the patent expires. The most important problem is, therefore, the efficiency of utilizing the limited number of marketable applications of the basic discovery. It should be mentioned that there is always a threat that one or more of the rival firms will also stumble upon the basic discovery during the waiting period ρ. According to the specification of the gene R&D race, this threat is represented by a constant exogenous instantaneous probability of “re-discovery”. If pursuing the basic research is very inexpensive in comparison to the application development, rival firms may choose to continue investing in it in hope of discovering the same gene before the leading firm patents it and enjoys temporary monopoly status. Under any protection regime, a rival firm discovering the gene at time φ>λ can only benefit from it by becoming an industry leader if it patents it before λ+ρ. In the absence of intellectual property rights (IPR) protection, a rival firm discovering a gene at time λ can only benefit from it if it discovers it before λ+ρ thereby securing λ+ρ-φ applications before all firms start racing for them. While it is reasonable to assume that the firms are still racing for the basic discovery

71 during the period between λ and λ+ρ, as they still do not know that the discovery has already been made, it is also reasonable to assume that everybody learns the news about the basic discovery as soon as it is made and, under the “first to invent” system, independent discovery would not prevent the earlier inventor from obtaining the patent. Yet another way to treat the “re-discovery” problem is to assume that the cost of basic R&D is high enough to prevent rivals from continuing this research once they learn that the discovery has been made. Otherwise, the presence of a constant exogenous threat of re-discovery during the “secret” stage of application development shortens ρ, but leaves the ordinal results of the analysis unchanged. Below, some basic patent protection regimes are considered: scope and length protection of the basic discovery, which can be inclusive and additional, analyze their welfare implications, and discuss their relative advantages and disadvantages in the framework of the agbiotechnology innovation process. Then, some extensions to the basic model are developed, such as heterogeneity of applications’ profitability and the possibility of licensing.

3.4. BASE CASE.

3.4.1. Scope protection Under scope protection, a patent guarantees a given number of applications for an arbitrarily long (possibly infinite) period of time. This definition can be related to legal practice. Patent applications are filed with the US Patent Office. The core of an application is a set of claims about the innovation that can range from very specific to very general. Obviously, more general claims, if granted, correspond to greater protection than more specific ones. Approval of the claims by the Patent Office involves considerable discretion which, together with infringement suits that are likely to be filed after the patent is granted, defines the scope of patent protection. Another interpretation of scope protection is a “license to hunt” for applications in a broad field, which is granted on the basis of demonstrated usefulness of a product or process. While these

72 procedures cannot define scope with precision, the model assumes that there exists a policy instrument available to the government that defines the number of applications granted to a patent holder, s. Alternatively, firms could be assumed to form expectations as to which applications would be protected. A very broad scope is identical to total protection of a gene and, therefore, to indefinite length protection. A range of narrower scopes can be interpreted in the context of the leniency of the claim review by the Patent Office and patent enforcement by the courts. Scope protection can have two forms: - Additional scope protection, sA, means that applications already developed by the patent applicant by the time of filing to the Patent Office do not count as part of the scope granted. Under this regime, the leading firm that waits for a period of ρ before patenting gets ρ + sA applications. - Inclusive scope protection, sI, means that applications developed before patenting count as part of the scope - the patentee gets max(ρ, s I ) applications. Even when a certain number of applications are protected by the scope, a certain length of protection is likely to be granted to each application. We define this individual application length protection as τ. In general, we assume that there is a difference between the social surpluses under the monopolistic and competitive provision of applications. Real life practice of charging significant price premiums, “technology fees”, for GM crops by the seed companies that license the technology from the seed developers suggests that the patent protected seed monopoly tends to undersupply the goods. Therefore, social surplus from an innovation under competitive provision is most certainly larger than under monopolistic one, unless of course there is perfect price discrimination. While GM crops’ price discrimination is certainly possible, it is unlikely that such discrimination can truly equate the monopolistic and competitive social surpluses. w defines the PV of per period social surplus (welfare) from competitive provision of an application, and the per period surplus from monopolistic provision is v= βw , 0 < β <1.

73 3.4.1.1. Inclusive scope protection: This regime is consistent with the restrictions on pre-filing activities that exist in U.S. patent law, for example, the statutory bar in section 102(b) of the Patent Act “is intended to motivate the inventor to apply for a patent soon after invention” (Miller and Davis, 1983). Obviously, such a protection mechanism encourages immediate patenting in all cases, as procrastination does not increase the scope of the patent. The patentee simply develops the s applications granted by the patent, which takes him s periods (licensing, which we introduce later, changes that) and enjoys monopoly status on the applications granted by the patent for a period of τ (τ can also be infinity, in which case the present value of an application is v/r). The private payoff from being the first to make the discovery is the sum of the discounted present values of the monopolistic streams of profits from each application developed under the inclusive scope patent protection:

s τ V IS = ∑(1+ r)−i ∑v(1+ r)− j . (3.4.1.1) i=0 j=0 For analytical convenience, we use a continuous equivalent:

τ  s  v(1− e−rτ ) V IS = v e−rt dt e−rt dt = (1− e−rs ) ∫ ∫  2 . (3.4.1.2) 0  0  r It is easy to see that the private payoff is increasing in both the scope of the gene’s patent protection and in the length protection of individual applications: ∂V IS v ∂V IS v = e−rτ (1− e−rs ) > 0 , and = e−rs (1− e−rτ ) > 0 . (3.4.1.3) ∂s r ∂τ r

The social surplus from this type of protection consists of the monopoly surplus, equal to the private payoff, and the additional surplus that results from competitive development and provision of the remaining d-s applications: w s+τ w s+(d −s) / N W IS = βwV IS + ∫ e −rt dt + N ∫ e −rt dt = r τ r s w w βwV IS + e −rτ (1 − e −rs ) + Ne −rs (1 − e −r(d −s) / N ) . (3.4.1.4) r 2 r 2

74 Clearly, social welfare declines in both the scope and length of individual application length protection, which can be verified by assuming a limiting case of β =1, in which

∂W IS v case = e−rs (1− e−r(d −s) / N )(1− N) < 0 . (3.4.1.5) ∂s r However, WIS is increasing in the number of firms in the industry, N. The basic tradeoff the social planner faces here is that between increasing welfare by reducing the amount of protection granted to the basic innovation and applications developed from it, and encouraging innovation by raising the private payoff, VIS, via strengthening intellectual property rights (IPR) protection. While, ex post, it is always socially optimal to give no property rights to the innovator, leaving application development and marketing to competitive forces, such behavior on behalf of policy makers would completely discourage R&D investment. Graphically, the relationship between the private payoff and the social surplus from the innovation is illustrated in the Figure 3.3.

W, V

WIS

v(1-e-rd)/r2

VIS

d s, t

Figure 3.3. Innovator Payoff and Welfare as Functions of Inclusive Scope Protection

75

3.4.1.2. Additional scope protection: With additional scope protection, the number of applications developed from the basic discovery, the GM crops that “fit” into the patent claim, is additional to the crops already developed by the time of patenting. In other words, the patentee has monopoly power over the applications granted by the patent and over the ones that were developed prior to patenting. An intuitive explanation for such a situation could be that the patent claim itself can be specified more broadly once some applied research has been done with the basic discovery. During this period, the knowledge can be enhanced and refined, and thus new opportunities to claim truly novel ideas found. Clearly, under additional scope protection of the basic invention, the inventor benefits not only from early patenting, but also from doing some applied work prior to it: the private tradeoff is now between discounting the monopoly profits at a lower rate and effectively broadening the scope of protection by patenting later. Let us define the additional scope protection as s, and a delay in patenting as ρ . Whenever ρ > 0 is privately optimal, two sub-cases of the additional scope protection regime are possible: 1) The scope is relatively small, so that the patentee does not develop all the applications himself: ρ(s) + s < d . In this case, the application “pool” is not exhausted after the patent expires, and an accelerated competitive development and supply ensue. 2) ρ(s) + s > d : the application pool is exhausted before the patent expires. The “borderline” between these two cases is s which is defined by the equation ρ(s) + s = d . We consider both cases below.

1) Using the reasoning from the analysis of inclusive scope, the private payoff to the inventor in the first case is,

s −rτ τ   v(1− e ) V AS (s < s) = v e−rt dt ρe−rρ + e−rρ e−rt dt = e−rρ {}rρ + (1− e−rs ) . (3.4.1.6) ∫0  ∫  2  0  r The first order condition is,

76 −rτ AS v(1− e ) ∂V = e−rρ {}e−rs − rρ , which implies that the optimal waiting time before ∂ρ r patenting is,

−rs ρ(s < s) = e r . (3.4.1.7) The privately optimal waiting time declines with s (d(ρ(s))/ds<0), the intuition being that the larger the reward from protection (s), the higher the opportunity cost of the last application developed before patenting. However, d(ρ(s)+s)/ds>0 and d2(ρ(s)+s)/ds2<0: so that increasing additional scope protection inevitably delays the date of patent expiration and therefore the competitive stage of diffusion. Another interesting observation is that ρ is independent of the length protection of applications: if applications granted by the patent and those developed outside the patent scope enjoy the same length protection, this length does not affect the private optimization problem. The most important implication of this result is that, whenever possible, individual application length protection should be given priority in policy design, as it does not have the negative “side-effects” of scope protection.

The private maximized private payoff,

−rτ −rτ v(1− e ) v(1− e ) −rs AS V AS (s < s) = e −rρ (s) = e −e , ( ∂V > 0 ), (3.4.1.8) r 2 r 2 ∂s now is strictly larger than in the case of inclusive patent scope (V AS (s < s) > V IS (s) ) (see Appendix Section 1 for a proof). It should be mentioned that, for d and r large enough, ρ+s ≈ s due to the asymptotic properties of the exponential function. For these values, the first subcase of additional scope protection prevails. However, for reasonable values of d and r, both subcases are feasible, as the table below illustrates. 32

32 To add validity to this argument, it makes sense to mention that discounting, and therefore timing of decisions, has been important in economics exactly because it matters for values that are within real-life reasonable intervals, i.e., there is little reason to bother about the PV of a payment that is a week away or about a difference in the PV of a return that comes in 100 or 105 years. This is because interest rates reflect the opportunity cost of resources. 77 Size of the Interest rate Scope s that leaves no room for application “pool” competitive development 20 0.15 ≈20 20 0.12 ≈19 20 0.1 ≈18 20 0.09 ≈17.5 20 0.08 ≈17 20 0.07 ≈16 20 0.06 ≈12 20 0.055 ≈9 20 0.05 ≈1

Table 3.1. Sensitivity of s to the Discount rate

An important conclusion from this observation is that the nature of private and social welfare from scope protection is almost exclusively determined by exogenous factors: the size of the application pool and the discount rate.

2) When ρ(s) + s = d , the application pool is exhausted exactly when the patent expires. There is no reason for the inventor to wait so long that ρ+s exceeds d: had the application “pool” been larger, the inventor would wait longer before patenting, but now procrastination implies giving up applications granted by the scope. Thus, for scopes s > s , the privately optimal waiting time is ρ(s > s) = d − s . Assuming, for analytical convenience and without loss of generality, that infinite length protection is granted to each application, the private payoff from s > s is:

1− e−rτ  d  e−r(d −s) V AS (s > s) = (d − s)e−r(d −s) + e−rt dt = r(d − s) +1− e−rs . (3.4.1.9)  ∫  2 [] r  d −s  r 78 It is easy to verify that V AS (s > s) > V IS (s < s) . Also, V AS (s > s) is concave in s, while V AS (s < s) is mostly convex, due to the relatively shorter waiting period. Figure 3.4 illustrates.

Vas

as V2 (s)

as V1 (s)

~ s d s

Figure 3.4. Innovator Payoff under Additional Scope Protection.

Offering larger scope protection has two opposite effects on welfare. On the one hand, it improves it by reducing the time the innovator waits before patenting. On the other, because ρ(s) declines at the rate of less than one, increasing the scope delays the patent expiration time at which the speed of diffusion increases by the number of firms that will develop the remaining applications competitively. The more applications are left for this competitive development and the more firms there are in the industry, the stronger the second influence and vice versa. Also, the smaller the scope, the faster ρ(s) decreases in response to an increase in s and thus the stronger the first effect. Technically, the welfare under additional scope protection is, assuming

τ v e−rt dt = 1/r: ∫0

79 w (d −ρ−s) / N W AS (s < s) = βwV AS (s < s) + Ne−r(ρ+s) ∫e−rt dt = r 0 r(d −ρ−s) r(d −ρ−s) − −rs  −  AS w −r(ρ+s) N 1 −e −rs N βwV (s < s) + 2 Ne (1− e ) = 2 e βw + wNe (1− e ) r r   (3.4.1.10) and e−r(d −s) W AS (s > s) = βwV AS (s > s) = βw []r(d − s) +1− e−rs . (3.4.1.11) r 2

Several observations are in order. The maximum value of W AS (s < s) is limited by two factors: the minimum value of ρ(s) + s (s ≥1) and the maximum speed at which remaining applications can be developed by the competitive firms after the patent expires. While the minimum ρ(s) + s is clearly e-r/r+1, the maximum speed at which the remaining d- (ρ(s) + s) applications can be developed during the competitive stage is [d- (ρ(s) + s) ]-1. This reflects the indivisibility of intra-firm applied R&D work or, in more simple terms, shows that the firms in the industry can neither develop more than one application at a time nor cooperate so as to share the work among themselves in order to speed up the development. Thus, for a given scope s, having more than d- (ρ(s) + s) firms in the industry does not increase the social surplus. The maximum welfare in the first subcase is thus,

1 −r maxW AS (s < s, N ≥ (d − ρ − s)) = e −e [1+ e −2r (d − ρ − s)], (3.4.1.12) r 2 and in the second subcase, 1− e−rd maxW AS (s > s) = βw . (3.4.1.13) r 2 ∂W AS (s > s) = e −r(d −s) r(d − s) > 0 , (3.4.1.14) ∂s when the scope reaches s , the competitive effect disappears, and therefore W AS (s > s) clearly increases in s because there is no competitive development effect, i.e., the inventor develops all applications and increasing the scope only facilitates their 80 introduction. Therefore, for scopes larger than s , s=d is clearly preferable for both the social and private surplus maximization, as it provides both higher welfare and higher private payoff.

AS However, ∂W (s < s) can be either positive or negative. When s< s , ∂s increasing the scope trades earlier introduction of monopolistically developed applications, which is coincidental with patenting time, for shorter period of accelerated competitive development. Differentiation of W AS (s < s) with respect to s shows that it increases in s up to a certain s*(r,N) below which the effect of shortening the waiting time dominates the one of leaving more time for competitive application development. On the interval (s*, s ), W AS (s < s) is decreasing, as the relationship of the two effects is reversed. Thus, for scopes smaller than s , there usually exists an s*< s that locally maximizes welfare by providing the best tradeoff between early introduction and competitive development. However, this comes at the cost of an arbitrarily small private reward to the innovator. Graphically, the dependence of additional scope protection welfare on the scope is illustrated in Figure 3.5 (section 2 of the Appendix contains the technical details). ** For any possible minimal private payoff requirement, scopes in between s m and

* ** d are grossly inferior to scopes equal to d or within (sm , sm ) . As the private payoff function Vas(s) is monotonically increasing in s for all possible scopes, the arguments above also apply to the welfare as a function of the private payoff – Was(V(s)). The section below provides a welfare comparison between inclusive and additional scope patent protection.

81 WFas as WF1

WF2(d)

as WF2

* * s ** d additional scope, s, sm sm s or private payoff, VAS(s)

Figure 3.5. Welfare under Additional Scope Protection.

3.4.1.3. Welfare comparison The primary purpose of this modeling exercise is to find how efficient different patent regimes are in maximizing social welfare while providing a certain minimum reward to the inventor in order to ensure private R&D, as well as a certain expected discovery date. Finding the exact tradeoff between the social surplus from innovation diffusion and basic R&D intensity requires making assumptions about the exact relationship between the uncertain basic research and the application development production functions. However, the discovery/patent race and diffusion models belong to different classes, and the two processes have a different nature. Thus, only most general results from the analysis of the former can be carried over to the latter. For notational convenience, an additional assumption is made that the social surpluses from competitive and monopoly provision of applications are equal. Later it is shown that this assumption, however, does not restrain the generality of the conclusions. Suppose the policy maker maximizes social welfare from innovation diffusion, but also must ensure that the discoverer gets a minimum reward of V . 82 - Under the inclusive scope regime, the minimum scope is defined by 1 V = (1− e−rs ) , and the resulting welfare is the sum of the private payoff and the r 2 surplus from the ensuing competitive development stage. Expressing the members containing ρ(s) in terms of V , the welfare is, 1 1 W IS (V ) = V + e −rs N(1− e −r(d −s) / N ) = V + N(1− r 2V )[1− e −rd / N (1− r 2V ) −1/ N ]. r 2 r 2 (3.4.1.15) - Under the additional scope regime, when s AS < s , the required scope is given by

1 −rs V = e−e , and, r 2 1 W AS (V | s < s) = V + N(r 2Ve−rs )[1− e−rd / N (r 2Ve−rs )−1/ N ]. (3.4.1.16) r 2 1 When s AS > s , the necessary scope is defined by V = e−r(d −s) (r(d − s) +1− e−rd ) , and r 2 the associated welfare is W AS (V | s ≥ s) = V , but simply because in this subcase, as we showed earlier, the maximum possible protection is both socially and privately optimal, 1 the welfare is W AS = []1− e−rd > V . (3.4.1.17) r 2 Comparing the welfare under inclusive and the first case of additional scope protection proves that inclusive scope protection is more efficient because it provides higher welfare for any feasible private payoff V to the innovator. (Section 3 of the Appendix contains a proof.) An important additional observation that should be made from this comparison is that the results above are affected neither by the number of firms in the industry nor by the length protection of individual applications. Also, the social surplus from monopolistic provision being smaller than that from competitive provision only strengthens our findings, as it is precisely due to the longer private development and provision stage that inclusive scope protection is preferable to additional scope protection, and therefore, the welfare from the former is more sensitive to a decrease in β - the parameter measuring the difference between the monopoly and competitive 83 provision surpluses. Graphically, the comparison between social surpluses (welfare) from the inclusive and additional scope protection is represented in the Figure 3.6.

WF

WFIS

WFas WF(d) WFas(d)

* * s s** d s sm m s

Figure 3.6. Social Welfare under Inclusive and Additional Scope Protection

3.4.2. Length protection. Under the length protection regime, the discoverer of the gene is granted an exclusive monopoly right for marketing applications during a period of T. Length protection, at least theoretically, can be of two types: inclusive and additional. Inclusive length protection might be justified by an assumption that the patent authorities can determine when the invention was made and grant the length T starting from the actual invention date. In this case, immediate patenting is always privately optimal, and the private payoff

84 and welfare are very similar to inclusive scope protection.33 However, additional length protection, under which an innovation is protected for a period T since the date of patenting, seems to be a much more realistic assumption. Below, we discuss the case of such patent protection design. Again, for notational convenience, we assume that β =1, i.e., there is no difference between monopoly and competitive provision surpluses. This assumption can only be restrictive when a protection regime with longer monopoly diffusion stage is more socially desirable, which we show is never the case.

Case 1: d is large enough so that ρ(T) +T < d . Clearly, the inventor has an incentive to wait before patenting in order to develop and introduce more applications that will be protected for the same length of time. The private payoff function consists of the present values of applications developed by the patentee before and after patenting:

T T T L −rρ −rt −rρ −rx −rρ 1 rρ +1 −rT −rT  V = ρe ∫ e dt + e ∫ ∫ e dxdt =e  (1− e ) − e T  . (3.4.2.1) 0 0 t r  r  The privately optimal pre-patenting time is determined by equating the marginal benefit and the marginal loss from the delay. The marginal benefit is the present value of the last application developed before patenting that will be protected for the time T. The marginal loss is the value of delaying marketing the first patented application. The privately optimal waiting time is, e −rT T ρ * (T) = , (3.4.2.2) 1− e −rT which is decreasing and convex (see the proof in section 4 of the Appendix). Substituting the optimal ρ gives the private payoff as a function of the length protection: e−rρ (T ) V L (T < T ) = (1− e−rT ) , (3.4.2.3) r 2 which is an increasing function of T (see section 5 of the Appendix).

33 However, with introduction of licensing in the model, which we do later, such inclusive length protection becomes superior to any other type of protection as it is always privately optimal to license. 85 The time to patent expiration ρ(T)+T (the monopoly diffusion time, during which the patentee has the monopoly power over the invention) is increasing and convex in T (see appendix section 6 for technicalities). The intuition behind this result is that it is not privately optimal to respond to an increase in T with a waiting time reduction that is bigger than the increase. Consider a situation in which some initial T0 is increased to T1. The inventor can now enjoy monopoly status for a longer time - the value of post-patent protection increases, which warrants shortening the pre-patenting waiting time used to develop more applications. If the new increased length T1 protected only ρ(T0 ) +T0 applications, ρ(T0 ) − ρ(T1) would be equal to T1-T0, but because an increase in the protection length also permits developing more applications before patenting (so that more of them are “milked” under the monopoly status), ρ(T ) decreases by less than T1-

T0. ρ(T) under length protection is always greater than an equivalent ρ(s=T) under the additional scope protection (see section 7 of the Appendix). This is due to the fact that the incentive to delay patenting is now stronger, as the applications granted by the length patent are protected only for a limited period of time: all protection stops at the moment of patent expiration. Thus, length protection is less effective than additional, and therefore inclusive, scope as it leads to the most significant delay in introduction of applications due to delaying the date of patenting. The social welfare for this unrestricted subcase of length patent protection can be written as the sum of the private payoff, the competitive provision surplus from the applications developed by the patentee after the patent expires, and the surplus from the competitive diffusion stage:

1 1 (d −ρ −T ) / N W L (T < T ) = V L + e −r(ρ +T ) (ρ + T ) + e −r(ρ +T ) N ∫ e −rt dt . (3.4.2.4) r r 0 Length protection welfare is always decreasing in T regardless of the other parameters, because the reduction in the waiting time ρ(T) in response to an increase in the protection length is much weaker than in the case of additional scope protection and thus never compensates for the loss of competitive diffusion time (see section 8 of the Appendix for details). 86

Case 2: d is small enough so that ρ(T) + T > d . Here, diffusion of all applications happens under the monopoly status of the patentee. The ranges of d and r that define which subcase prevails are quite similar to the ranges for the additional scope protection, but generally they are a little larger signifying, in particular, that there is a stronger incentive for the inventor to wait. The borderline case, T , is defined by the equation ρ(T ) +T = d . If licensing is not allowed, it is clear that all possible applications will be developed and initially marketed by the original inventor. However, unlike under the additional scope regime, the inventor will wait for longer than d-T when T > T , because he retains his monopoly position for ρ+T>d . The private payoff is now constrained by the application pool size:

T d −ρ T −rρ L −rρ  −rt −rx  e  −rT 1 −r(d −ρ )  V (T > T ) = e ρ∫ e dt + ∫∫e dxdt = ρ − de + (1− e ) ,  0 0 t  r  r  (3.4.2.5) ∂V L e−rρ e−rρ (T ) = []de−rT − ρ , and hence ρ * = de−rT , and V L (T > T ) = (1− e−r(d −ρ (T )) ) . ∂ρ r r 2 (3.4.2.6) ρ(T > T ) is clearly decreasing in T, and VL is increasing in T. Thus, as there is no competitive application development, increasing T improves the welfare by decreasing ρ(T ) but reduces it by delaying the patent expiration time at which the monopoly provision of applications is replaced by the competitive provision This result is similar to the one shown for the additional scope protection regime when ρ(s)+s>d. The social welfare in this subcase is,

e−r(ρ +T ) e−r(ρ +T ) d −ρ W L (T > T ) = V L (T > T ) + ρ(T ) + ∫ e−rt dt , (3.4.2.7) r r 0 and it is increasing and concave in T (see section 9 of the appendix for proof).

87 Welfare comparisons: When we use the same efficiency criterion, i.e., maximum welfare given a minimum private payoff V , it turns out that, when licensing is not an option, length protection of the basic invention is inferior to additional scope protection in the sense that welfare for any given feasible private payoff V is strictly smaller under length protection. First, let us discuss the case of d and r large enough so that ρ(T) +T < d . Below, it is shown that length protection of a basic discovery is socially inferior to additional scope protection for all feasible private payoffs. The proof consists of several parts: 1) In evaluating the efficiency of a particular patent protection regime, the only variables of interest are the private payoff from protection (V) and the date of basic invention patent expiration, i.e., the duration of the monopolistic diffusion period, after which the competitive diffusion stage starts. This date is defined as ρ(s) + s in the case of additional scope protection and ρ(T) + T in the case of length protection. The shorter the monopolistic development stage for a given private payoff, the more socially efficient/desirable is the IPR protection regime. 2) The monopolistic diffusion stage under length protection is longer than under additional scope protection: ρ(T) +T > ρ(s) + s for s ≤ T (see section 10 of the Appendix). 3) In order to attain a given fixed private payoff V , the length T should be greater than s (see section 11 of the Appendix for the proof). Thus, given the monotonicity of the private payoff functions, T>s for any given level of V . Argument (2) above shows that the time to patent expiration is also larger under the length protection when T>s, which means that the social surplus is smaller in this case. By virtue of argument in (1) above, the welfare from additional scope protection is more efficient than the length protection, as it delivers higher social surplus for any given private payoff that provides sufficient R&D incentive.

Let us now move to the case of d and r small enough so that ρ(T) + T > d . Before, we showed that T ≤ s AS . It also happens that when s = T > max[s,T ], V L (T) < V AS (s)

88 (see section 12 of the Appendix for the proof). Thus, for the second sub-case of length patent protection, i.e., when the length is so relatively long that it does not leave any room for competitive application development and the welfare is just a multiple of the private payoff, length protection is inferior to additional scope protection and, therefore, to the inclusive scope protection as well: W L (V ) < W AS (V ) .

3.5. EXTENSIONS

3.5.1. Heterogeneity of applications. Assume that applications of the basic discovery have heterogeneous values, i.e., they can be arranged from the most to the least profitable. Such heterogeneity is real, particularly in biotechnology, genetic modification of corn or soybeans is definitely more profitable than the same modification of (gene inserted into) something less widely produced or less beneficially affected by the new trait. It is clear that, under equivalent patent protection of all applications, unless patents discriminate between applications depending on their value, which is unlikely, the inventor will always develop the most valuable applications first. During subsequent competitive development, competing firms will also give first priority to developing the remaining most valuable applications. It is easy to see that such heterogeneity does not change but only strengthens the conclusions of the basic model: both social and private losses from delaying introduction of applications developed prior to patenting (from ρ) are greater than when all applications have equal value. Moreover, the relative value of all applications introduced later is less than the discounted constant value originally assumed. In other words, heterogeneity of application values only amplifies the importance of timing in the model and thus the conclusions. Technically, application heterogeneity can be accommodated by multiplying the discounted stream of profits from an innovation by a decreasing function of the number of already introduced applications. The best way to illustrate this is to represent heterogeneity as an increase in the discount rate r that is used for discounting the revenue

89 flows from individual applications by specifying the per period revenue from an ith application as ve−qi , where i=(1,d) is the number of already introduced applications and 0 < q <1. It can be verified that all of the model’s conclusions will hold after this adjustment has been made. The value of each individual application may also depend on how many applications have been/will be introduced, i.e., applications are substitutes. In this case, the value diminishing effect of discounting may be partially or totally offset by the incentive to delay introduction of applications in order to more fully “harvest” the already existing ones. Depending on how this affects the discounting rule, the conclusions of the model might be reversed. However, such a situation is not likely in agricultural biotechnology, as different crops with the same genetic modification do not interfere into each other’s profitability.

3.5.2. Licensing. Assume that, after an innovation has been patented, the patentee can license it to other firms in the industry. In the framework of this model, licensing is in fact a royalty agreement: it gives licensees the right to develop and market applications in exchange for a royalty fee for the time the patent is in force. The royalty fee α is a fraction of the value of every application developed under the license (0<α<1), which depends on the relative bargaining power of the licensor and the licensees, i.e., α defines the terms of the licensing contract.34 If monopoly profits are larger than under competition, one might expect the licensing contract to specify the exact output volume and pricing in order to maintain the maximized collusive or monopoly profit that results in a lower social welfare. On the other hand, such provisions might be illegal. For the time being, we abstract from these considerations by assuming that the monopoly surplus is equal to the social one, which can be justified by assuming price discrimination, some of which is

34 One might argue that the industry leader may build extra capacities once the discovery is made and thus make licensing redundant. A possible objection to this would be to point to the various rigidities as well as to the scarcity of the industry specific recourses that must be employed in building such extra capacity. If these scarce resources are competitively consumed by the firms in the industry, their price will be driven up to a level at which the leader does not find it more rational/profitable than any other competitor firm to increment her existing capacity. 90 present in agricultural biotechnology, e.g., take the regional differences in prices. Below, we consider the consequences of licensing under the patent protection regimes considered in the base case.

Licensing under inclusive length protection of the basic invention: Introduction of licensing clearly does not change the incentive to patent immediately. It is also easy to see that licensing to all firms is always privately optimal if there are enough applications in the pool and the protection length is small enough so that d ≥ NT . However, if d ≤ NT , the invention will be licensed to at most n = d /T −1 firms. As we show below, this regime turns out to be the most efficient of all when licensing is allowed.

Licensing under inclusive scope protection of the basic invention: Again, introduction of licensing does not change the incentive to patent immediately. However, whether an inventor licenses the development of some applications granted by the patent to other firms depends on the discount factor, the scope, and the licensing terms. The private payoff to the inventor who licenses to n licensees on licensing terms of α under inclusive scope protection of s is (assuming for notational convenience the PV of the stream of profits from a single application to be 1/r):

1 s /(n+1) (1+αn) V IS (r,s,α,n) = (1+αn) e−rt dt = (1− e−rs /(n+1) ) is greater or smaller than ∫ 2 r 0 r 1 V IS (r,s,α,n = 0) = (1−e−rs). (3.5.1.1) r2 Closer examination of the first order condition with respect to n, the number of licensees, reveals that the optimal number of licensees n* equals 0 or N for most cases (only for

* * very small ranges of s and α is n* finite), and that ∂n > 0 , ∂n > 0 : ∂s ∂α ∂V IS (r, s,α,n) α(1+ n) rs = 0 => (1− e−rs /(n+1) ) = e−rs /(n+1) . ∂n 1+αn n +1 (3.5.1.2)

91 The figure below illustrates sensitivity of optimal licensing scope to the licensing terms and the protection scope - the same shape applies to both parameters: when they are unfavorable (too small), n*=0; when s and α large enough, n*=N , and 0

Small scope/ Intermediate scope/ Large scope/ V(n) Poor licensing V(n) licensing terms V(n) Good licensing terms terms

V(0)

IS IS IS * s s * s n =0 N n* N n =N

Figure 3.7. The Effects of Licensing under Inclusive Scope Protection

The logic behind this is that, the bigger the scope, the more unprofitable it is for the patent holder to develop the last applications covered by the scope himself as they get discounted more heavily. It is always rational to license an ith application granted by the patent if e-ri, the discount factor, is smaller than the revenue share provided by the licensing terms, α. The same logic applies to explaining the sensitivity to the licensing terms, α. Thus, a mere possibility of licensing does not always guarantee that it is privately optimal. It is obvious that welfare under inclusive scope protection is never smaller when licensing is allowed because licensing facilitates the development of applications (see section 13 of the Appendix for the details). The important implication of these results is that increasing the scope of protection under the inclusive scope regime, as well as 92 improving the licensing terms, increases incentives to license. Thus, having to provide/ensure a relatively high payoff to the inventor, e.g., ensure high inventive efforts via increasing the patent scope also increases the incentive to license and thereby speeds the diffusion and increases the social welfare/surplus from the discovery. Alternatively, when nothing more than only a small private reward to the innovator is considered necessary, the small patent scope that provides it results in low social welfare because small scopes discourage licensing and therefore protract diffusion. When increasing both the welfare and the private payoff are the only goals, and the minimum inclusive scope that triggers licensing to all the N firms is smaller than d, full inclusive scope protection is clearly optimal, as the accelerated development starts from the patenting date, also providing the highest possible private payoff given the licensing terms, α. However, a set of values of r, d, and α exists for which licensing can never be privately optimal and therefore won’t take place.

Licensing under additional scope protection of the basic invention: Suppose that, for legal and commercial secrecy reasons, licensing is possible only after patenting. Following the logic of analysis of the incentives to license under inclusive scope protection, it is clear that, if sAS and α are high enough to induce licensing, the opportunity cost of waiting before patenting and licensing is now higher – the sAS applications granted by the patent are developed by n+1>0 firms, and thus their PV increases. Therefore, the larger the patent scope and the more favorable the licensing terms, the sooner the inventor will patent. The welfare implications of introducing licensing are the same as in the case of inclusive scope. And the analysis of the differences between inclusive and additional scope protection is the same as in the base case, when licensing was not considered an option. These conclusions are confirmed by a more formal analysis below. Suppose that the scope is small enough so that the private optimization decision is unconstrained by the size of the applications pool: ρ(s) + s ≤ d . Then, the private payoff (again assuming infinite protection of applications granted by the scope) is,

93 v  s /(1+n)  v V AS (s < s) = e−rρ ρ + (1+ αn) e −rt dt = e −rρ rρ + (1+ αn)(1− e −rs /(1+n) ) , (3.5.1.3) l  ∫  2 [] r  0  r as opposed to the payoff with no licensing:

v  s  v V AS (s < s) = e−rρ ρ + e−rt dt = e −rρ rρ +1− e −rs . (3.5.1.4) nl  ∫  2 [] r  0  r First, suppose that optimal ρ(s) is the same as when licensing is not allowed. Then, the analysis is exactly the same as in the case of inclusive scope protection, (we only compare the after-patent payoffs, (1+αn)(1− e−rs /(1+n) ) and 1− e−rs ), and investigate whether the former is bigger than the latter for n∈[1, N]. If it is, licensing is privately optimal, so that the resulting welfare and the private payoff are greater than when licensing is not allowed. However, just as in the case of inclusive scope protection, the licensing terms must be favorable enough, and the scope must be beyond a certain minimal value that triggers licensing. Below this scope, licensing to any number of firms is not rational from the inventor’s point of view, and the welfare and protection regime efficiency analysis for the base case apply. Second, let us determine how licensing affects ρ(s). On the one hand, if it is profitable to license (i.e., (1+αn)(1− e−rs /(1+n) ) >1− e−rs ), the inventor can wait longer before patenting thus developing more applications while still getting the same profit from the additional scope protection after patenting. On the other hand, intuitively we can expect that, if licensing increases the after-patenting private payoff, the balance between accumulating unpatented applications and patenting early is tilted towards the early patenting, and thus the optimal waiting time ρ(s) is smaller. Below, among other things, we show that, when licensing is privately optimal, it can only shorten the pre-patenting waiting period. The optimal waiting time under the additional scope protection with licensing is : 1 ρ AS (s,α,n) = ()e −rs /(1+n) −αn(1− e−rs /(1+n) ) < ρ AS (s,α,n = 0) , (3.5.1.5) l r l and the private payoff, is a decreasing function of ρ(s,α,n) :

94 1 V AS (s,α,n) = e−rρ (s,α ,n) . (3.5.1.6) l r 2 (see section 14 of the Appendix for proof). As the private payoff is a decreasing function of ρ , and ρ is the only parameter in the payoff function that is affected by licensing, the inventor resorts to licensing only if it makes him wait for a shorter time before patenting. In other words, only those parameter combinations that, under licensing, induce a shorter waiting time, make licensing rational by increasing the private payoff. Therefore, if the inventor decides to license, he will patent earlier (see section 15 of the Appendix). The intuition behind this result is analogous to the one behind the waiting time being a declining function of scope. When the returns from the post-patent stage of application development increase due to a broader scope or to better licensing terms, the marginal value of waiting, becomes smaller than the marginal sacrifice from it. In comparison to the previous situation, this warrants a negative adjustment to the wait time ρ . Just as in the basic case, there exists a scope, s , defined by ρ(s,α,n) + s = d , because ρ(s,α,n) + s is increasing in s: 0 < ∂ρ + s <1. Beyond s , the optimal waiting ∂s time equals d-s, and is characterized by all applications being developed by the inventor and the licensees (i.e., there is no competitive development). One can verify that, as ρ(s > s) > ρ(s < s) , s with licensing is larger than the s with no licensing. The private payoff, v V AS (α,n, s > s) = e−r(d −s) []r(d − s) + (1+αn)(1− e−rs /(1+n) ) , (3.5.1.7) l r 2 is increasing in both s and α, and is increasing in n for the same combinations of s and α that were specified for the inclusive scope and for the first subcase of the additional scope protection. This analysis might lead one to the conclusion that, just as in the case of inclusive scope protection, maximum scope protection (s=d) guarantees the highest possible welfare and private payoff. This is true only for cases when α and s=d induce licensing. Note that both α and d are exogenous in the model, as they cannot be directly influenced by government policies. Otherwise, combinations of higher welfare and smaller private 95 reward to the inventor are available, and may be more optimal depending on the basic research “production function”. Besides, both the private payoff and welfare remain inferior to the ones obtained from inclusive scope protection, unless a zero waiting period is ensured by a combination of α and s=d. Thus, the general superiority of inclusive scope protection over the additional scope proven for the basic case also holds when licensing is allowed.

Licensing under length protection of the basic invention: Licensing is more attractive under length protection because the accelerated application diffusion is not limited by the fraction of the application pool that is granted by the scope protection. In fact, unless the number of applications that can be developed by the firms during T is limited by d, it is always optimal to license on any terms to as many firms as possible during the protection period T. The private payoff with licensing is,  T TT  V L (T,α, n) = e −rρ ρ e −rt dt + (1 + αn) e −rx dxdt = l  ∫ ∫∫   0 0 t  . (3.5.1.8) e −rρ []rρ(1 − e −rT ) + (1 + αn)(1 − e −rT (1 + rT )) r 2 If length protection is inclusive, ρ =0 and licensing is clearly both privately and socially optimal. With regard to the much more realistic additional length protection, comparison with the no licensing case shows that, under the length protection of the basic invention, licensing always unambiguously increases the private payoff. This is due to the fact that it is now a period of monopoly status, not the number of applications, that is granted to the innovator. Therefore, even under the most unfavorable licensing terms, it is profitable to license if the application pool is big enough not to be exhausted by cooperative development. The optimal ρ is:

e −rT rT −αn(1− e −rT (1+ rT)) αn(1− e−rT (1+ rT )) ρ L (T,α,n) = = ρ L (T,α,n = 0) − . r(1− e −rT ) r(1− e−rT ) (3.5.1.9)

96 Section 16 of the Appendix shows that the patentee will wait for a shorter time when licensing is allowed: ρ L (T,α,n) < ρ L (T,α,n = 0) . Clearly, the same logic as in case of additional scope protection explains this decrease in the optimal waiting time. Substituting the optimal ρ in the expression for V L gives

e−rρ (T ,α ,n) e−rρ (T ,α ,n=0) V L (T,α,n) = (1− e−rT ) > V L (T,α,n = 0) = (1− e−rT ) , (3.5.1.10) r 2 r 2 which confirms that licensing is always privately beneficial.

Now, consider the case when the pool of applications to be developed is so small (or the number of firms is large enough) in comparison to the length of the patent that ρ(T,α,n) + (1+ n)T > d , so that an additional influence appears. Licensing application development and marketing to other firms now means that fewer of applications are left to the inventor – applications become a scarce resource. In this situation, the payoff function is,  d −ρ  T n+1 T L −rρ  −rt −rx  V (T > T ,α,n) = e ρ∫ e dt + (1+ αn) ∫∫e dxdt . (3.5.1.11)  0 0 t    Comparing it to the payoff with no licensing, V L (T,n = 0) , shows that licensing is not always optimal. However, applications will be licensed more readily in comparison to additional scope protection because the inequality above holds for less favorable licensing terms (see section 17 of the Appendix for details). The optimal ρ is,

e −rT r(d − ρ) + αn[e−rT (1+ r(d − ρ)) −1] ρ(T > T ) = <. ρ(T < T ) (3.5.1.12) r(1− e −rT ) (see section 18 of the appendix). Thus, both the private payoff and welfare from length protection with licensing are in most cases higher and only sometimes equal to the private payoff and welfare when licensing is not allowed. However, the logic of our base case discussion of comparative efficiency of different patent protection regimes fully applies to the case of

97 licensing producing the following ranking in terms of social desirability: inclusive length, inclusive scope, additional scope, additional length.

3.6. CONCLUSIONS In considering the basic case, it has been shown that, when encouragement of private R&D is provided by a patent that grants the inventor temporary monopoly power over marketable applications of the discovery, inclusive scope protection is better than additional scope protection, and additional scope protection is better than length protection of the basic discovery for all possible values of discount rate r, size of the application pool d, and the number of firms in the industry N. The main criterion for making this judgment was what was called “protection regime efficiency”, namely the size of social welfare that still ensures a certain fixed (or minimum) private payoff to the inventor V : max[WF(s,T,d,r, N |V = V )] . Alternatively, the efficiency criterion can be formulated as the maximum private payoff given a certain social welfare from the innovation diffusion. Welfare was also found to be increasing in the number of firms in the industry. As, according to most R&D literature, competition also facilitates the basic R&D process, a greater number of firms in the industry is beneficial for both stages of the invention process. The main reason for the superiority of inclusive patent scope protection is that it induces the inventor to patent immediately after making a discovery, i.e., after winning the basic R&D race, rather than to wait in order to develop applications that will also later be protected by the patent. Under additional scope and length protection, an inventor almost always has an incentive to develop a few marketable applications before patenting the discovery in order to have them protected by the patent in addition to the ones developed after patenting. Delayed patenting is socially undesirable because it delays the diffusion of the invention’s marketable applications and restrains the opportunities for competitive application development and introduction. Still, additional scope protection is superior to length protection of the basic discovery because the latter effectively grants

98 relatively longer protection to the applications developed before patenting, thus increasing the incentive to delay it. Narrowing additional scope or length patent protection presents policy makers with a tradeoff between a positive effect of shortening the monopoly diffusion period due to weaker intellectual property rights (IPR) protection, and two negative effects: decreasing the private payoff from patent protection, which almost surely delays the basic discovery date, and increasing the delay before patenting, which shortens the competitive diffusion stage. This tradeoff, however, is absent when the application pool is significantly small, and particularly when the interest rate is also small, in which case it is always privately optimal for the inventor to patent only after all applications have been developed by the inventor. In this case, granting the basic invention more extensive protection is both socially and privately optimal because it shortens the patenting delays, benefiting both the inventor and the society. However, giving up the competitive development stage in this situation makes the largest attainable social surplus smaller than the socially optimal surplus in cases where the competitive development stage is feasible. Besides, patent protection becomes an imprecise policy tool, as maximum protection in this case dominates any other. It is worth pointing out how unfortunate it is that the best imaginable mechanism for ensuring optimal private R&D and innovation diffusion – simply paying the inventor an amount V* that ensures the first social best from the federal budget – is rendered infeasible by the lack of information about the R&D “production function” that is available to policy makers and by the redistribution costs. An important general conclusion is that there is a difference between the nature of “basic” R&D which, though benefiting from competition among the R&D firms, is essentially a tournament where the discovery date is largely determined by the reward for being the first, and the application development stage during which firms simply compete in the markets for heterogeneous products. As we argue, the socially feasible reward for making the basic discovery is always restricted to some form of monopoly right granted to the inventor, but monopoly is always detrimental to competitive markets, and the more extensive or durable the monopoly, the more the social loss from patent protection.

99 Therefore, if the inventor has limited resources for developing applications, mechanisms should be devised for encouraging development and introduction of the discovery’s applications by more than one firm while preserving a monopoly right extensive enough to ensure the discoverer gets a proper reward. As is shown in section 3.5.2 of the essay, licensing may be both privately and socially optimal. Licensing in this case is equivalent to an autocratic policy of breaking the secrecy of the basic invention in order to speed up its diffusion, that is, if commercial espionage is illegal. However, licensing is different as it is undertaken only when it is privately optimal. While licensing is always socially desirable as it increases welfare, it is not always privately optimal. Unfavorable licensing terms, large patent scopes, and high discount factors (low interest rates) discourage licensing. Besides, the scope of licensing may be limited by the size of the pool of applications that can be developed from the original basic invention. Nevertheless, introduction of voluntary licensing never harms either the patent holder or society. It also preserves the general ranking of protection regimes in terms of the welfare they provide given a certain fixed private payoff to the inventor. The only exception is that length protection, which was proven to be inferior to any scope protection in the base case, now has the advantage of encouraging licensing more strongly than the other protection regimes, but this encouragement is only present for a very limited range of the patent length, T. The conclusions about licensing are also robust to the applications of the basic discovery being of heterogeneous value, as the argument about the base case being robust to it fully applies to licensing as well. The only possible objection to licensing in the framework of this model is that, if there is a significant difference between the social surpluses from monopolistic and competitive application provision and if the licensing contracts make the licensees maintain prices and output levels at, or close to, the monopoly levels, elimination of the competitive development and marketing stage due to proliferation of licensing may in fact reduce the social surplus. The results of the analysis under the assumption of collusive behavior of the licensees are quite straightforward: the beneficial effects of

100 licensing are diminished when there is a negative difference between the monopoly, or collusive, and competitive surplus (defined earlier as β). When this is the case, licensing may no longer be socially optimal, which might reverse the ranking of protection regimes, something that should be taken into account while designing patent policies.

101 APPENDIX A TECHNICAL SOLUTION OF THE DYNAMIC OLIGOPSONY GAME IN THE FIRST ESSAY

Section A.1. Using equations (5) and (6), together with the supply (3 and 8), demand, and IP cost functions as specified above (11), and collecting terms, firm i’s problem can be written as

∞ −rt G G G G 2 max J i = e {KQit − w Qit − L(Qit ) + M}dt (A.1) QG ∫ it 0 where K, L, and M are coefficients that are linear combinations of the model’s exogenous parameters:

G N N N T I K = p − p + a + 2b Qt + c − µ T N L = 2n(µ /Qt − b ) (A.2) T N N N T T M = Qt [ p − a − b Qt ]/ n − cQt / n. The model is thus linear-quadratic, and an analytic solution exists. Each firm maximizes (A.1) with respect to its input purchases, and subject to the GM supply adjustment equation (3),

G G G G G w&t = s(a + b nQit − w t ) ,

G G Qit ≥ 0, w0 , and given the Nash behavior of the rivals. Under these specifications, the open-loop equilibrium of the oligopsony game is represented by n equilibrium processing strategies, which are given by simultaneous solution to a system of equations (A.1) for every firm, and equation (3). The Hamiltonian for every firm is

−rt G G 2 G G −rt G G G G Hi = e {KQit + L(Qit ) / 2 − wt Qit + M }+ e {s(a + b Qit − wt }. 102

The maximum principle gives the following optimality conditions:

G G G 35 K − wt − LQit + λit snb = 0 (A.3)

& −rt −rt −rt G −rt − λit e + λit re = −e Qit − sλiit e (A.4)

G To show that the equilibrium is symmetric, it is enough to solve for Qit in (A.3) and substitute it in (A.3) to get a differential equation & G λit L − λit (snb + L(s + r)) = K − wt . (A.5) Solving it and applying the transversality condition gives

∞ 1 −(snb +L(s+r )(τ −t) / L λit = e (K − wt )dτ . (A.6) L ∫t

Clearly, λit=λjt , i ≠ j , as they equal the RHS of (A.6) that does not contain any firm- specific parameters. It follows from (A.3) and the strict concavity of the Hamiltonian in

G G G Qit that Qit =Q jt , ∀ i ≠ j . The model’s solution gives the following stationary equilibrium values for the processors’ input purchases and prices:

G* (r + s)(K − a) T N * Q = = Q / n − Q i , (A.7) i (bn − L)(s + r) + sbn and

* asbn − aL(r + s) + nb(r + s)K wG = (A.8) (bn − L)(s + r) + sbn

To solve for the optimal strategies of the oligopsonistic processors, equation (3) is differentiated with respect to t and expressions for λ , λ&, and QG are substituted into it from equations (A.3) , (A.4), and (3) respectively. In more detail (omitting the G superscripts to avoid clutter): 1) Differentiating the equation of motion gives & w&&t = snbQit − sw&t .

35 It can be shown that condition (2.11) is equivalent to the MR=MC – λisnb, where – λisnb is the long-run effect of an incremental change in the input supply. 103 1 Also, Q = (w&/ s + w − a) . it nb t t

2) Solving for λ from (A.3) and substituting the expression for Qit from (1.3) gives

1  nb − L L aL  λt = wt − w&t + − K snb  nb snb nb  Differentiating w. r. to time produces nb − L L λ& = w& − w&& . t t s (nb ) 2 t (snb ) 2 & 3) Substituting this λt (w&&t , w&t ) and λt (w&t , wt ) together with Qit (w&t , wt ) into (A.4) (2.12) produces an awkward expression

L nb − L w&t wt − a r + s  nb − L L aL  − w&&t + w&t = + + wt − w&t + − K , (snb) 2 s(nb) 2 snb nb snb  nb snb nb  which reduces to a second order differential equation that the Nash equilibrium input price trajectory must satisfy:

w&&G + Aw&G + BwG = F , (A.9) where w&&G = (d 2 wG ) / dt 2 ; A = −r / L; s B = − []2snb + nbr − L(r + s) ; L 1 F = − []snbK (r + s) + as(snb − L(r + s)) . L A particular solution to this equation is F/B which is exactly the stationary equilibrium price w*. The roots of the characteristic equation associated with the homogeneous part of (A.9) are both real (this is true since B is negative). If we take the stable solution, the following is the open-loop Nash equilibrium trajectory:

G G * G G * Dt w t = w + (w 0 − w )e , (A.10) where, D = −1/ 2(A + A2 − 4B) < 0 . Equation (A.10) effectively describes the whole adoption process.

104 As pointed out earlier, closed-loop (feedback) equilibrium is similar to the open loop, and the ordinal effects in the model are the same under both structures. The discussion of the comparative dynamics below also pertains to a closed-loop (feedback) setup under which, arguably, the oligopsonists behave more rationally.

Section A.2. The purpose of this appendix is to clarify the process of rising levels of GM crop adoption while its price actually falls. The intuitive explanation is that the fall in the GM crop price is more than offset by the producers’ learning about the crop’s profitability, safety, and other positive characteristics. To provide an illustration, consider a simple example from a discrete version of the model. The GM crop inverse supply function is

G G G wt = s(a + bQt ) + (1− s)wt−1 , or (B.1) wG − (1− s)wG t t−1 = a + bQG . 36 s t The left hand side of the equation above can be identified with an “effective” or “perceived” price on which producers base their adoption decisions.

G G The condition for Qt to increase in comparison to Qt−1 is

G G G G wt − wt−1 > (1− s)(wt−1 − wt−2 ) ∀ t. (B.2) It is possible that, while the rate of price decline is actually decreasing, i.e.,

G G G G wt − wt−1 < wt−1 − wt−2 , the condition above holds. Consider a simple numerical example: a=30;

36 Note that the derivative of the left hand side is positive if the price is monotonically declining, which confirms once again that conservative adopter behavior slows down the diffusion process.

105 b=5; s=0.5;

Q0=0; w0=300, w1=250, w2=230, w3=225.

Then, Q1=34, Q2=36, and Q3=38 –output is increasing despite falling prices, all due to learning and other factors that make producer acceptance gradual (and “backward” looking too). Note that, with fully rational and informed producers, production volume

Q3=38 can be achieved in the first period for the price of only 220. This illustrates the essence of this modeling exercise. Condition (B.2) holds in all our simulation results, which confirms that it is always rational to expand the GM purchases so that the prices do not fluctuate, i.e., decline monotonically.

106 APPENDIX B DERIVATIONS OF THE FORMULAE USED IN THE THIRD ESSAY

Section 1.

−rτ (1− e ) −rs V AS (s) −V IS (s) = []e−e + e−rs −1 > 0 , as V AS (s) −V IS (s) is monotonically r 2 decreasing in s for s ≥ 0 :

∂ −rs (V AS (s) −V IS (s)) = −re −rs (1− e −e ) < 0 , and ∂s 1 V AS (0) −V IS (0) = > 0 and lim(V AS (s) −V IS (s))= 0 . er 2 s→∞

Section 2.

r(d −ρ−s) ∂W AS (s < s) ∂V AS (s < s) ∂  w −  = +  Ne−r(ρ+s) (1− e N ) =  2  ∂s ∂s ∂s  r  βw w e−r(ρ +s) + e−r(ρ +s) N[]e−r(d −(ρ +s))/ N (N −1) / N −1 (1− e−rs ) , 1r42 43 1r 424 4 4 4 4 4 4 434 4 4 4 4 4 4 >0 <0 and, ∂W AS (s < s) > 0 if (1− e −rs )[N − e −r(d −(ρ +s)) / N (N −1)]< β (“=” for s=s*, > for s>s* ). ∂s

107

Section 3. In order to show that inclusive scope protection is more efficient because it provides higher welfare for any feasible private payoff V , first compare 1− r 2V and r 2Ve−rs , having in mind that the s < s here is additional scope protection. By rewriting 1 the comparison as 1 r 2V (1+ e −rs ) and noting that max[V AS (s < s)] = exp(−e−rs ) , r 2 one can verify that 1− r 2V > r 2Ve−rs for all 0 < s < s , as r 2V (1+ e−rs ) < exp(−e−rs )(1+ e−rs ) and 2 / e < exp(−e −rs )(1+ e −rs ) < 1 for all 0 < s < s .

1− r 2V Now, define Q = r 2Ve−rs and α = >1. Then, r 2Ve−rs W IS (V ) −W AS (V | s ≤ s) = αQ(1− e−rd / N (αQ)−1/ N ) − Q(1− e−rd / N (Q)−1/ N ) =

Q(α −1) − e−rd / N Q( N −1)/ N (α ( N −1) N −1) > 0 , as (N −1) / N <1and e−rd / N <1. Comparing welfare under inclusive and the second case of additional scope protection (s > s) shows that inclusive scope protection is again more efficient because it provides higher welfare for any given feasible private payoff to the innovator: 1 W IS (V ) −W AS (V | s > s) = N(1− r 2V )[1− e−rd / N (1− r 2V )−1/ N ]> 0. r 2 This supremacy of inclusive over additional scope protection is because the former does not provide any incentives for delaying innovation. Besides, a whole range

* ** of additional scope protection regimes, (0, sm ) ∪ (sm ,d) , should never be used as they are dominated by other values of sAS. Also, for s > s , optimal s is always equal to d. This makes additional scope protection an imprecise policy tool.

Section 4. The derivative of the private payoff,

L 1 ∂V = e −rρ [](1− e −rT ) − (rρ +1)(1− e −rT ) + re −rT T = e −rρ [e −rT T − ρ(1− e −rT )]= 0, ∂ρ r e −rT T gives the privately optimal waiting time: ρ * (T) = . 1− e −rT 107 ∂ρ(T ) 1− rT rTe −2rT 1− (rT + e −rT ) = e −rT − = e −rT <0, because rT+e-rT>1 for all ∂T 1− e −rT (1− e −rT ) 2 (1− e −rT ) 2 T>0 (it is monotonically increasing in T and equals 1 for T=0). Also, the maximum unrestricted ρ is:

 e−rTT   e−rT (1−T)  1 max[ρ] = lim  = lim  = . This value defines whether the first case  −rT   −rT  T →01− e  T →0 re  r ever takes place at all, because the waiting time is limited by the number of applications that can be developed from the basic invention, and, therefore, max[ρ] = min(d,1/ r) .

Section 5.

∂V L (T < T ) e −rρ (T )  ∂ρ(T) e −r(ρ (T )+T )  1− (rT + e −rT ) = e −rT − (1− e −rT ) = 1− > 0 .    −rT  ∂T r  ∂T  r  1− e 

Section 6. T 1− e−rT (1+ rT ) ρ(T) + T = , and d(ρ(T) +T) / dT = > 0 . 1− e −rT (1− e−rT )2

Section 7. e−rT T 1 ρ * (T ) = ≥ ρ * (s AS = T ) = e−rT for all s and T. 1− e−rT r Rearranging reduces the inequality to a self-explanatory rT + e−rT ≥ 1. It also follows that, for any given d and r, T < s AS .

Section 8.

1 1 (d −ρ −T ) / N W L (T < T ) = V L + e−r(ρ+T ) (ρ + T ) + e−r(ρ+T ) N ∫e−rt dt = r r 0

1 1 T 1 (d −ρ (T )−T ) / N ρ(T)e−rρ (T ) + e−rρ (T ) ∫e−rt dt + e−r(ρ (T )+T ) N ∫e−rt dt = r r 0 r 0 e−rρ (T ) {}rρ(T ) + (1− e−rT ) + e−rT N(1− e−r(d −ρ (T )−T )/ N ) . r 2 108 To prove that welfare under length protection is always decreasing in T regardless of the other parameters, define ∂ρ as x, e−rT as e* , and e−r(d −ρ −T )/ N as e** . The ∂T derivative of WL can then be written as, ∂W L (T > T ) e−rρ e−rρ = − x[]rρ +1− e* + e*N(1− e** + []rx + re* − re*N(1− e** ) − re*e** (1+ x) = ∂T r r 2 e −rρ []e* − e* N(1 − e** ) − e*e** (1 + x) − rxρ + xe* − xe* N(1 − e** ) = r e −rρ []e* (1 + x) − e* N(1 − e** )(1 + x) − e*e** (1 + x) − rxρ = r e −rρ {}()1 + x []e* − e* N(1 − e** ) − e*e** − rxρ = r e −rρ {}e* ()1 + x ()1 − e** ()1 − N − rxρ < 0 for all N ≥1, as r ∂ρ 1 − e −rT (1 + rT ) 1 + x =1 + = > 0. ∂T (1 − e −rT ) 2 Further differentiation of WL proves that it is also convex in T. Thus, the highest possible welfare that can be obtained from length protection is either, 1 W L (T → 0, ρ = 1/ r) = []1+ N(1− e −r(d −1/ r) / N , er 2 or, e−rd d W L (T → 0, ρ = d) = , depending on the relative magnitudes of d and T. r

Section 9.

e−r(ρ+T ) e−r(ρ+T ) d −ρ W L (T > T ) = V L (T > T ) + ρ(T) + ∫e−rt dt = r r 0

e−r(ρ +T ) e−rρ V L (T > T ) + []rρ(T ) +1− e−r(d −ρ ) = []rρ(T) +1− e−r(d −ρ ) . r 2 r 2 W L (T > T ) is increasing and concave in T:

∂W L (T > T ) e−rρ ∂ρ e−rρ ∂ρ e−rρ ∂ρ = − (1− e−r(d −ρ ) ) − e−r(d −ρ ) = − = ∂T r ∂T r ∂T r ∂T

109 e −rρ − (−rde −rT ) = e −r(ρ +T ) d > 0 . r ∂ 2W L (T > T ) Therefore, < 0. ∂T 2 Section 10. The lengths of the monopoly diffusion stages (before the patent expires) under the two regimes are: T ρ(T ) +T = >1/ r under length protection, and, 1− e−rT ρ(s) + s = e−rs / r + s >1/ r under scope protection. Assume s=T. Then, the inventor will always wait longer before patenting under the length protection: rT − (e−rT + rT )(1− e −rT ) e −rT (rT + e −rT −1) (ρ(T) + T ) − (ρ(s) + s) = = > 0 . r(1− e −rT ) r(1− e −rT ) Thus, ρ(T) +T > ρ(s) + s for all s=T . Besides, as we showed above that both ( ρ(s) + s ) and ( ρ(T ) +T ) are monotonically increasing in s and T, ρ(T) +T > ρ(s) + s for s ≤ T .

Section 11. Both VL(T) and VAS(s) are monotonically increasing in their arguments. In order to attain a given fixed private payoff V , the length T should be greater than s. To show this, compare the two components of the private payoffs for T=s in order to see that each of them is strictly greater in case of additional scope: Private Surplus Additional Scope Length

T from applications 1 τ −rρ −rt e−rρ ρ (or e−rt dt ) > e ρ e dt ∫0 developed before r ∫0 patenting

−rρ −rρ from applications 1 s e T T e e−rρ e−rt dt = (1− e−st ) > e−rρ e−rxdxdt = (1− e−rT − rTe−rT ) developed after r ∫0 r 2 ∫0 ∫t r 2 patenting

110 Section 12. Now, we show that, when s = T > (s,T ) , V L (T) < V AS (s) . Proof: e−e(d −s) e−eρ (T ) V (s > s) = (r(d − s) +1− e−rs ) , and V (T > T ) = (1− e−r(d −ρ (T )) ) . r 2 r 2 To show that the inequality above holds, it is enough to show that d − s > ρ(T = s) = de−rT (=s) . This is true for s ∈(0,d] because d − s − de−rs is monotonically decreasing in s: ∂(d − s − de−rs ) = dre−rs −1< 0 ( dre−rs <1 because ss is needed to guarantee the same private payoff. This means that the time to patent expiration, T + ρ(T ) , is definitely greater than s + ρ(s) , hence shorter

competitive development stage. Thus, W L (V ) < W AS (V ) . Q.E.D.

Section 13. Technically,

 s /(n+1) (d −s) / N   s (d −s) / N  W IS −W IS = (1+ n) e−rt dt + e−rs /(n+1) N e−rt dt − e−rt dt + e−rs N e−rt dt L NL  ∫ ∫  ∫ ∫   0 0  0 0  = (1+ n)(1− e−rs /(n+1) ) − (1− e−rs ) + N(1− e−r(d −s)/ N )(e−rs /(n+1) − e−rs ) . 1 424 4 44 434 4 4 4 1 424 4 4 4 434 4 4 4 A B B > 0 , and the fact that A > 0 can be shown by verifying that A(n=0 and n=∞)>0 and that A is monotonically increasing in n.

Section 14. Differentiating the private payoff function, v ∂V = e−rρ [](,1+αn)e−rs /(1+n) −αn − rρ ∂ρ r 111 gives the optimal waiting time under the additional scope protection with licensing: 1 ρ AS (s,α,n) = ()e −rs /(1+n) −αn(1− e −rs /(1+n) ) < ρ AS (s,α,n = 0) . l r l The private payoff, which is a decreasing function of ρ(s,α,n) is:

AS v −rρ (s,α ,n)  1 −rs /(1+n) −rs /(1+n) −rs /(1+n)  Vl (s,α,n) = e r ()e −αn(1− e ) + (1+αn)(1− e ) = r 2  r  1 = e−rρ (s,α ,n) . r 2

Section 15. If the inventor decides to license, he will patent earlier:

1   ρ(s,α,n > 0) − ρ(s,α,n = 0) = e −rs /(1+n) − e −rs −αn(1− e −rs /(1+n) ) < 0. r 1 424 434 1 424 434  a b  Clearly, both a and b are positive, but, for α and s small enough, the difference can be positive, in which case licensing is not undertaken.37 When the returns from the post-patent stage of application development increase due to a broader scope or to better

−rρ licensing terms, the marginal value of waiting, ∂(e ρ / r) , becomes smaller than the ∂ρ

∂  e−rρ  marginal sacrifice from it,  (1+αn)(1− e−rs /(1+n) ) . In comparison to the previous  2  ∂ρ  r  situation, this warrants a negative adjustment to the waiting time before patenting, ρ .

∂ρ AS 1 It can also be verified that l = n(e−rs /(1+n) −1) < 0 and ∂α r ∂ρ AS 1+αn l = − e−rs /(1+n) ∈(−1.0) . Therefore, there exist α and s that are high enough to ∂s 1+ n induce a zero waiting period.

Section 16.

37 Same can be proven by stating that, in order for licensing to take place, V AS (ρ,α,n > 0) must be greater than V AS (ρ,α,n = 0) , i.e., e−rs /(1+n) − e−rs −αn(1− e−rs /(1+n) ) < 0 - the same inequality. 112 Differentiating the private payoff gives the optimal ρ :

∂V L e −rρ l = [](1− rρ)(1− e −rT ) − (1+ αn)(1− e −rT (1+ rT )) , ∂ρ r

e −rT rT −αn(1− e −rT (1+ rT)) αn(1− e−rT (1+ rT )) ρ L (T,α,n) = = ρ L (T,α,n = 0) − r(1− e −rT ) r(1− e−rT )

Thus, ρ L (T,α,n) < ρ L (T,α,n = 0) , as e−rT (1+ rT) <1, which can be verified by taking the limits (T=0 and T → ∞ ) and seeing that the expression is monotonically declining in T. Substituting the optimal ρ in the expression for V L gives

e−rρ (T ,α ,n) e−rρ (T ,α ,n=0) V L (T,α,n) = (1− e−rT ) > V L (T,α,n = 0) = (1− e−rT ) , r 2 r 2 which confirms that licensing under the length protection is privately beneficial.

Section 17. The payoff function is:  d −ρ  T n+1 T L −rρ  −rt −rx  V (T > T ,α,n) = e ρ∫e dt + (1+αn) ∫∫e dxdt = 0 0 t  

−rρ d −ρ   −r  e  −rt n+1 −rT d − ρ  2 rρ(1− e ) + (1+αn)1− e − e r . r   n +1  Comparing it to the payoff when there is no licensing, V L (T,n = 0) , shows that the patent holder will license if,

d −ρ  −r d − ρ   n+1 −rT  −r(d −ρ ) −rT (1+αn)1− e − e r  > ()1− e − e r(d − ρ) ,  n +1  i.e., licensing is not always optimal. However, applications will be licensed more readily in comparison to additional scope protection because the inequality above holds for less favorable licensing terms.

Section 18. Differentiating V L (T > T ,α,n) with respect to ρ gives, 113 r d −ρ d −ρ − ρ −r −r ∂V e  −rT r −rT d − ρ −rT  = − rρ(1− e ) −αn[ (e − e n+1 ) − e n+1 − r e  . ∂ρ r  1+ n n +1  The optimal ρ is thus:

e −rT r(d − ρ) + αn[e−rT (1+ r(d − ρ)) −1] ρ(T > T ) = , r(1− e −rT ) which is clearly less than the ρ(T < T ) , as (d − ρ) < T in this case. Alternatively,

d −ρ d −ρ d − ρ  −r d − ρ 1 −r  −rT  n+1 −rT −rT n+1  ρ(T > T ,α,n) = r e −αn1− e − r e − (e − e ), n +1  n +1 1+ n  d − ρ d − ρ which is equal to ρ(T < T ,α,n) if = T . Therefore, as < T , the privately n +1 n +1 optimal waiting time is always longer when T > T .

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