Journal of Industrial Organization Educationdiscovery of the same or similar invention, although they restrict the ability of firms to copy inventions made by others. The dynamics

Journal of Industrial OrganizationEducation

Volume1, Issue1 2006 Article 8

Competition and Innovation

Richard J. Gilbert∗

∗Economics Department, University of California, Berkeley, [email protected]

Copyright c©2006 The Berkeley Electronic Press. All rights reserved.

Competition and Innovation

Richard J. Gilbert

Abstract

A vast and often confusing economics literature relates competition to investment in innova-tion. Following Joseph Schumpeter, one view is that monopoly and large scale promote investmentin research and development by allowing a firm to capture a larger fraction of its benefits and byproviding a more stable platform for a firm to invest in R&D. Others argue that competition pro-motes innovation by increasing the cost to a firm that fails to innovate. This lecture surveys theliterature at a level that is appropriate for an advanced undergraduate or graduate class and attemptsto identify primary determinants of investment in R&D. Key issues are the extent of competitionin product markets and in R&D, the degree of protection from imitators, and the dynamics ofR&D competition. Competition in the product market using existing technologies increases theincentive to invest in R&D for inventions that are protected from imitators (e.g., by strong patentrights). Competition in R&D can speed the arrival of innovations. Without exclusive rights to aninnovation, competition in the product market can reduce incentives to invest in R&D by reduc-ing each innovator’s payoff. There are many complications. Under some circumstances, a firmwith market power has an incentive and ability to preempt rivals, and the dynamics of innovationcompetition can make it unprofitable for others to catch up to a firm that is ahead in an innovationrace.

KEYWORDS: R&D, game theory, dynamics

“What we have got to accept is that [the large-scale establishment or unit of control] has come to be the most powerful engine of [economic] progress and in particular of the long-run expansion of total output...In this respect, perfect competition is not only impossible but inferior, and has no title to being set up as a model of economic efficiency.” Joseph Schumpeter (1942). “The best of all monopoly profits is a quiet life.” J.R. Hicks (1935)

I. Introduction There is broad agreement among economists that research and development is a major source of economic growth. Although estimates differ, most studies show a high correlation between R&D expenditures and productivity growth after accounting for investment in ordinary capital. Studies also show that the social return to investment in R&D is higher than the private return (Griliches, 1992), which suggests that policies that promote innovation can pay large dividends for society. One way to achieve these benefits is to promote industry structures that offer greater incentives for innovation, including policies toward mergers and laws that govern exclusionary conduct. This lecture reviews the economic theory relating competition to innovative activity. We use the term innovation to describe both the act of invention and the activity required to bring the invention to the market. As a general statement, the incentive to innovate is the difference in profit that a firm can earn if it invests in R&D compared to what it would earn if it did not invest. These incentives depend on many factors, including: the characteristics of the invention, the strength of intellectual property protection, the extent of competition before and after innovation, barriers to entry in production and R&D, and the dynamics of R&D. Innovations may be new products or new processes. A product innovation is a new or improved good or service. A process innovation lowers the cost of producing a good or service. It is more difficult to make general statements about incentives for product innovations because a firm’s profit before and after innovation occurs depends on fixed costs, price competition and the mix of other products in its portfolio. Even without investment in R&D, firms may supply too many or too few products from the perspective of total economic welfare. See, e.g., Dixit and Stiglitz (1977). The strength of intellectual property protection determines the extent to which the inventor can exploit the potential of her discovery to add value to the economy. I assume that patent protection, when it exists, gives the inventor

1

Gilbert: Competition and Innovation

Published by The Berkeley Electronic Press, 2006

permanent and total protection from imitation. While this is an extreme assumption of “exclusive rights” to an invention, it serves to illustrate the consequences of strong intellectual property rights. Keep in mind that patent protection does not guarantee that the inventor will be able to prevent competition from 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 most industries (see, e.g., See Levin et al. (1985), Cohen and Levin (1989), and Hall and Ziedonis (2001)).1 Firms have “non-exclusive” intellectual property rights to their inventions when others can independently invent similar products or processes without infringing on the inventor’s rights. Non-exclusive intellectual property rights are similar to trade secrets. Non-exclusive rights do not prevent independent discovery of the same or similar invention, although they restrict the ability of firms to copy inventions made by others. The dynamics of the innovation process affect incentives to invest in R&D. A firm may be able to pre-empt competitors in R&D if a head start in the innovation process gives the firm a discrete advantage in securing an exclusive right to the innovation. If that is not the case, firms can simultaneously engage in R&D, each with a reasonable expectation that its R&D expenditures will generate a significant return. The many different predictions of theoretical models of R&D lead some to conclude that there is no coherent theory of the relationship between competition and investment in innovation. That is not quite correct. The models have clear predictions, although they differ in important ways that can be related to market and technological characteristics. It is not that we don’t have a model of competition and R&D, but rather that we have many models and it is important to know which model is appropriate for each market context. Researchers should distinguish the different theories when formulating empirical tests of the relationship between competition and innovation. We begin with a process innovation that lowers the constant marginal cost of producing a product. Section II presents the benchmark cases of socially optimal investment in R&D and investment in R&D by a monopoly that is protected from both product market and R&D competition. Section III introduces competition in R&D. Section IV examines product innovation with exclusive IP rights. Section V returns to process innovations, but assumes that inventors have only non-exclusive intellectual property rights. Section VI examines the consequences of dynamic competition in R&D.

1 The pharmaceutical industry is a notable exception.

2

Journal of Industrial Organization Education, Vol. 1 [2006], Iss. 1, Art. 8

http://www.bepress.com/jioe/vol1/iss1/8

II. Process Innovations: Social Optimum and Pure Monopoly These two cases require no assumptions about the nature of intellectual property rights. In the case of socially optimal R&D, we assume that the invention is available for use under conditions of perfect competition and the public pays for the cost of R&D with no deadweight costs for society. In the case of a pure monopoly, IP rights are irrelevant because there is no competition. This discussion generally follows Tirole (1987). Socially optimal innovation incentives A homogenous good is sold at price p and produced at constant marginal cost, c. Demand is q(p) with ( ) / 0dq p dp < . Given the production technology, total economic welfare reaches a maximum when price is equal to marginal cost. In the socially optimal allocation there are no profits and total welfare is equal to consumer surplus.

( ) ( ) ( ) .c

W c S c q x dx∞

= = ∫

Note that ( ) / ( )dW c dc q c= − . For an innovation that reduces the marginal production cost by a small amount, the social value of the innovation is proportional to the amount consumed when the price is equal to the marginal production cost. This simple observation is key to understanding the social value of innovation incentives under different market structures. The change in total welfare from a discrete investment in R&D that lowers the marginal cost of making the good to c1 < c0 is

01

0 1

1 0

( )( ) ( ) ( )

cc

c c

dW xW c W c W dx q x dx

dx− ≡ ∆ = =∫ ∫ (1)

This is the total achievable benefit to society from R&D that reduces marginal cost from c0 to c1. It is the area c1c0bd in Figure 1.

3



d

b

Quantityq(c1)q (c0)0

c1

c0

Price

demand

∆W

Figure 1. Social value of process innovation

Monopoly in production (pre- and post-innovation) and in R&D Figure 2 illustrates the monopolist’s profit from a drastic innovation. A process innovation is drastic if the monopoly price with the innovation is lower than the marginal cost before the innovation: pm(c1) < c0. It is drastic in the sense that no firm with the old technology can compete with a firm that has the new technology when the firm with the new technology chooses a monopoly price. The new technology makes the old technology obsolete. Figure 3 shows the monopolist’s profit from a non-drastic innovation, for which pm(c1) ≥ c0. The figures show the profits earned by the monopolist with the old and new technologies; πm(c0) and πm(c1) respectively.

4



pm(c1)

Quantityqm(c1)qm(c0)0

πm(c1)

πm(c0)

c1

c0

Price

pm(c0)

demand

Figure 2. Monopoly profits with drastic innovation

qm(c0) Quantity0

πm(c1)

πm(c0)

c1

c0

demand

pm(c0)

qm(c1)

Figure 3. Monopoly profits with non-drastic innovation

5



Assume the monopolist charges a uniform price, pm. Define ))(()( cpqcq mm ≡

and note that )(cqdc

dppcdc

d mmmmm

−=∂

∂+∂

∂= πππ . The change in monopoly

profits from the cost reduction is

01

0 1

1 0( )( ) ( ) ( ) .

cc mm m m m

c c

d xc c dx q x dxdx

ππ π π− ≡ ∆ = =∫ ∫ (2)

Compare the social and monopoly incentive for innovation. From equations (1) and (2) we have

0

1

[( ( ) ( ))] 0,c

m m

c

W q x q x dxπ∆ − ∆ = − ≥∫ (3)

because q(c) ≥ qm(c), with a strict inequality if q(c) > qm(c) for any ],[ 10 ccc ∈ . If a monopolist charges all consumers a single price, the monopoly value of a process innovation is (weakly) less than the social value. The monopoly profit from the cost reduction is less than the social benefit because the monopolist produces less than the socially optimal level. Innovation replaces the monopolist’s old profit stream, πm(c0), with a new profit steam, πm(c1). This replacement effect lowers the monopolist’s incentive to invest in R&D. But this is not the reason why the monopolist’s incentive to invest in R&D is lower than the socially optimal incentive. There is a replacement effect for society as well, because invention replaces one value stream with another. The difference in the value of R&D follows from differences in socially optimal and monopoly outputs. If the monopolist were able to price discriminate perfectly, it would produce efficiently with and without the innovation and the monopoly value of the process innovation would equal its social value. Next, we consider the effects of competition on incentives to innovate when inventions have the protection of exclusive intellectual property rights. III. Competition for Process Innovations with Exclusive IP Rights There are two different cases to consider. In the first case there is perfect competition in the old technology and competition to invest in a new process

6



innovation. In the second case there is a monopoly in the old technology and competition to invest in the new process innovation. In both cases we assume that the winner of the R&D competition has an exclusive intellectual property right to the new process. Competition in production pre-innovation and competition in R&D

With perfect competition, pre-innovation each firm earns 0)( 0 =cπ . There is no replacement effect because with perfect competition there are no pre-innovation profits to replace. For a drastic innovation, the successful inventor’s profit from invention is the monopoly profit )( 1cmπ . Figure 2 shows that 1 1 0( ) ( ) ( ).c m m m mc c cπ π π π π∆ = > ∆ = − The comparison of innovation incentives is less clear for a non-drastic innovation (Figure 3). Competition from the old technology limits the inventor’s price to c0, which is less than its monopoly price. The inventor’s corresponding output is q(c0). Noting this, we can write the inventor’s profit as

mc

c

mc

c

c dxxqdxcqcqcc ππ ∆=>=−=∆ ∫∫0

1

0

1

)()()()( 0010 .

The incentive to invest in R&D when there is pure competition pre-innovation is higher than the incentive to invest in R&D under pure monopoly, because there is no replacement effect in the case of pure competition. A monopoly has a stream of profits that is lost (replaced) by innovation. Competitors have nothing to lose from innovation, and hence more to gain. How do R&D incentives for a perfectly competitive industry compare to socially optimal incentives? In Figure 4 the social value of a drastic process innovation that lowers constant marginal production costs from c0 to c1 is the area c1c0bd. For the case of perfect competition in the pre-innovation market, we have ∆πc = πm(c1), which is less than the social value of the innovation. For a non-drastic innovation, we have

Wcqccc ∆≤−=∆ )()( 010π , where the inequality is strict unless demand is perfectly inelastic.

7



c1

pm(c1)

b

d

Quantityqm(c1)qm(c0)0

πm(c1)

c0

Price

demand

Figure 4. R&D incentives for drastic innovation with perfect competition in the old technology.

This analysis shows that cW π∆≥∆ and the previous analysis showed that

mc ππ ∆>∆ . Thus we conclude that .c mW π π∆ ≥ ∆ > ∆ The first inequality is also strict except for the case of perfectly inelastic demand. Monopoly in production pre-innovation and competition in R&D Following Gilbert and Newbery (1982), we now assume that initially there is a single firm in the industry with the old technology, c0. There is competition in R&D, which we assume takes a particular stylized form: firms “bid” for a patent, which is awarded to the highest bidder. A firm that is outside the industry would be willing to bid up to ),( 01 ccdπ . This is the firm’s duopoly profit when the firm has marginal cost c1 and a rival has marginal cost c0. The incumbent would bid up to ),()( 101 ccc dm ππ − . The first term is the monopoly profit with marginal cost c1. By winning the patent the firm retains its monopoly position and lowers its marginal cost from c0 to c1. The second term is the profit the firm would earn

8



when it has marginal cost c0 and a rival wins the patent and enters with marginal cost c1. We assume that payoffs do not depend on the identity of the firm. The monopolist has (weakly) more to gain from the patent because 1 0 1 1 0( ) ( , ) ( , ).m d dc c c c cπ π π− ≥ This follows because the monopoly profit with marginal cost c1 is at least as large as the sum of the duopoly profits. This is an example of preemptive competition. The incentive to preempt is driven by what Tirole (1997) calls the “efficiency effect”. This is the gap between monopoly profits and total industry profits with competition. The efficiency effect increases the monopolist’s incentive to invest in R&D when preemption is feasible. Note that in general this result holds only for a firm that has a monopoly in the old technology. Suppose there are n identical incumbent firms. Each has profit ),...,( 00 ccnπ . The first entry denotes the firm’s marginal cost; the remaining entries denote the marginal costs of the other firms. If one of them wins the patent, its profit is ),...,,( 001 cccnπ and the other incumbents earn

),...,,( 100 cccnπ . (Firms are symmetric, so the ordering does not matter.) If a new firm enters with the new technology, it earns ),...,,( 0011 cccn+π and the incumbent firms earn ),...,,( 1001 cccn+π . An incumbent has a greater incentive to bid for the patent only if

),...,,(),...,,(),...,,( 00111001001 ccccccccc nnn ++ >− πππ . This inequality does not hold in general. An example is Nash-Cournot competition with (c0 – c1) sufficiently small. Table 1 summarizes our results.

Table 1. Innovation incentives under different market structures Old Technology New Technology Incentive to invent

Monopoly Monopoly 1 0( ) ( )m m mc cπ π π∆ = −

Perfect Competition

Competition for patent monopoly

1( )c m cπ π∆ = > mπ∆ if drastic

0 1 0( ) ( )c c c q cπ∆ = − > mπ∆ otherwise

Monopoly Monopoly + Competition for Patent Monopoly

1 0 1 1 0( ) ( , ) ( , )m d dc c c c cπ π π− ≥

9



IV. Product Innovation with Exclusive IP Rights We have limited our analysis to process innovations that lower the marginal 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 many of the breakthroughs that spur economic growth and advance consumer welfare.2 The analysis of innovation incentives is more complicated for product innovations for at least two reasons. First, even firms that act as competitive price-takers can earn positive profits when they offer differentiated products. This means that a competitive firm also faces a replacement effect from the profit that it could earn using the pre-innovation products. Second, a new product changes the ability of a monopolist to discriminate among consumers. For a process innovation, a reasonable assumption is that the new technology dominates the old technology and hence the old process technology is irrelevant to the profit that the monopolist can earn with the new process. This is not necessarily a good assumption for product innovations. A new product can allow a firm with a portfolio that includes the old product to differentiate its offerings and extract more surplus from consumers than would be possible using only the new product. For example, the willingness to pay for a new product could be inversely correlated with the willingness to pay for a monopolist’s old product. This could allow the firm to bundle the two products and charge a price that extracts most of the available surplus. By improving the monopolist’s ability to price discriminate among consumers an innovation can increase a monopolist’s profit by more than the profit that a new competitor can earn. As in the case of a process innovation, a monopolist’s incentive to invest in R&D for a new product is the difference in the monopoly profits with and without the new product. Assuming away differences in managerial efficiency, competition ensures that a competitor’s profit using the old product is no greater than a monopolist’s profit using only the old product. Hence the replacement effect should be less for a competitive firm, although it is not likely to be zero when firms sell differentiated products. This implies that a competitor has a greater net incentive to invest in product innovation. However, the replacement effect is only half of the equation. A monopolist may be able earn more with the new product than a competitor could earn when it sells the new product in competition with the former monopolist. We cannot make a general conclusion that for product innovations a monopolist has a lower incentive to invent. An ordering of incentives for product innovation in monopoly and competitive markets is difficult to obtain even if the innovation is drastic. A 2 The National Science Foundation estimated that in 1981, about 75% or all industry R&D was directed to product innovations. National Science Foundation (2004).

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product innovation is drastic if the competitor’s profit with the new product is the same as if it were a monopolist 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 monopolist 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 monopolist if we impose a stronger condition on the characteristics of the new product. A competitor will have a greater incentive to innovate if the new product makes the old product obsolete, so that a firm with the new product has no use for the old product and a firm with the old product cannot earn a profit if another firm has the new product. Any innovation that makes the old product obsolete is also drastic, but the opposite need not be the case. If the new product makes the old product obsolete, the competitor’s gross benefit from innovation is no less than the monopolist’s and it faces a smaller replacement effect. Hence the competitor’s net benefit would be larger in this case. See Greenstein and Ramey (1998) for an example of incentives to invest in product innovation with vertically differentiated products and Gilbert (2006) for an example of R&D incentives with both horizontal and vertical differentiation. V. Competition and Innovation with Non-Exclusive Intellectual Property Rights The pure monopoly incentives to invest in R&D are the same with exclusive and non-exclusive rights, because by assumption there are no rivals for IP rights to exclude. Moving beyond the pure monopoly case, the competitive incentives to invest in R&D depend on the extent of competition and the ease of imitation. We assume that with non-exclusive rights firms cannot prevent duplicative invention, but they can prevent copying. An example 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 same invention.

We return to the simpler case of process innovation. Suppose the innovation is drastic. As a consequence competition will occur only among firms that invest successfully in R&D. Let c1 be the constant marginal cost of production with the process innovation. Following Dasgupta and Stiglitz (1980), index the firms by i = 1,...,N and suppose that n ≤ N identical firms invest in R&D and compete as Nash-Cournot competitors with the new process. Omitting the cost of R&D, each firm makes a profit 1 1( , ) ( ) ( ).i ic n p c q pπ = − (4)

11



Profit maximization implies the inverse elasticity rule

1 1

f

p cp ε− = (5)

where εf is the firm-specific elasticity of demand. Substituting equation (5) into equation (4), it follows that each firm’s profit from invention is /i fpq ε . In the Nash-Cournot case with symmetric firms, εf = nε, where ε is the elasticity of demand for the entire market and n is the number of firms that successfully invent. In this symmetric Nash-Cournot case, each firm’s incentive to invent is

ε2)(

nppQ where Q(p) is the industry demand at price p. For the case of constant

elasticity of demand, ε2

)(n

ppQ is a declining function of n if nε > 1; this is required

for existence of a symmetric Nash-Cournot equilibrium. In this case the incentive to invent is a declining function of the number of firms in the industry. If R&D incurs a cost, K, and the firms are symmetric, then with free entry into R&D the number of firms is the largest number n for which

11 ( ) ( ) .p c Q p Kn

− ≥ (6)

Substituting (5) in (6) with εf = nε, and assuming that firms just break even, gives

1 .nKpQ nε

= (7)

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, implying that the industry R&D intensity is a decreasing function of the number of firms that invest in R&D. In this model increasing competition reduces industry R&D intensity. In this sense greater competition reduces R&D expenditures. Also, note that R&D is redundant with non-exclusive rights. It would be more efficient to have one firm engage in cost-reducing R&D and to distribute the results of that R&D industry-wide.

12



VI. Innovation Dynamics R&D unfolds over time, but the analysis so far has been essentially static. Firms invest in R&D, one or more firms succeed, and the industry moves to a new post-innovation equilibrium. This section considers how the dynamics of R&D investment affects our conclusions. We begin with a simple model of equilibrium R&D investment 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

)(Nρ with 0)0( =ρ , 0)( >′ Nρ and 0)( <′′ Nρ . The socially optimal number of R&D projects is the solution to max ( ) .

NN V NRρ −

The private value of the invention is Πp. The social value of the invention when it is supplied privately is Vp. This can be less than the (gross) social value V* to the extent that there are any deadweight losses from non-competitive pricing or imperfect price discrimination. With patent protection, the social optimum investment in R&D is

*( ) .pN V R

Nρ∂ =∂

(8)

The market equilibrium investment in R&D is given by

( ) .c

pc

N RN

ρ Π = (9)

Equations (9) and (10) imply that N* exceeds Nc if

p

p

VN

NN

NΠ>

∂

)()(

)(

ρρ

ρ,

when N = Nc; 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 Nc.

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Payoffsand costs

NR

ρ(N)Πp

N* N c

ρ(N)V

Number of R&D projects

0

Figure 5. Private and social returns to R&D.

Exponential Discovery Process Next we add some real dynamics into the R&D investment activity. We assume that the probability that discovery will occur before date t takes the specific exponential form ( ) 1 .htF t e−= −

The probability density for discovery at date t is

( )( ) .htdF tf t hedt

−= =

Let T be the actual date of discovery. The probability that discovery will occur in a time interval ),( ttt ∆+ conditional on no discovery before date t is

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th

tt

t etF

dftTtttp ∆−

∆+

−=−

=≥∆+∫

1)(1

)(),(

ττth∆→ as 0→∆t .

The discovery probability is proportional to h, which is called the hazard rate (in this application, a better description is the success rate). Assume:

• The hazard rate depends only on current R&D expenditures, • n firms compete 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 firm that that engages in R&D has to pay a fixed cost, F. • Each firm has a flow rate of expenditure on R&D, xi(t), which continues as

long as it engages in R&D. The probability that firm i makes a discovery at date t is

( )( ) ( ) .ih x ti ip t h x e−=

The probability that firm i wins the patent race at date t is pi(t) times the probability that all other firms fail to discover the product at or before t. This is

1

( )( )( )( ) ( ) .

n

jj ji

h x th x th x t

i ij i

h x e e h x e =

−−−

≠

∑=∏

Firm i chooses xi to maximize (see Reinganum, 1981)

.)())((0

))((

0

))((11 FdteetxdteetxVhV rt

ttxh

irt

ttxh

ii

j

n

jj

n

j −∑

−∑

= −∞ −

−∞ −

∫∫ ==

.)]())(([0

)))(((1 FdtetxtxVh

n

jj trtxh

ii −∑

−= ∫∞ +−

= (10)

15



The first term within the integral in equation (10) is the firm’s expected value per unit of time from winning the patent race. The second term within the integral is the flow cost of R&D, which ends when anyone discovers the patent. Performing the integration in (10), each firm would choose xi to maximize

1

( ) .( )

i ii n

jj

Vh x xV Fh x r

=

−= −+∑

If firms have symmetric R&D capabilities, each firm chooses the same rate of R&D investment, xc and the equilibrium number of firms is the largest number N for which 0≥NV and .01 <+NV Total investment in R&D is Nxc. The corresponding expected discovery time, 1/c cT Nx= . The number of firms that compete in the market is an equilibrium condition that depends on the fixed cost of R&D, the discovery technology, the time rate of discount, and the payoff to the winner of the patent race. If all firms have the same R&D technology, we conclude that:

a) All firms that engage in R&D spend the same constant amount xc until discovery, after which they stop investing in R&D.

b) The probability of discovery at or before date t is 1 - ( ) ,CNh x te where

N is the number of firms engaged in R&D. The larger is N, the more likely is discovery by any date, t. In this sense, more competition implies more investment in R&D and a higher probability of success.

c) The equilibrium number of firms that engage in R&D is a decreasing function of the sunk cost, F.

d) Conditional on F, the equilibrium number of firms that engage in R&D is a decreasing function of the discount rate, r.

Incumbent Monopoly Facing Competition with Exponential Discovery Assume:

(i) One established firm (m) and one potential entrant (e). (ii) The established firm has a flow profit π(v0) from an old technology. (ii) If the established firm discovers the new product, its flow profit

increases to π(v1), with present value Π (v1) discounted to the date of discovery.

(iii) If the entrant is first to invent, it has a present value profit Π(v1,v0) and the incumbent has a present value profit Π(v0,v1).

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As in the symmetric exponential model, the entrant’s expected payoff from an R&D investment rate xe when the incumbent invests at the rate xm is

( ( ) ( ))1 0

0

( ( ) ( , ) ) .e mh x h x t rte e eV h x v v x e e dt F

∞− + −= Π − −∫ (11)

The incumbent’s expected present value is

( ( ) ( ))0 1 0 1

0

( ( ) ( ) ( ) ( ) ( , ) ) .e mh x h x t rtm m e mV v h x v h x v v x e e dtπ

∞− + −= + Π + Π −∫ (12)

The first term in the first integral in equation (12) is the incumbent’s flow rate of monopoly profit from the old technology. This profit flow continues if no one has invented the new technology by date t, which occurs with probability

( ( ) ( )) .e mh x h x te− + The second term is the incumbent’s expected profit if it is first to invent, which occurs with probability ( ( ) ( ))( ) .e mh x h x t

mh x e− + The third term is the incumbent’s expected profit if the rival is first to invent, which occurs with probability ( ( ) ( ))( ) .e mh x h x t

eh x e− + The last term in the integral is the cost of the R&D program, which continues if no one has invented the new technology by date t. As in the symmetric model, each firm’s optimal rate of R&D investment taking the other firm’s investment rate as fixed is a constant until discovery occurs. The expected present value for a potential competitor is

1 0( , ) ( )( , )( ) ( )

e ee e m

e m

v v h x xV x x Fh x h x r

Π −= −+ +

(13)

and for the incumbent monopolist it is

0 1 0 1( ) ( ) ( ) ( , ) ( )( , ) .( ) ( )

m e mm m e

e m

v v h x v v h x xV x x Fh x h x r

π + Π + Π −= −+ +

(14)

Reinganum (1983) shows that if the innovation is drastic, then at a Nash equilibrium the incumbent invests in R&D at a rate that is strictly less than the rate of investment by the potential entrant. If the innovation is drastic, the value functions (13) and (14) reduce to

17



1( ) ( )( , )( ) ( )

e ee e m

e m

v h x xV x x Fh x h x rΠ −= −

+ +

and

0 1( ) ( ) ( )( , ) .( ) ( )

m mm m e

e m

v v h x xV x x Fh x h x r

π + Π −= −+ +

The expected profits differ only in that incumbent has the profit flow π(v0). This causes the incumbent to invest strictly less than the potential entrant. For a non-drastic innovation, the incumbent may invest more than the potential entrant if Π(v1) - Π(v1,v0) - Π(v0,v1) is sufficiently large. A More General Model Predictions about competition in patent races depend on the stochastic relationship between R&D expenditures and discovery. The model in Fudenberg et al. (1983) generates equilibrium investments that differ sharply from the exponential model in Reinganum (1981). In their model firms invest heavily in R&D when their experience levels are close. If one firm gets sufficiently ahead, others drop out of the R&D race and the leader continues to invest at a more moderate pace. This is in sharp contrast to the equilibrium predictions in Reinganum’s model, where firms continue at the same rate until one of them makes a discovery. Are general statements possible? Doraszelski (2003) considers a model in which the probability of success is exponential at any point in time with a success rate that depends on both current and cumulative R&D expenditures. This simple twist makes the model much more general, but also much more difficult to solve and most of the results rely on numerical simulations. The simulations show that the more complicated hazard rate function can support a wide range of competitive behavior in a patent race. In particular, a firm that lags a rival in cumulative R&D experience may optimally invest more than its rival to catch up. The reason why is intuitive. Because the probability of success increases with a firm’s cumulative experience, a firm that is in the lead can reduce its expenditure on R&D and exploit the enhanced success probability from its large knowledge stock. This “knowledge effect” gives a follower the opportunity to catch up by spending more on R&D. When the knowledge effect is large, the dynamics of the patent race do not reinforce dominance and there is instead an equalization effect. Firms with less cumulative R&D experience work harder to catch up to firms with larger knowledge stocks, while firms with large

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knowledge stocks tend to scale back their expenditures on R&D and coast on the value created by their past investments. Doraszelski (2003) also shows that a firm may increase or decrease its R&D expenditures in response to an increase in a rival’s knowledge stock and firms may or may not compete most 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 cumulative R&D, then there are diminishing returns to experience and the knowledge effect implies that a follower always invests more than the leader in R&D. If the success probability is a convex function of cumulative R&D, then R&D generates increasing returns, which gives a firm an incentive to invest and build up its knowledge capital. Even in this case, Doraszelski’s simulations show that a follower has an incentive to invest to catch up to the leader once its own knowledge stock becomes sufficiently large. Predictions of the equilibrium outcomes 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 firm that is ahead in the R&D competition can maintain its lead and guarantee success. Knowing this, other firms may choose to abandon the R&D race without a fight. Preemption is more difficult when discovery is uncertain, and in some cases a firm that is behind in the R&D race has incentives to work harder and close the gap that separates it from the current leader. Under these circumstances the dynamics of R&D competition can create incentives for R&D investments that erode the position of a market leader. VII. Beyond Profit-Maximization Many of the models we have discussed so far predict a monotonic relationship between the extent of competition and innovative output. For example, in the patent race model with exponential discovery probabilities, increasing the number of R&D competitors advances the expected date at which discovery occurs (Reinganum, 1981). In the Dasgupta-Stiglitz (1980) model of cost-reducing R&D with non-exclusive property rights, increasing the number of competitors reduces the amount of cost-reduction. The effect of competition is also monotonic in this model, although in the opposite direction. There is an intuitive argument that moderate levels of competition should be most effective in promoting innovation. In highly competitive markets the incentive to innovate may be low because the innovator’s small scale of operations may limit its benefit from a new technology. In markets that are close to monopolies, the Arrow replacement effect should dominate. To the extent that market concentration is a reasonable proxy for the degree of competition, this suggests that intermediate levels of market

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concentration are the most fertile environments for innovative activity. However, few models that rely solely on the pursuit of profit-maximization generate innovation incentives that peak at moderate levels of competition.3 Leibenstein (1966) argued that managers do not apply the effort necessary to reach the frontier of the firm’s production function, and this slack is greater for managers who are not exposed to significant competition. The owners of firms (the principals) want managers, acting as their agents, to exert effort to run the firm in an efficient manner. 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 managers to make changes in operating procedures that can be stressful and can impose severe hardships on some workers. Hicks (1935) said it well when he wrote that “The best of all monopoly profits is a quiet life.” Martin (1993) develops a model in which owners offer incentives to privately informed managers to prod them to invest in cost-reducing R&D. In other respects the model is similar to that in Dasgupta and Stiglitz (1980) and indeed the model predictions are also similar. Investment in cost-reducing R&D is a decreasing function of the number of firms in the industry; the greater the number of competitors, the higher is the equilibrium level of the marginal cost. Private information, alone, does not change the result that competition lowers incentives for cost-reducing R&D with non-exclusive intellectual property rights. Schmidt (1997) and Aghion et al. (1999) generate stronger results about the disciplining effect of competition by allowing for the possibility of bankruptcy. Bankruptcy has punitive consequences for a firm’s managers, who are at least temporarily out of a job, and they exert effort to avoid this unhappy state. In Aghion et al. (1999) adopting a new technology imposes an adjustment cost in addition to the direct expense associated with the technology that managers (or engineers) wish to minimize. Innovation keeps the company more efficient and reduces the likelihood of bankruptcy. All else equal, competition makes bankruptcy more likely. In their model managers innovate more in competitive markets because competition holds managers’ feet to the fire. The risk of bankruptcy is low in monopolistic markets, and so is the need to innovate, so managers of monopoly firms can enjoy the quiet life. The model in Aghion et al. (1999) illustrates how monopoly profits can shield managers from the hard work of being innovative, but it does not lead to a robust conclusion that competition promotes innovation. As the authors note, managerial preferences could diverge from profit maximization because they are

3 The dynamic model in Aghion et al. (2002) generates an inverted-U relationship between R&D and market concentration, but the model assumes a rather special sequential structure for innovation.

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loathe to innovate or because they are “techno-freaks” who enjoy adopting the latest new technology. If managers have an inclination to overspend on new technologies, competition would slow innovation by making bankruptcy more likely and forcing managers to be more efficient and innovate less. The effects of competition on managerial performance also depend on whether firms are active in credit markets. Managers may have to act efficiently to avoid bankruptcy if their firms are saddled with debt. In Aghion et al. (1999) competition affects managerial payoffs solely through the risk of bankruptcy. Schmidt (1997) incorporates the profits from cost reduction in the utility function of the firm’s owners and derives conditions under which competition leads to more or less effort by managers to reduce costs. In Schmidt’s model greater competition has two opposing consequences for managerial effort and innovation. By reducing each firm’s demand, greater competition lowers the incentive to innovate, as in the models developed by Dasgupta and Stiglitz (1980) and Martin (1993). Greater competition also increases the risk of bankruptcy, which encourages managers to innovate to preserve their jobs and makes it easier for the owner to induce additional effort.4 By increasing the risk of bankruptcy, competition results in more innovative effort. But competition also lowers the return to a cost-reducing innovation by reducing the output of each firm. Thus, there are two effects that act in different directions. Under reasonable assumptions, the output effect should dominate if competition is sufficiently intense, which suggests that investment in cost-reducing effort should peak at some intermediate level of market concentration. Thus Schmidt’s model can generate a relationship between innovation and competition that has an “inverted-U” shape, as opposed to the monotonic relationship in most other models of innovation that ignore managerial incentives. Although these results are insightful, this line of inquiry would benefit from additional theoretical and empirical research. Furthermore, the results include the usual caveat that R&D investment can be redundant with non-exclusive intellectual property rights, and maximizing R&D effort is not the same as maximizing innovative output. We have not even delved into the vast empirical literature on the relationship between competition and innovation. This discussion of the theory should make you better able to interpret the empirical results. I refer those who are interested in the empirical literature to the survey in Gilbert (2006).

4 This assumes that managers are not indifferent between working for the firm and taking another job. If they were indifferent, that would limit the ability of the owner to induce additional effort.

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References

Aghion, Philippe, Mathias Dewatripont, and Patrick Rey (1999), “Competition, Financial Discipline and Growth,” The Review of Economic Studies, vol. 66, pp. 825-852.

Aghion, Philippe, Nicholas Bloom, Richard Blundell, and Peter Howitt (2002), “Competition and Innovation: An Inverted-U Relationship,” National Bureau of Economic Research, Working paper 9269, Cambridge, MA.

Arrow, Kenneth J. (1962), “Economic Welfare and the Allocation of Resources to Invention,” in R.R. Nelson (ed.), The Rate and Direction of Economic Activity, Princeton University Press, N.Y.

Cohen, Wesley M. and Richard C. Levin (1989), “Empirical Studies of Innovation and Market Structure,” in R. Schmalensee 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,” Economic Journal, vol. 90, pp. 266-293.

Dixit, Avinash and Joseph Stiglitz (1977), “Monopolistic Competition and Optimum Product Diversity,” American Economic Review, vol. 67, pp. 297-308.

Fudenberg, Drew, Richard Gilbert, Joseph Stiglitz and Jean Tirole (1983), “Preemption, Leapfrogging and Competition in Patent Races,” European Economic Review, vol. 22, pp. 3- 32.

Gilbert, Richard J. (2006), “Looking for Mr. Schumpeter: Where Are We in the Competition-Innovation Debate?”, forthcoming in Josh Lerner and Scott Stern (eds), Innovation Policy and Economy, NBER, MIT Press.

Gilbert, Richard and David Newbery (1982), “Preemptive Patenting and the Persistence of Monopoly,” American Economic Review, vol. 72(2), pp. 514-526.

Greenstein, Shane and Garey Ramey (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 Economics, vol. 94, pp. S29-47.

Hall, Bronwyn and Rose Marie Ziedonis (2001), “The Patent Paradox Revisited: An Empirical Study of Patenting in the U.S. Semiconductor Industry, 1979-1995,” Rand Journal of Economics, vol. 32, pp. 101-28.

Hicks, J. R. (1935), “Annual Survey of Economic Theory: The Theory of Monopoly,” Econometrica, 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

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Some Schumpeterian Hypotheses,” American Economic Review, vol. 75, pp. 20-24.

Leibenstein, Harvey (1966), “Allocative Efficiency versus X-Efficiency,” American Economic Review, vol. 56, no. 3, pp. 392-415.

Martin, Stephen (1993), “Endogenous Firm Efficiency in a Cournot Principal-Agent Model,” Journal of Economic Theory, vol. 59, pp. 445-450.

National Science Foundation (2004), “Product versus process applied research and development, by selected industry,” available at http://www.nsf.gov/sbe/srs/iris.

Reinganum, Jennifer F. (1981), “Dynamic games of innovation,” Journal of Economic Theory, vol. 25, pp. 21-41.

Reinganum, Jennifer F. (1983), “Uncertain Innovation and the Persistence of Monopoly,” American Economic Review, vol. 73, pp. 741-748.

Schmidt, Klaus M. (1997), “Managerial Incentives and Product Market Competition,” The Review of Economic Studies, vol. 64, no. 2, pp. 191-213.

Schumpeter, Joseph A. (1942), Capitalism, Socialism, and Democracy. New York: Harper and Brothers. (Harper Colophon edition, 1976.)

Tirole, Jean (1997), The Theory of Industrial Organization, MIT Press.

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Documents

Journal of Industrial Organization Educationdiscovery of the same or similar invention, although they restrict the ability of firms to copy inventions made by others. The dynamics