Journal of Industrial Organization Education Volue 1, Issue 1 2006 Article 8 Copetition and Innovation Richard J. Gilbert Econoics Departent, University of California, Berkeley, gilbert@econ.berkeley.edu Copyright c 2006 The Berkeley Electronic Press. All rights reserved.
Copetition and Innovation Richard J. Gilbert Abstract A vast and often confusing econoics literature relates copetition to investent in innovation. Following Joseph Schupeter, one view is that onopoly and large scale proote investent in research and developent by allowing a fir to capture a larger fraction of its benefits and by providing a ore stable platfor for a fir to invest in R&D. Others argue that copetition prootes innovation by increasing the cost to a fir that fails to innovate. This lecture surveys the literature at a level that is appropriate for an advanced undergraduate or graduate class and attepts to identify priary deterinants of investent in R&D. Key issues are the extent of copetition in product arkets and in R&D, the degree of protection fro iitators, and the dynaics of R&D copetition. Copetition in the product arket using existing technologies increases the incentive to invest in R&D for inventions that are protected fro iitators (e.g., by strong patent rights. Copetition in R&D can speed the arrival of innovations. Without exclusive rights to an innovation, copetition in the product arket can reduce incentives to invest in R&D by reducing each innovator s payoff. There are any coplications. Under soe circustances, a fir with arket power has an incentive and ability to preept rivals, and the dynaics of innovation copetition can ake it unprofitable for others to catch up to a fir that is ahead in an innovation race. KEYWORDS: R&D, gae theory, dynaics
Gilbert: Copetition and Innovation What we have got to accept is that [the large-scale establishent or unit of control] has coe to be the ost powerful engine of [econoic] progress and in particular of the long-run expansion of total output...in this respect, perfect copetition is not only ipossible but inferior, and has no title to being set up as a odel of econoic efficiency. Joseph Schupeter (1942. The best of all onopoly profits is a quiet life. J.R. Hicks (1935 I. Introduction There is broad agreeent aong econoists that research and developent is a ajor source of econoic growth. Although estiates differ, ost studies show a high correlation between R&D expenditures and productivity growth after accounting for investent in ordinary capital. Studies also show that the social return to investent in R&D is higher than the private return (Griliches, 1992, which suggests that policies that proote innovation can pay large dividends for society. One way to achieve these benefits is to proote industry structures that offer greater incentives for innovation, including policies toward ergers and laws that govern exclusionary conduct. This lecture reviews the econoic theory relating copetition to innovative activity. We use the ter innovation to describe both the act of invention and the activity required to bring the invention to the arket. As a general stateent, the incentive to innovate is the difference in profit that a fir can earn if it invests in R&D copared to what it would earn if it did not invest. These incentives depend on any factors, including: the characteristics of the invention, the strength of intellectual property protection, the extent of copetition before and after innovation, barriers to entry in production and R&D, and the dynaics of R&D. Innovations ay be new products or new processes. A product innovation is a new or iproved good or service. A process innovation lowers the cost of producing a good or service. It is ore difficult to ake general stateents about incentives for product innovations because a fir s profit before and after innovation occurs depends on fixed costs, price copetition and the ix of other products in its portfolio. Even without investent in R&D, firs ay supply too any or too few products fro the perspective of total econoic welfare. See, e.g., Dixit and Stiglitz (1977. The strength of intellectual property protection deterines the extent to which the inventor can exploit the potential of her discovery to add value to the econoy. I assue that patent protection, when it exists, gives the inventor Published by The Berkeley Electronic Press, 2006 1
Journal of Industrial Organization Education, Vol. 1 [2006], Iss. 1, Art. 8 peranent and total protection fro iitation. While this is an extree assuption of exclusive rights to an invention, it serves to illustrate the consequences of strong intellectual property rights. Keep in ind that patent protection does not guarantee that the inventor will be able to prevent copetition fro others, either legally by inventing-around the new technology or illegally by infringing the patent, and several studies have shown that patents do not confer substantial protection in ost industries (see, e.g., See Levin et al. (1985, Cohen and Levin (1989, and Hall and Ziedonis (2001. 1 Firs have non-exclusive intellectual property rights to their inventions when others can independently invent siilar products or processes without infringing on the inventor s rights. Non-exclusive intellectual property rights are siilar to trade secrets. Non-exclusive rights do not prevent independent discovery of the sae or siilar invention, although they restrict the ability of firs to copy inventions ade by others. The dynaics of the innovation process affect incentives to invest in R&D. A fir ay be able to pre-ept copetitors in R&D if a head start in the innovation process gives the fir a discrete advantage in securing an exclusive right to the innovation. If that is not the case, firs can siultaneously engage in R&D, each with a reasonable expectation that its R&D expenditures will generate a significant return. The any different predictions of theoretical odels of R&D lead soe to conclude that there is no coherent theory of the relationship between copetition and investent in innovation. That is not quite correct. The odels have clear predictions, although they differ in iportant ways that can be related to arket and technological characteristics. It is not that we don t have a odel of copetition and R&D, but rather that we have any odels and it is iportant to know which odel is appropriate for each arket context. Researchers should distinguish the different theories when forulating epirical tests of the relationship between copetition and innovation. We begin with a process innovation that lowers the constant arginal cost of producing a product. Section II presents the benchark cases of socially optial investent in R&D and investent in R&D by a onopoly that is protected fro both product arket and R&D copetition. Section III introduces copetition in R&D. Section IV exaines product innovation with exclusive IP rights. Section V returns to process innovations, but assues that inventors have only non-exclusive intellectual property rights. Section VI exaines the consequences of dynaic copetition in R&D. 1 The pharaceutical industry is a notable exception. http://www.bepress.co/jioe/vol1/iss1/8 2
Gilbert: Copetition and Innovation II. Process Innovations: Social Optiu and Pure Monopoly These two cases require no assuptions about the nature of intellectual property rights. In the case of socially optial R&D, we assue that the invention is available for use under conditions of perfect copetition and the public pays for the cost of R&D with no deadweight costs for society. In the case of a pure onopoly, IP rights are irrelevant because there is no copetition. This discussion generally follows Tirole (1987. Socially optial innovation incentives A hoogenous good is sold at price p and produced at constant arginal cost, c. Deand is q(p with dq( p/ dp < 0. Given the production technology, total econoic welfare reaches a axiu when price is equal to arginal cost. In the socially optial allocation there are no profits and total welfare is equal to consuer surplus. W( c S( c q( x dx. = = Note that dw ( c/ dc = q( c. For an innovation that reduces the arginal production cost by a sall aount, the social value of the innovation is proportional to the aount consued when the price is equal to the arginal production cost. This siple observation is key to understanding the social value of innovation incentives under different arket structures. The change in total welfare fro a discrete investent in R&D that lowers the arginal cost of aking the good to c 1 < c 0 is c dw ( x W( c W( c W = dx = q( x dx 1 0 dx c1 c0 (1 c0 c1 This is the total achievable benefit to society fro R&D that reduces arginal cost fro c 0 to c 1. It is the area c 1 c 0 bd in Figure 1. Published by The Berkeley Electronic Press, 2006 3
Journal of Industrial Organization Education, Vol. 1 [2006], Iss. 1, Art. 8 Price deand c 0 b W c 1 d 0 q (c 0 q(c 1 Quantity Figure 1. Social value of process innovation Monopoly in production (pre- and post-innovation and in R&D Figure 2 illustrates the onopolist s profit fro a drastic innovation. A process innovation is drastic if the onopoly price with the innovation is lower than the arginal cost before the innovation: p (c 1 < c 0. It is drastic in the sense that no fir with the old technology can copete with a fir that has the new technology when the fir with the new technology chooses a onopoly price. The new technology akes the old technology obsolete. Figure 3 shows the onopolist s profit fro a non-drastic innovation, for which p (c 1 c 0. The figures show the profits earned by the onopolist with the old and new technologies; π (c 0 and π (c 1 respectively. http://www.bepress.co/jioe/vol1/iss1/8 4
Gilbert: Copetition and Innovation Price deand p (c 0 π (c 0 c 0 p (c 1 π (c 1 c 1 0 q (c 0 q (c 1 Quantity Figure 2. Monopoly profits with drastic innovation deand p (c 0 c 0 π (c 0 π (c 1 c 1 0 q (c 0 q (c 1 Quantity Figure 3. Monopoly profits with non-drastic innovation Published by The Berkeley Electronic Press, 2006 5
Journal of Industrial Organization Education, Vol. 1 [2006], Iss. 1, Art. 8 Assue the onopolist charges a unifor price, p. Define q ( c q( p ( c dπ π π dp and note that = + = q (c. The change in onopoly dc c p dc profits fro the cost reduction is c1 c0 dπ ( x 1 0 = = dx c0 c1 (2 π ( c π ( c π dx q ( x dx. Copare the social and onopoly incentive for innovation. Fro equations (1 and (2 we have c0 W π = [( q( x q ( x] dx 0, (3 c1 because q(c q (c, with a strict inequality if q(c > q (c for any c [ c 0, c1 ]. If a onopolist charges all consuers a single price, the onopoly value of a process innovation is (weakly less than the social value. The onopoly profit fro the cost reduction is less than the social benefit because the onopolist produces less than the socially optial level. Innovation replaces the onopolist s old profit strea, π (c 0, with a new profit stea, π (c 1. This replaceent effect lowers the onopolist s incentive to invest in R&D. But this is not the reason why the onopolist s incentive to invest in R&D is lower than the socially optial incentive. There is a replaceent effect for society as well, because invention replaces one value strea with another. The difference in the value of R&D follows fro differences in socially optial and onopoly outputs. If the onopolist were able to price discriinate perfectly, it would produce efficiently with and without the innovation and the onopoly value of the process innovation would equal its social value. Next, we consider the effects of copetition on incentives to innovate when inventions have the protection of exclusive intellectual property rights. III. Copetition for Process Innovations with Exclusive IP Rights There are two different cases to consider. In the first case there is perfect copetition in the old technology and copetition to invest in a new process http://www.bepress.co/jioe/vol1/iss1/8 6
Gilbert: Copetition and Innovation innovation. In the second case there is a onopoly in the old technology and copetition to invest in the new process innovation. In both cases we assue that the winner of the R&D copetition has an exclusive intellectual property right to the new process. Copetition in production pre-innovation and copetition in R&D With perfect copetition, pre-innovation each fir earns π ( c 0 = 0. There is no replaceent effect because with perfect copetition there are no pre-innovation profits to replace. For a drastic innovation, the successful inventor s profit fro invention is the onopoly profit π c. Figure 2 shows that ( 1 π = π ( c > π = π ( c π ( c. c 1 1 0 The coparison of innovation incentives is less clear for a non-drastic innovation (Figure 3. Copetition fro the old technology liits the inventor s price to c 0, which is less than its onopoly price. The inventor s corresponding output is q(c 0. Noting this, we can write the inventor s profit as c π = c0 c0 ( c0 c1 q( c0 = q( c0 dx > q ( x dx = π. c1 c1 The incentive to invest in R&D when there is pure copetition pre-innovation is higher than the incentive to invest in R&D under pure onopoly, because there is no replaceent effect in the case of pure copetition. A onopoly has a strea of profits that is lost (replaced by innovation. Copetitors have nothing to lose fro innovation, and hence ore to gain. How do R&D incentives for a perfectly copetitive industry copare to socially optial incentives? In Figure 4 the social value of a drastic process innovation that lowers constant arginal production costs fro c 0 to c 1 is the area c 1 c 0 bd. For the case of perfect copetition in the pre-innovation arket, we have π c = π (c 1, which is less than the social value of the innovation. For a nondrastic innovation, we have c π = c c q( c W, ( 0 1 0 where the inequality is strict unless deand is perfectly inelastic. Published by The Berkeley Electronic Press, 2006 7
Journal of Industrial Organization Education, Vol. 1 [2006], Iss. 1, Art. 8 Price deand c 0 b p (c 1 π (c 1 c 1 d 0 q (c 0 q (c 1 Quantity Figure 4. R&D incentives for drastic innovation with perfect copetition in the old technology. c This analysis shows that W π and the previous analysis showed that c π > π. Thus we conclude that c W π > π. The first inequality is also strict except for the case of perfectly inelastic deand. Monopoly in production pre-innovation and copetition in R&D Following Gilbert and Newbery (1982, we now assue that initially there is a single fir in the industry with the old technology, c 0. There is copetition in R&D, which we assue takes a particular stylized for: firs bid for a patent, which is awarded to the highest bidder. A fir that is outside the industry would d be willing to bid up to π ( c 1, c0. This is the fir s duopoly profit when the fir has arginal cost c 1 and a rival has arginal cost c 0. The incubent would bid d up to π ( c1 π ( c0, c1. The first ter is the onopoly profit with arginal cost c 1. By winning the patent the fir retains its onopoly position and lowers its arginal cost fro c 0 to c 1. The second ter is the profit the fir would earn http://www.bepress.co/jioe/vol1/iss1/8 8
Gilbert: Copetition and Innovation when it has arginal cost c 0 and a rival wins the patent and enters with arginal cost c 1. We assue that payoffs do not depend on the identity of the fir. The onopolist has (weakly ore to gain fro the patent because π ( c π ( c, c π ( c, c. d d 1 0 1 1 0 This follows because the onopoly profit with arginal cost c 1 is at least as large as the su of the duopoly profits. This is an exaple of preeptive copetition. The incentive to preept is driven by what Tirole (1997 calls the efficiency effect. This is the gap between onopoly profits and total industry profits with copetition. The efficiency effect increases the onopolist s incentive to invest in R&D when preeption is feasible. Note that in general this result holds only for a fir that has a onopoly in the old technology. Suppose there are n identical incubent firs. Each has profit π n( c 0,..., c0. The first entry denotes the fir s arginal cost; the reaining entries denote the arginal costs of the other firs. If one of the wins the patent, its profit is π n( c1, c0,..., c0 and the other incubents earn π n( c0, c0,..., c1. (Firs are syetric, so the ordering does not atter. If a new fir enters with the new technology, it earns π n+ 1( c1, c0,..., c0 and the incubent firs earn π n+ 1( c0, c0,..., c1. An incubent has a greater incentive to bid for the patent only if π c, c,..., c π ( c, c,..., c π ( c, c,...,. n ( 1 0 0 n+ 1 0 0 1 > n+ 1 1 0 c0 This inequality does not hold in general. An exaple is Nash-Cournot copetition with (c 0 c 1 sufficiently sall. Table 1 suarizes our results. Table 1. Innovation incentives under different arket structures Old Technology New Technology Incentive to invent Monopoly Perfect Copetition Monopoly Copetition for patent onopoly Monopoly Monopoly + Copetition for Patent Monopoly π = π ( c π ( c 1 0 π = ( > c π c 1 c π = ( c c q( c > 0 1 0 π if drastic π ( c π ( c, c π ( c, c d d 1 0 1 1 0 π otherwise Published by The Berkeley Electronic Press, 2006 9
IV. Product Innovation with Exclusive IP Rights We have liited our analysis to process innovations that lower the arginal cost of producing a product. These results do not apply directly to product innovations, which are significant both because they account for a large fraction of total R&D expenditures and because they include any of the breakthroughs that spur econoic growth and advance consuer welfare. 2 The analysis of innovation incentives is ore coplicated for product innovations for at least two reasons. First, even firs that act as copetitive price-takers can earn positive profits when they offer differentiated products. This eans that a copetitive fir also faces a replaceent effect fro the profit that it could earn using the pre-innovation products. Second, a new product changes the ability of a onopolist to discriinate aong consuers. For a process innovation, a reasonable assuption is that the new technology doinates the old technology and hence the old process technology is irrelevant to the profit that the onopolist can earn with the new process. This is not necessarily a good assuption for product innovations. A new product can allow a fir with a portfolio that includes the old product to differentiate its offerings and extract ore surplus fro consuers than would be possible using only the new product. For exaple, the willingness to pay for a new product could be inversely correlated with the willingness to pay for a onopolist s old product. This could allow the fir to bundle the two products and charge a price that extracts ost of the available surplus. By iproving the onopolist s ability to price discriinate aong consuers an innovation can increase a onopolist s profit by ore than the profit that a new copetitor can earn. As in the case of a process innovation, a onopolist s incentive to invest in R&D for a new product is the difference in the onopoly profits with and without the new product. Assuing away differences in anagerial efficiency, copetition ensures that a copetitor s profit using the old product is no greater than a onopolist s profit using only the old product. Hence the replaceent effect should be less for a copetitive fir, although it is not likely to be zero when firs sell differentiated products. This iplies that a copetitor has a greater net incentive to invest in product innovation. However, the replaceent effect is only half of the equation. A onopolist ay be able earn ore with the new product than a copetitor could earn when it sells the new product in copetition with the forer onopolist. We cannot ake a general conclusion that for product innovations a onopolist has a lower incentive to invent. An ordering of incentives for product innovation in onopoly and copetitive arkets is difficult to obtain even if the innovation is drastic. A 2 Journal of Industrial Organization Education, Vol. 1 [2006], Iss. 1, Art. 8 The National Science Foundation estiated that in 1981, about 75% or all industry R&D was directed to product innovations. National Science Foundation (2004. http://www.bepress.co/jioe/vol1/iss1/8 10
Gilbert: Copetition and Innovation product innovation is drastic if the copetitor s profit with the new product is the sae as if it were a onopolist with only the new product (i.e., no one would buy the old product. Even if the innovation is drastic, this does not exclude the possibility that a onopolist could use both products to increase its profits by differentiating its offerings. We can conclude that incentives to invest in a new product are lower for the onopolist if we ipose a stronger condition on the characteristics of the new product. A copetitor will have a greater incentive to innovate if the new product akes the old product obsolete, so that a fir with the new product has no use for the old product and a fir with the old product cannot earn a profit if another fir has the new product. Any innovation that akes the old product obsolete is also drastic, but the opposite need not be the case. If the new product akes the old product obsolete, the copetitor s gross benefit fro innovation is no less than the onopolist s and it faces a saller replaceent effect. Hence the copetitor s net benefit would be larger in this case. See Greenstein and Raey (1998 for an exaple of incentives to invest in product innovation with vertically differentiated products and Gilbert (2006 for an exaple of R&D incentives with both horizontal and vertical differentiation. V. Copetition and Innovation with Non-Exclusive Intellectual Property Rights The pure onopoly incentives to invest in R&D are the sae with exclusive and non-exclusive rights, because by assuption there are no rivals for IP rights to exclude. Moving beyond the pure onopoly case, the copetitive incentives to invest in R&D depend on the extent of copetition and the ease of iitation. We assue that with non-exclusive rights firs cannot prevent duplicative invention, but they can prevent copying. An exaple is a process innovation that is held as an enforceable trade secret. The trade secret right prevents copying, but does not prevent independent discovery of the sae invention. We return to the sipler case of process innovation. Suppose the innovation is drastic. As a consequence copetition will occur only aong firs that invest successfully in R&D. Let c 1 be the constant arginal cost of production with the process innovation. Following Dasgupta and Stiglitz (1980, index the firs by i = 1,...,N and suppose that n N identical firs invest in R&D and copete as Nash-Cournot copetitors with the new process. Oitting the cost of R&D, each fir akes a profit π ( c, n = ( p c q( p. (4 i 1 1 i Published by The Berkeley Electronic Press, 2006 11
Journal of Industrial Organization Education, Vol. 1 [2006], Iss. 1, Art. 8 Profit axiization iplies the inverse elasticity rule p c p = (5 ε 1 1 f where ε f is the fir-specific elasticity of deand. Substituting equation (5 into equation (4, it follows that each fir s profit fro invention is pqi / ε f. In the Nash-Cournot case with syetric firs, ε f = nε, where ε is the elasticity of deand for the entire arket and n is the nuber of firs that successfully invent. In this syetric Nash-Cournot case, each fir s incentive to invent is pq( p where Q(p is the industry deand at price p. For the case of constant 2 n ε pq( p elasticity of deand, is a declining function of n if nε > 1; this is required 2 n ε for existence of a syetric Nash-Cournot equilibriu. In this case the incentive to invent is a declining function of the nuber of firs in the industry. If R&D incurs a cost, K, and the firs are syetric, then with free entry into R&D the nuber of firs is the largest nuber n for which 1 ( p c 1 Q( p K. (6 n Substituting (5 in (6 with ε f = nε, and assuing that firs just break even, gives nk pq 1 =. (7 nε The left-hand-side of equation (7 is the aggregate R&D intensity for the entire industry: the ratio of total industry R&D to total sales. The right-hand-side is clearly decreasing in n, iplying that the industry R&D intensity is a decreasing function of the nuber of firs that invest in R&D. In this odel increasing copetition reduces industry R&D intensity. In this sense greater copetition reduces R&D expenditures. Also, note that R&D is redundant with non-exclusive rights. It would be ore efficient to have one fir engage in cost-reducing R&D and to distribute the results of that R&D industrywide. http://www.bepress.co/jioe/vol1/iss1/8 12
Gilbert: Copetition and Innovation VI. Innovation Dynaics R&D unfolds over tie, but the analysis so far has been essentially static. Firs invest in R&D, one or ore firs succeed, and the industry oves to a new postinnovation equilibriu. This section considers how the dynaics of R&D investent affects our conclusions. We begin with a siple odel of equilibriu R&D investent with free entry. An R&D project costs R and discovers the new process or product with probability p. The R&D project is successful if it succeeds at any date and there is no discounting. The probability that at least one of N R&D projects succeeds is ρ (N with ρ ( 0 = 0, ρ ( N > 0 and ρ ( N < 0. The socially optial nuber of R&D projects is the solution to ax ρ( NV NR. N The private value of the invention is Π p. The social value of the invention when it is supplied privately is V p. This can be less than the (gross social value V* to the extent that there are any deadweight losses fro non-copetitive pricing or iperfect price discriination. With patent protection, the social optiu investent in R&D is * ρ( N V p = R. N (8 The arket equilibriu investent in R&D is given by c ρ( N p Π = R. (9 c N Equations (9 and (10 iply that N * exceeds N c if ρ( N ρ( N Π > ρ( N V N p p, when N = N c ; that is, if the elasticity of the discovery probability exceeds the ratio of private to social benefit. Figure 5 illustrates the R&D payoffs. If the opposite is true, then N * is less than N c. Published by The Berkeley Electronic Press, 2006 13
Journal of Industrial Organization Education, Vol. 1 [2006], Iss. 1, Art. 8 Payoffs and costs ρ(nv NR ρ(nπ p 0 N* N c Figure 5. Private and social returns to R&D. Nuber of R&D projects Exponential Discovery Process Next we add soe real dynaics into the R&D investent activity. We assue that the probability that discovery will occur before date t takes the specific exponential for Ft ( = 1 e ht. The probability density for discovery at date t is df( t ht f ( t = = he. dt Let T be the actual date of discovery. The probability that discovery will occur in a tie interval ( t, t + t conditional on no discovery before date t is http://www.bepress.co/jioe/vol1/iss1/8 14
Gilbert: Copetition and Innovation p( t, t + t T t = t + t t f ( τ dτ 1 F ( t = 1 e h t h t as t 0. The discovery probability is proportional to h, which is called the hazard rate (in this application, a better description is the success rate. Assue: The hazard rate depends only on current R&D expenditures, n firs copete to discover a new product. The discovery is protected by a patent that it is worth V to the first to invent; subsequent inventors earn nothing. Each fir that that engages in R&D has to pay a fixed cost, F. Each fir has a flow rate of expenditure on R&D, x i (t, which continues as long as it engages in R&D. The probability that fir i akes a discovery at date t is p t ( ( ( h x i t i = h xi e. The probability that fir i wins the patent race at date t is p i (t ties the probability that all other firs fail to discover the product at or before t. This is n h( xj t h( x ( j i t h x t j 1 ( i = ( i. j i hx e e hx e = Fir i chooses x i to axiize (see Reinganu, 1981 V i j= 1 = Vh( x ( t e 0 = [ Vh ( x 0 i n h( x ( t t j e x ( t ] e rt dt n + ( t i i 0 i n j= 1 x ( t e h( x ( t t j e rt dt F. ( h ( x j ( t r t j = 1 dt F. (10 Published by The Berkeley Electronic Press, 2006 15
Journal of Industrial Organization Education, Vol. 1 [2006], Iss. 1, Art. 8 The first ter within the integral in equation (10 is the fir s expected value per unit of tie fro winning the patent race. The second ter within the integral is the flow cost of R&D, which ends when anyone discovers the patent. Perforing the integration in (10, each fir would choose x i to axiize V i = Vh( xi xi n F. hx ( + r j= 1 j If firs have syetric R&D capabilities, each fir chooses the sae rate of R&D investent, x c and the equilibriu nuber of firs is the largest nuber N for which VN 0 and V N +1 < 0. Total investent in R&D is Nx c. The c c corresponding expected discovery tie, T = 1/ Nx. The nuber of firs that copete in the arket is an equilibriu condition that depends on the fixed cost of R&D, the discovery technology, the tie rate of discount, and the payoff to the winner of the patent race. If all firs have the sae R&D technology, we conclude that: a All firs that engage in R&D spend the sae constant aount x c until discovery, after which they stop investing in R&D. C Nh( x b The probability of discovery at or before date t is 1 - t e, where N is the nuber of firs engaged in R&D. The larger is N, the ore likely is discovery by any date, t. In this sense, ore copetition iplies ore investent in R&D and a higher probability of success. c The equilibriu nuber of firs that engage in R&D is a decreasing function of the sunk cost, F. d Conditional on F, the equilibriu nuber of firs that engage in R&D is a decreasing function of the discount rate, r. Incubent Monopoly Facing Copetition with Exponential Discovery Assue: (i (ii (ii (iii One established fir ( and one potential entrant (e. The established fir has a flow profit π(v 0 fro an old technology. If the established fir discovers the new product, its flow profit increases to π(v 1, with present value Π (v 1 discounted to the date of discovery. If the entrant is first to invent, it has a present value profit Π(v 1,v 0 and the incubent has a present value profit Π(v 0,v 1. http://www.bepress.co/jioe/vol1/iss1/8 16
Gilbert: Copetition and Innovation As in the syetric exponential odel, the entrant s expected payoff fro an R&D investent rate x e when the incubent invests at the rate x is ( ( e ( ( ( ( 1, 0 + h x t rt e = e Π e. 0 V h x v v x e e dt F (11 The incubent s expected present value is ( ( e ( ( ( 0 ( ( 1 ( ( 0, 1 h x + h x t rt = π + Π + e Π. 0 V v h x v h x v v x e e dt (12 The first ter in the first integral in equation (12 is the incubent s flow rate of onopoly profit fro the old technology. This profit flow continues if no one has invented the new technology by date t, which occurs with probability ( h( xe h( x t e +. The second ter is the incubent s expected profit if it is first to ( ( e ( invent, which occurs with probability hx ( h x h x t e +. The third ter is the incubent s expected profit if the rival is first to invent, which occurs with ( ( e ( probability hx ( h x h x t e e +. The last ter in the integral is the cost of the R&D progra, which continues if no one has invented the new technology by date t. As in the syetric odel, each fir s optial rate of R&D investent taking the other fir s investent rate as fixed is a constant until discovery occurs. The expected present value for a potential copetitor is Π( v, v h( x x 1 0 e e Ve( xe, x = F hx ( e + hx ( + r (13 and for the incubent onopolist it is π ( v +Π ( v h( x +Π( v, v h( x x V x x F 0 1 0 1 e (, e =. hx ( e + hx ( + r (14 Reinganu (1983 shows that if the innovation is drastic, then at a Nash equilibriu the incubent invests in R&D at a rate that is strictly less than the rate of investent by the potential entrant. If the innovation is drastic, the value functions (13 and (14 reduce to Published by The Berkeley Electronic Press, 2006 17
Journal of Industrial Organization Education, Vol. 1 [2006], Iss. 1, Art. 8 and Π( v h( x x 1 e e Ve( xe, x = F hx ( e + hx ( + r π ( v +Π( v h( x x V x x F 0 1 (, e =. hx ( e + hx ( + r The expected profits differ only in that incubent has the profit flow π(v 0. This causes the incubent to invest strictly less than the potential entrant. For a nondrastic innovation, the incubent ay invest ore than the potential entrant if Π(v 1 - Π(v 1,v 0 - Π(v 0,v 1 is sufficiently large. A More General Model Predictions about copetition in patent races depend on the stochastic relationship between R&D expenditures and discovery. The odel in Fudenberg et al. (1983 generates equilibriu investents that differ sharply fro the exponential odel in Reinganu (1981. In their odel firs invest heavily in R&D when their experience levels are close. If one fir gets sufficiently ahead, others drop out of the R&D race and the leader continues to invest at a ore oderate pace. This is in sharp contrast to the equilibriu predictions in Reinganu s odel, where firs continue at the sae rate until one of the akes a discovery. Are general stateents possible? Doraszelski (2003 considers a odel in which the probability of success is exponential at any point in tie with a success rate that depends on both current and cuulative R&D expenditures. This siple twist akes the odel uch ore general, but also uch ore difficult to solve and ost of the results rely on nuerical siulations. The siulations show that the ore coplicated hazard rate function can support a wide range of copetitive behavior in a patent race. In particular, a fir that lags a rival in cuulative R&D experience ay optially invest ore than its rival to catch up. The reason why is intuitive. Because the probability of success increases with a fir s cuulative experience, a fir that is in the lead can reduce its expenditure on R&D and exploit the enhanced success probability fro its large knowledge stock. This knowledge effect gives a follower the opportunity to catch up by spending ore on R&D. When the knowledge effect is large, the dynaics of the patent race do not reinforce doinance and there is instead an equalization effect. Firs with less cuulative R&D experience work harder to catch up to firs with larger knowledge stocks, while firs with large http://www.bepress.co/jioe/vol1/iss1/8 18
Gilbert: Copetition and Innovation knowledge stocks tend to scale back their expenditures on R&D and coast on the value created by their past investents. Doraszelski (2003 also shows that a fir ay increase or decrease its R&D expenditures in response to an increase in a rival s knowledge stock and firs ay or ay not copete ost severely when their knowledge stocks are equal. Specific results depend on the shape of the success probability as a function of R&D experience. If the success probability is a concave function of cuulative R&D, then there are diinishing returns to experience and the knowledge effect iplies that a follower always invests ore than the leader in R&D. If the success probability is a convex function of cuulative R&D, then R&D generates increasing returns, which gives a fir an incentive to invest and build up its knowledge capital. Even in this case, Doraszelski s siulations show that a follower has an incentive to invest to catch up to the leader once its own knowledge stock becoes sufficiently large. Predictions of the equilibriu outcoes of patent races depend on the precise nature of the discovery technology. When experience is critical to innovation and there is little or no uncertainty in the discovery process, a fir that is ahead in the R&D copetition can aintain its lead and guarantee success. Knowing this, other firs ay choose to abandon the R&D race without a fight. Preeption is ore difficult when discovery is uncertain, and in soe cases a fir that is behind in the R&D race has incentives to work harder and close the gap that separates it fro the current leader. Under these circustances the dynaics of R&D copetition can create incentives for R&D investents that erode the position of a arket leader. VII. Beyond Profit-Maxiization Many of the odels we have discussed so far predict a onotonic relationship between the extent of copetition and innovative output. For exaple, in the patent race odel with exponential discovery probabilities, increasing the nuber of R&D copetitors advances the expected date at which discovery occurs (Reinganu, 1981. In the Dasgupta-Stiglitz (1980 odel of cost-reducing R&D with non-exclusive property rights, increasing the nuber of copetitors reduces the aount of cost-reduction. The effect of copetition is also onotonic in this odel, although in the opposite direction. There is an intuitive arguent that oderate levels of copetition should be ost effective in prooting innovation. In highly copetitive arkets the incentive to innovate ay be low because the innovator s sall scale of operations ay liit its benefit fro a new technology. In arkets that are close to onopolies, the Arrow replaceent effect should doinate. To the extent that arket concentration is a reasonable proxy for the degree of copetition, this suggests that interediate levels of arket Published by The Berkeley Electronic Press, 2006 19
Journal of Industrial Organization Education, Vol. 1 [2006], Iss. 1, Art. 8 concentration are the ost fertile environents for innovative activity. However, few odels that rely solely on the pursuit of profit-axiization generate innovation incentives that peak at oderate levels of copetition. 3 Leibenstein (1966 argued that anagers do not apply the effort necessary to reach the frontier of the fir s production function, and this slack is greater for anagers who are not exposed to significant copetition. The owners of firs (the principals want anagers, acting as their agents, to exert effort to run the fir in an efficient anner. This effort could include investing in and thinking creatively about new processes and products. The activity of invention requires ingenuity, hard work, and risk-taking, and often requires anagers to ake changes in operating procedures that can be stressful and can ipose severe hardships on soe workers. Hicks (1935 said it well when he wrote that The best of all onopoly profits is a quiet life. Martin (1993 develops a odel in which owners offer incentives to privately infored anagers to prod the to invest in cost-reducing R&D. In other respects the odel is siilar to that in Dasgupta and Stiglitz (1980 and indeed the odel predictions are also siilar. Investent in cost-reducing R&D is a decreasing function of the nuber of firs in the industry; the greater the nuber of copetitors, the higher is the equilibriu level of the arginal cost. Private inforation, alone, does not change the result that copetition lowers incentives for cost-reducing R&D with non-exclusive intellectual property rights. Schidt (1997 and Aghion et al. (1999 generate stronger results about the disciplining effect of copetition by allowing for the possibility of bankruptcy. Bankruptcy has punitive consequences for a fir s anagers, who are at least teporarily out of a job, and they exert effort to avoid this unhappy state. In Aghion et al. (1999 adopting a new technology iposes an adjustent cost in addition to the direct expense associated with the technology that anagers (or engineers wish to iniize. Innovation keeps the copany ore efficient and reduces the likelihood of bankruptcy. All else equal, copetition akes bankruptcy ore likely. In their odel anagers innovate ore in copetitive arkets because copetition holds anagers feet to the fire. The risk of bankruptcy is low in onopolistic arkets, and so is the need to innovate, so anagers of onopoly firs can enjoy the quiet life. The odel in Aghion et al. (1999 illustrates how onopoly profits can shield anagers fro the hard work of being innovative, but it does not lead to a robust conclusion that copetition prootes innovation. As the authors note, anagerial preferences could diverge fro profit axiization because they are 3 The dynaic odel in Aghion et al. (2002 generates an inverted-u relationship between R&D and arket concentration, but the odel assues a rather special sequential structure for innovation. http://www.bepress.co/jioe/vol1/iss1/8 20
Gilbert: Copetition and Innovation loathe to innovate or because they are techno-freaks who enjoy adopting the latest new technology. If anagers have an inclination to overspend on new technologies, copetition would slow innovation by aking bankruptcy ore likely and forcing anagers to be ore efficient and innovate less. The effects of copetition on anagerial perforance also depend on whether firs are active in credit arkets. Managers ay have to act efficiently to avoid bankruptcy if their firs are saddled with debt. In Aghion et al. (1999 copetition affects anagerial payoffs solely through the risk of bankruptcy. Schidt (1997 incorporates the profits fro cost reduction in the utility function of the fir s owners and derives conditions under which copetition leads to ore or less effort by anagers to reduce costs. In Schidt s odel greater copetition has two opposing consequences for anagerial effort and innovation. By reducing each fir s deand, greater copetition lowers the incentive to innovate, as in the odels developed by Dasgupta and Stiglitz (1980 and Martin (1993. Greater copetition also increases the risk of bankruptcy, which encourages anagers to innovate to preserve their jobs and akes it easier for the owner to induce additional effort. 4 By increasing the risk of bankruptcy, copetition results in ore innovative effort. But copetition also lowers the return to a cost-reducing innovation by reducing the output of each fir. Thus, there are two effects that act in different directions. Under reasonable assuptions, the output effect should doinate if copetition is sufficiently intense, which suggests that investent in costreducing effort should peak at soe interediate level of arket concentration. Thus Schidt s odel can generate a relationship between innovation and copetition that has an inverted-u shape, as opposed to the onotonic relationship in ost other odels of innovation that ignore anagerial incentives. Although these results are insightful, this line of inquiry would benefit fro additional theoretical and epirical research. Furtherore, the results include the usual caveat that R&D investent can be redundant with non-exclusive intellectual property rights, and axiizing R&D effort is not the sae as axiizing innovative output. We have not even delved into the vast epirical literature on the relationship between copetition and innovation. This discussion of the theory should ake you better able to interpret the epirical results. I refer those who are interested in the epirical literature to the survey in Gilbert (2006. 4 This assues that anagers are not indifferent between working for the fir and taking another job. If they were indifferent, that would liit the ability of the owner to induce additional effort. Published by The Berkeley Electronic Press, 2006 21
Journal of Industrial Organization Education, Vol. 1 [2006], Iss. 1, Art. 8 References Aghion, Philippe, Mathias Dewatripont, and Patrick Rey (1999, Copetition, Financial Discipline and Growth, The Review of Econoic Studies, vol. 66, pp. 825-852. Aghion, Philippe, Nicholas Bloo, Richard Blundell, and Peter Howitt (2002, Copetition and Innovation: An Inverted-U Relationship, National Bureau of Econoic Research, Working paper 9269, Cabridge, MA. Arrow, Kenneth J. (1962, Econoic Welfare and the Allocation of Resources to Invention, in R.R. Nelson (ed., The Rate and Direction of Econoic Activity, Princeton University Press, N.Y. Cohen, Wesley M. and Richard C. Levin (1989, Epirical Studies of Innovation and Market Structure, in R. Schalensee and R.D. Willig (eds., Handbook of Industrial Organization, vol. II. Dasgupta, Partha and Joseph Stiglitz (1980, Industrial Structure and the Nature of Innovative Activity, Econoic Journal, vol. 90, pp. 266-293. Dixit, Avinash and Joseph Stiglitz (1977, Monopolistic Copetition and Optiu Product Diversity, Aerican Econoic Review, vol. 67, pp. 297-308. Fudenberg, Drew, Richard Gilbert, Joseph Stiglitz and Jean Tirole (1983, Preeption, Leapfrogging and Copetition in Patent Races, European Econoic Review, vol. 22, pp. 3-32. Gilbert, Richard J. (2006, Looking for Mr. Schupeter: Where Are We in the Copetition-Innovation Debate?, forthcoing in Josh Lerner and Scott Stern (eds, Innovation Policy and Econoy, NBER, MIT Press. Gilbert, Richard and David Newbery (1982, Preeptive Patenting and the Persistence of Monopoly, Aerican Econoic Review, vol. 72(2, pp. 514-526. Greenstein, Shane and Garey Raey (1998, Market Structure, Innovation and Vertical Product Differentiation, International Journal of Industrial Organization, vol. 16, pp. 285-311. Griliches, Zvi (1992, The Search for R&D Spillovers, Scandinavian Journal of Econoics, vol. 94, pp. S29-47. Hall, Bronwyn and Rose Marie Ziedonis (2001, The Patent Paradox Revisited: An Epirical Study of Patenting in the U.S. Seiconductor Industry, 1979-1995, Rand Journal of Econoics, vol. 32, pp. 101-28. Hicks, J. R. (1935, Annual Survey of Econoic Theory: The Theory of Monopoly, Econoetrica, Vol. 3, No. 1., pp. 1-20. Levin, Richard C., Wesley M. Cohen, and David C. Mowery (1985, R&D Appropriability, Opportunity, and Market Structure: New Evidence on http://www.bepress.co/jioe/vol1/iss1/8 22
Gilbert: Copetition and Innovation Soe Schupeterian Hypotheses, Aerican Econoic Review, vol. 75, pp. 20-24. Leibenstein, Harvey (1966, Allocative Efficiency versus X-Efficiency, Aerican Econoic Review, vol. 56, no. 3, pp. 392-415. Martin, Stephen (1993, Endogenous Fir Efficiency in a Cournot Principal- Agent Model, Journal of Econoic Theory, vol. 59, pp. 445-450. National Science Foundation (2004, Product versus process applied research and developent, by selected industry, available at http://www.nsf.gov/sbe/srs/iris. Reinganu, Jennifer F. (1981, Dynaic gaes of innovation, Journal of Econoic Theory, vol. 25, pp. 21-41. Reinganu, Jennifer F. (1983, Uncertain Innovation and the Persistence of Monopoly, Aerican Econoic Review, vol. 73, pp. 741-748. Schidt, Klaus M. (1997, Managerial Incentives and Product Market Copetition, The Review of Econoic Studies, vol. 64, no. 2, pp. 191-213. Schupeter, Joseph A. (1942, Capitalis, Socialis, and Deocracy. New York: Harper and Brothers. (Harper Colophon edition, 1976. Tirole, Jean (1997, The Theory of Industrial Organization, MIT Press. Published by The Berkeley Electronic Press, 2006 23