cooperation versus competition in product innovation

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Cooperation versus competition inproduct innovationMiguel González-Maestre & Diego Peñarrubiaa Departamento de Fundamentos del Análisis Económico,Universidad de Murcia, 30100, Murcia, Spain

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Econ. Innov. New Techn., 2005, Vol. 14(4), June, pp. 305–318

COOPERATION VERSUS COMPETITION INPRODUCT INNOVATION

MIGUEL GONZÁLEZ-MAESTRE∗ and DIEGO PEÑARRUBIA†

Departamento de Fundamentos del Análisis Económico, Universidad de Murcia,30100 Murcia, Spain

(Received May 2004)

This paper analyzes the optimal antitrust policy in the context of a patent race. In a simplified model, we identifythe conditions under which allowing cooperation yields greater welfare than imposing competition. In view of ourresults, we discuss, critically, the current European policy towards R&D cooperation.

Keywords: Competition; Product innovation; Antitrust policy; Joint ventures; Knowledge externalities

JEL Classification: L41, O31

1 INTRODUCTION

This paper deals with the effects of cooperation agreements among firms in the developmentand exploitation of new products. In particular, we focus on the role played by the antitrustpolicy on the welfare effects associated to this type of R&D agreements, which usually takesthe form of research joint ventures (RJVs).

Allowing cooperation in R&D, and the joint exploitation of its results, is one of themain exceptions in the European antitrust legislation.1 The European legislation regardingR&D seems to reflect the Schumpeterian view that competition in the market of the newproduct reduces the incentives to innovate. However, some contributions have shown thatincreasing competition might increase the overall incentives to invest in R&D. In partic-ular, Loury (1979), Lee and Wilde (1980) and more recently Yin and Zuscovitch (1995)have stressed two important effects that tend to create too much investment in an inno-vation race. First, each firm ignores the duplication of its R&D effort with respect to theone exerted by its rivals. Second, potential entrants ignore the negative effects of theirfuture R&D activity on their rivals’ profits. As these authors assume that the social valueof innovation equals the private value, their main result is that there are too many firms in

∗ Corresponding author. E-mail: [email protected]† E-mail: [email protected] In particular, Commission Regulation (EU) 418/85 states that ‘it should be provided that the exemption will

continue to apply, irrespective of the parties’ market shares, for a certain period after the commencement of jointexploitation (· · · ) particularly after the introduction of an entirely new product, and to guarantee a minimum periodof return on the generally substantial investments involved’. See also paragraph 54 of the European Guidelines onHorizontal Cooperation Agreements.

ISSN 1043-8599 print; ISSN 1476-8364 online © 2005 Taylor & Francis Group LtdDOI: 10.1080/1043859042000269070

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306 M. GONZÁLEZ-MAESTRE AND D. PEÑARRUBIA

TABLE I Rates of return to R&D capital.

USA Canada

Private Social Private Social

Chemical products 0.153 0.261 0.25 0.81Non-electrical machinery 0.222 0.537 0.24 0.94Electrical products 0.192 0.24 0.38 0.38Transportation equipment 0.1 0.127 0.28 0.29

the free-entry equilibrium, exerting too much effort.2 Thus their conclusions tend to rein-force the European laws’ view that a permissive policy towards cooperation is desirablein this type of markets. However, it is interesting to note that the argument is different: intheir model, cooperation is desirable because it reduces the competitive incentive to inno-vate, whereas the European legislation is intended to increase this incentive by enhancingcooperation.

The aim of the European legislation is to increase the incentive to innovate because it con-siders that ‘Consumers can generally be expected to benefit from the increased volume andeffectiveness of R&D’ (Commission Regulation No418/85). The basic idea is that there is adiscrepancy between the social and the private incentive to innovate, due to some problems ofappropriability of the R&D benefits.3 There are many sources explaining this appropriabilityproblem (see, for instance Katz and Ordover, 1990), including the technological spillovers:those associated to the fact that one firm can employ the research done by another firm,without purchasing the right to do so. In a recent contribution, Sena (2004) discusses the dif-ferent forms of R&D spillovers and offers a survey of the empirical studies on this topic. Themicroeconomic literature has paid much attention to spillovers among firms in the same indus-try (intraindustrial spillovers), analyzing its strategic effects. In contrast, we will focus on theimpact of R&D investment on other industries (interindustrial spillovers). In two remarkableempirical contributions Bernstein and Nadiri (1988) and Bernstein (1989) have shown thatthe interindustrial spillovers (measured as the difference between private and social rate ofreturns) are very substantial in important industries like chemical products and non-electricalmachinery. This is reflected in Table I, which shows the comparisons between social andprivate rates of returns in USA and Canada.4

On the basis of this empirical evidence, our model combines the discrepancy between thesocial and the private value of innovation (which reflects a positive externality or spillover ofR&D on the rest of the society) and the negative externality associated to entry. As a result,in our model it is not always the case that the free-entry equilibrium involves too many firms,in contrast with the previous works by Loury (1979) and Lee and Wilde (1980). Moreover,our model identifies the conditions under which allowing cooperation among firms is a betterpolicy (in terms of welfare) than imposing competition (see Proposition 1). In particular, it is

2 They conclude that the first best policy involves a tax on the effort, combined with a restriction on the number offirms (which can be implemented by means of an entry tax).

3 An important branch in the literature concerning RJVs focuses on the role played by incentives problems associatedto asymmetric information. In this line, Battaggion and Garella (2001) argue, in a duopoly context, that full cooperationamong firms can improve the incentives for individual R&D efforts. In our analysis we will ignore this type of effectsand concentrate on the competitive role played by the presence of many potential competitors.

4 The private return is measured as the variable cost reduction in an industry due to its own R&D capital expansion.The social rate of return to an industry’s R&D capital consists of the private rate plus the interindustry marginal costreduction due to the spillovers generated by the industry’s R&D capital. The two first columns show the averagereturns in the years 1961, 1971 and 1981, obtained from the original values in Bernstein and Nadiri (1988) for USA.The two last columns show the average returns in the period 1963–1983, obtained by Bernstein (1989) for Canada.

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COOPERATION VERSUS COMPETITION IN PRODUCT INNOVATION 307

shown that a permissive policy towards cooperation is more likely to be optimal, the greater isthe private value of innovation and the greater is the probability of success of each individualR&D project.

The rest of the paper is organized as follows. In the next section we present the model.Section 3 explains our main results. In Section 4 we discuss the robustness of our results todifferent extensions and Section 5 gathers our conclusions.

2 THE MODEL

Let us assume there is a set of N potential competitors of a patent race. Each competitor canundertake a single project at cost ε > 0 and obtains a probability of success z. We will assumethat the social value of the innovation is 1. The timing of the game is as follows: first, thegovernment chooses its policy, consisting in either allowing or not cooperation among firms;second, each firm decides to enter or not in the innovation race and the number of projects ischosen by the firms; third, the nature determines the number of successful projects and finally,the profits at the product stage are determined.

Let us consider the competitive case, that is the case where the government chooses notto allow cooperation. If only one competitor is successful then it obtains a fraction R(0 <

R < 1) of the social value, which reflects a problem of appropriation of the gains associatedto innovation, as explained in the introduction. In the following analysis we will assumeRz > ε (i.e., expected profits are positive for at least one firm). If two or more competitorsare successful, then the private value obtained by each firm is given by

Ri = Rλi−1; i = 2, . . . , n; 0 ≤ λ ≤ 1 (1)

where i is the number of successful firms and λ is a parameter that reflects the rate at whichRi changes with competition. The assumed relationship between profits and number of firmsis established for tractability. Nevertheless, Appendix A shows that Eq. (1) can be interpretedas the reduced form of a more explicit modeling of market interactions between firms. Theexpected profits of firm i are given by

�C(n) = z

n−1∑i=0

Rλizi(1 − z)n−1−i (n − 1)!(n − 1 − i)!i! − ε

= zR(λz + 1 − z)n−1 − ε (2)

where �C(n) is the per-firm profit function when each firm develops its project independently(the competitive case). The last equality comes from the Newton’s binomial identity.5

5 A similar formulation is used by Sah and Stiglitz (1987) who consider the possibility that each firm undertakesmultiple projects but with an exogenous number of firms. In terms of our model, they only consider the case whereλ = 0 (i.e., zero private value of innovation with more than one successful firm). In this context they show that thenumber of developed projects is independent on the number of firms. Barros (1993) has extended the analysis tothe case of free entry and shows that in equilibrium each firm only develops one project and the total number ofproject is the same as in the model by Sah and Stiglitz. As we will see these conclusions change in our model so thatthe number of projects chosen under cooperation is different from the one obtained under competition.

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FIGURE 1 Number of firms and profits.

Under free entry, and in absence of risk aversion, the number of competitors at the Nashequilibrium (n′) is given by the condition of zero expected profits

�C(n′) = 0 −→ n′ = 1 + ln(ε) − ln(zR)

ln(λz + 1 − z)(3)

If the firms are allowed to cooperate (by forming a RJV that behaves as a cartel in theexploitation of the product)6 their joint expected profits are given by7

�M(n) = R[1 − (1 − z)n] − nε,

where �M(n) is the cartel’s profit function when their members decide to undertake n projects(the monopolist case). The joint profit-maximizing number of the cartel’s projects (n∗) isobtained by using the following first order condition

�M(n) − �M(n − 1) = Rz(1 − z)n−1 − ε = 0 −→ (4)

n∗ = 1 + ln(ε) − ln(zR)

ln(1 − z)(5)

Straightforward comparison between n∗ and n′ establishes the following.

LEMMA 1 The equilibrium number of firms under competition is greater than (respectivelyequal to) the number of projects developed under cooperation if and only if λ > 0 (respectivelyλ = 0), that is

n∗ < n′ ←→ λ > 0

n∗ = n′ ←→ λ = 0 (6)

The relationship between �C(n) and �M(n) is shown in Figure 1.

6 We only consider horizontal RJVs. Vertical RJVs have received much attention in the literature, but according torecent empirical studies horizontal RJVs are not irrelevant, as they represent about 36% of cooperative agreements(Tether, 2002).

7 The European Regulation establishes restrictions in terms of market shares, regarding RJVs that take place in analready existing product. As a consequence of this restrictions the RJVs of this type only contain some of the firmsin the market. However, there are not similar restrictions in the case of RJVs for a new product. In fact, it is easy toshow that in our model all the firms have an interest in taking part of the RJV.

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FIGURE 2 Potential competitors and developed projects.

In our previous analysis we have ignored the role of the total number of potential projectsN in the optimal cartel’s decision. There are four relevant intervals for N (in the rest of ouranalysis we assume that each firm in the cartel obtains the same share in the total cartel’sprofits):

• If N < n∗ the total number of potential projects is not enough to develop n∗ (the optimalnumber of projects developed by the cartel in the absence of this restriction). In this case,the cartel will include all the potential competitors and will develop N projects.

• If n∗ < N < n′ all the firms will enter the market and would like to form a cartel. If thecartel is allowed it will decide to undertake only n∗ projects.

• If n′ < N < n2, where n2 is defined by the condition �M(n∗)/n2 = �M(n′)/n′, the numberof firms is such that, under competition, there is no room for all the potential firms; but thisnumber is small enough to make preferable for the cartel an agreement with all the firmsand only n∗ projects, instead of developing n′ projects to deter entry.

• If N > n2 the incumbent firms’ optimal strategy is to deter entry by developing n′ projects.Note that, contrary to the competitive case, the n′ firms in the cartel obtain positive expectedprofits, as the cartel eliminates competition among firms when more than one project issuccessful.

Figure 2 illustrates the number of developed projects (n) as a function of the number ofpotential competitors. The discontinuous line represents the competitive case (nC), whereasthe continuous line indicates the collusive case (nM). Note that both lines coincide whenN ≤ n∗ and when N ≥ n2.

3 WELFARE ANALYSIS

According to our previous analysis, the antitrust policy regarding cooperation among firmsonly affects the equilibrium number of projects if n∗ ≤ N ≤ n2. Because, given the parametersof the model, total welfare depends only on the equilibrium number of projects, we willconcentrate on this interval. Moreover, to simplify the analysis we will focus in the case thatn′ ≤ N ≤ n2.8 We will assume that the social value of innovation is Si = 1. In Appendix Bwe show that if the social value of innovation is increasing with the number of firms thenthe arguments in favor of competition are reinforced. However, we will show that even if the

8 That is, N is assumed to be large enough to ensure that the free-entry condition is binding under competition.

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monopolist does not create distortion (that is Si is constant) competition might be sociallypreferable.

As Si = 1, the socially optimal number of projects (n0) is obtained by maximizing totalexpected welfare (W), with respect to n, which yields

W(n) = 1 − (1 − z)n − nε (7)

W(n0) − W(n0 − 1) = 0 −→ z(1 − z)n0−1 − ε = 0 −→ (8)

n0 = 1 + ln(ε) − ln(z)

ln(1 − z)(9)

By comparing Eqs. (5) and (9), and noticing that R < 1, it is easy to see that n∗ < n0.Intuitively, a social planner develops a greater number of projects than a private monopolybecause the social value of the innovation is greater than the private value. Because in theprevious section we have shown that n∗ < n′, there are only two possible orderings amongn∗, n′ and n0, as shown in Figure 3. It is clear that if n′ < n0 (case a) competition givesgreater welfare than cooperation, but if n′ > n0 there might be two possibilities: in case b1competition is still better than cooperation, but the conclusion changes in case b2. Therefore,it is necessary to compute the welfare at each situation, to make the relevant comparison.

Let us define

F ≡ W(n′) − W(n∗) = (1 − z)n∗ − (1 − z)n

′ + ε(n∗ − n′). (10)

From expression (10) and taking into account Eqs. (3) and (5), it follows that

F(λ, R, z, ε) = ε

zR(1 − z) − (1 − z)

(ε

zR

)ln(1−ε)/ ln(λz+1−z)

− ε ln

(zR

ε

) [1

ln(λz + 1 − z)− 1

ln(1 − z)

]. (11)

Let us define

c ≡ ε

zR< 1; a ≡ ln(1 − z)

ln(λz + 1 − z)> 1.

FIGURE 3 Number of projects and welfare.

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As c ≡ ε/(zR) < 1 and R < 1 it follows that c ∈ (ε/z, 1), R ∈ (ε/z, 1), ε ∈ (0, zR) andz ∈ (0, ε/R). We can rewrite F as

F = (1 − z)c − (1 − z)ca − ε(a − 1) ln c

ln(1 − z). (12)

Consider the following auxiliary result.

LEMMA 2 f (z) ≡ −((1 − z)/z) ln(1 − z) is strictly decreasing in the interval (0, 1),approaches 1 as z tends to 0 and 0 as z tends to 1.

Proof To see that df (z)/dz ≡ ((z + ln(1 − z))/z2) < 0 note that h(z) ≡ z + ln(1 − z)

equals zero at z = 0 and dh(z)/dz = 1 − (1/(1 − z)) < 0. Also, by using l’Hopital rule itfollows that

limz→0

f (z) = limz→0

1/(1 − z)

1/(1 − z)2= 1 and lim

z→1f (z) = lim

z→1

1/(1 − z)

1/(1 − z)2= 0.

�

Our main result is the following.

PROPOSITION 1 Assuming that n′ < N < n2, the comparison between competition andcooperation, in terms of welfare depends on parameters λ, R, z and ε as follows:

(i) If ε/z < f (z) then given λ, z and ε, there is R∗ such that competition gives higher (respec-tively lower) welfare than cooperation if and only if R < R∗ (respectively R > R∗). Ifε/z > f (z) then competition always gives lower welfare than cooperation.

(ii) If R < f (z) then given R, z and ε, there is λ∗ such that competition gives higher (respec-tively lower) welfare than cooperation if and only if λ < λ∗ (respectively λ > λ∗), providedthat F < 0 at λ = 1/2, but if F > 0 at λ = 1/2 then competition is always better thancooperation. If R > f (z) then competition always gives lower welfare than cooperation.

(iii) If R < f (z) then given λ, R and z, there is ε∗ such that competition gives higher (respec-tively lower) welfare than cooperation if and only if ε > ε∗ (respectively ε < ε∗). IfR > f (z) then competition always gives lower welfare than cooperation.

(iv) If R < f (ε/R) then given λ, R and ε, there is z∗ such that competition gives higher(respectively lower) welfare than cooperation if and only if z < z∗ (respectively z > z∗). IfR > f (ε/R) then competition always gives lower welfare than cooperation.

Proof Part (i):

∂F

∂c= (1 − z)(1 − αca−1) − ε

(a − 1)

c ln(1 − z),

∂2F

∂c2= −(1 − z)a(α − 1)ca−2 + ε

(a − 1)

c2 ln(1 − z)< 0.

Therefore F is strictly concave in c.As F = 0 at c = 1(R = ε/z), it follows that there can be atmost one value of c ∈ (ε/z, 1) such that F = 0. In turn, the monotonic decreasing relationship

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between c and R implies that there is at most one value of R > ε/z such that F = 0. Thus part(i) follows from the fact that F < 0 at R = 1 and that ∂F/∂R > 0 at R = ε/z if and only if

(a − 1)

(−(1 − z) − Rz

ln(1 − z)

)∂c

∂R> 0 ←→ R < f (z).

Part (ii): From Eq. (12) we obtain

∂F

∂a= −(1 − z)(ln c)ca − ε

ln c

ln(1 − z),

∂2F

∂a2= −(1 − z)(ln c)2ca < 0.

Therefore F is strictly concave in a. As F = 0 at a = 1, it follows that there can be at mostone value of a > 1 such that F = 0. Thus the proof of part (ii) follows from the monotonicincreasing relationship between a and λ and by the fact that ∂F/∂λ > 0 at λ = 0(a = 1) ifand only if

− log c

((1 − z)c − ε

ln(1 − z)

)∂α

∂λ

= − log c

((1 − z)

Rz− 1

ln(1 − z)

)ε∂α

∂λ> 0 ←→ R < −f (z).

Part (iii): Note that

signF = sign

[(1

R(1 − ca−1) + (a − 1) ln c

f (z)

)].

Let us define

H ≡ 1

R(1 − ca−1) + (a − 1) ln c

f (z)

∂H

∂ε= −(a − 1)

c

(ca−1

R− 1

f (z)

)∂c

∂ε.

Given that c is increasing in ε there can be at most one value for ε at which ∂H/∂ε = 0,which implies that H is quasiconcave in ε. As F = 0 at ε = Rz this property implies thatthere can be at most one ε < Rz such that F = 0. On the other hand, the previous derivativeis negative at ε = Rz(c = 1) if and only if R < f (z) and the result follows from the fact thatsign(H) < 0 for ε small enough.

Part (iv):

∂H

∂z=

(−(a − 1)

c

∂c

∂z− (ln c)

∂a

∂z

) (ca−1

R− 1

f (z)

)− (a − 1) ln c

(f (z))2

df (z)

dz.

Given that ∂a/∂z > 0 (see Appendix C), the previous expression is always negative if R >

f (z) and the result holds in this case because F = 0 at z = ε/R(c = 1). On the other hand,if R < f (z) then ∂H/∂z > 0 at z = ε/R and given that F < 0 as z approaches 1, it followsthat in this case there must be z∗ such that F = 0. Moreover, the proof of part (ii) shows thatH > 0 if ca−1/R − 1/f (z) > 0, which implies that H is negative at z∗ and, in consequence,z∗ is unique, which completes the proof. �

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FIGURE 4 Welfare comparisons in the (z, ε) space.

The role played by ε and z in Proposition 1 is illustrated in Figure 4, which representsthe two critical lines where F = 0 in the (z, ε) space. Along the line ε = zR, the number ofdeveloped projects is 1 under both the cooperative and competitive regime, whereas above thisline the number of projects is always 0. The region between both lines gives the pairs (z, ε)

such that competition is better, in terms of welfare, than cooperation (F > 0), whereas the restof the space corresponds to the case where cooperation is better than competition (F < 0).

Let us consider the intuition of this results. First, a high value of R means that the cooperativesolution is close to the social optimum (as the positive external effects are small in this case).Second, a high value of z means that each project has a significant damaging effect on theexpected profits of the rest of the firms in the competitive case (which involves a high negativeexternality). As a result, the arguments in favor of a permissive antitrust policy are reinforcedfor high values of both R and z. Conversely, imposing competition is a better policy for lowlevels of those parameters. Regarding λ, the intuition of the results relies on the fact that thegreater is this parameter, the lower is the intensity of competition in the product market inthe competitive case, which tends to create excessive entry. As a consequence, large valuesof λ make more likely excessive entry. Finally, competition is more likely to be better thancooperation, the higher the level of ε. This is perhaps the most paradoxical aspect of ourresults. At first sight one might think that if the effort required to undertake each project islarge then cooperation should be better than competition. The explanation to this apparentlycounterintuitive result is that the greater is ε the smaller is the discrepancy between the numberof firms under competition and under cooperation,9 which in turn makes more likely that bothlevels are below the social optimum.

To evaluate the welfare differences between both regimes, Table II shows the values ofn′, n∗, n0 and (W(n′) − W(n∗))/W(n∗) associated to different values of the vector(ε, z, R, λ).

According to these simulations, for small values of R, the welfare loss associated to cooper-ation, compared to competition, can be very large. On the other hand, the empirical evidence(see Tab. I) has shown that there are many industries where the private value of innovation issmall relative to its social value, (that is, where R is small). Our model suggests that, in thosecases, an active competition policy might have substantial welfare effects.

9 Note that from Eqs. (3) and (5) it follows that n′ − n∗ = [1/ ln(λz + 1 − z) − 1/ ln(1 − z)] ln(ε/zR), which isdecreasing in ε.

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TABLE II Welfare comparisons.

ε z R λ n∗ n′ n0 (W(n′) − W(n∗))/(W(n∗))(%)

0.02 0.05 0.5 0.25 5.35 6.84 18.86 19.60.01 0.05 0.5 0.25 18.86 24.97 32.38 9.50.02 0.5 0.5 0.25 4.64 6.37 5.64 −0.180.02 0.05 0.8 0.25 14.51 19.13 18.86 3.30.02 0.05 0.5 0.5 5.35 9.81 18.86 49.8

4 DISCUSSION OF ALTERNATIVE EXTENSIONS

Our simplified model ignores important aspects relative to cooperation in R&D. Let us discusssome of these aspects and their implication for the results.

First, we have concentrated on two type of externalities: the direct externalities on the restof the society (i.e., outside the industry) and the indirect externalities within the firms in theindustry that result purely from competition. In other words, we ignore the direct ‘specific’externalities among firms arising from aspects such as complementarity of efforts or knowl-edge externalities. If those type of externalities are considered then the arguments in favorof allowing firms to create RJVs are reinforced, as far as this is the only governance mecha-nism at the firms’ hands to deal with this problem. However, depending on the characteristicsof knowledge, such alternative mechanisms can be available. Let us consider some of themechanisms studied in the recent literature:

(i) By locating in the same geographical area, important knowledge externalities are usu-ally associated to interactions among skilled workers of different firms (Fujita andThisse, 2003). In consequence, the more important those interactions are, the more likelyis that co-location of activities is preferred to RJVs.

(ii) The possibility of creating technological platforms also weakens the arguments in favorof allowing RJVs. Technological platforms keep competition in the product market whileallowing cooperation (and internalization of spillovers) at the R&D stage. Recent empir-ical literature has stressed the relevance of technological platforms in important sectorslike the computer industry (Breshnahan and Greenstein, 1999).

(iii) A company might choose to create a technology spin-off firm as a device to commercializeits internal research output. This is a suitable mechanism to internalize knowledge exter-nalities when a significant amount of internal research output does not ‘fit’ well withthe parent firm. Some recent empirical literature has focussed largely on the Xerox’stechnology spin-off (Chesbrough, 2003).

(iv) Finally, long-term agreements about patents, such as patent pools or cross licenses are alsoalternative mechanisms to internalize knowledge externalities. However, the welfare andcompetition effects of these mechanisms are not clear (Shapiro, 2003; Denicolo, 2002)and comparisons with RJVs seems to be a non-trivial task.

Therefore, the existence of positive externalities between projects might change our resultsin two different directions:

(i) On one hand, the presence of other mechanisms tends to make cooperation by means ofRJVs, less attractive from the social point of view, as far as those alternative mechanisms

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internalize externalities without reducing competition. In this sense, our conjecture is thatthe inclusion of these new elements in our model would reinforce the idea that the moreimportant are the involved positive externalities (both, directly on the society and withinthe industry) the more likely is that competition is socially preferred to cooperation in theform of RJVs.

(ii) On the other hand, in absence of those alternative mechanisms, it seems that the argumentsin favor of cooperation are reinforced, as far as the direct externalities among firm withinthe industry are positive.

5 CONCLUSIONS

There are two main ideas involved in our model: first, under cooperation the number of projectsis too small because the cartel cannot appropriate all the social profits associated to innovation;second, under competition the equilibrium number of projects is greater than under the cartelbecause each competing firm does not internalize the negative effect of its project on therest of competitors. This negative externality tends to create excessive entry and resembles the‘business stealing’effect described by Mankiw and Whinston (1986). However, contrary to thisprevious contribution, our model explicitly considers the interactions between the stochasticaspects of innovation and product market competition, by assuming that each project has apositive probability of failure. In turn, we have shown that this probability has a non-trivialand counterintuitive role in our results.

On the basis of these ideas, we have compared competition versus cooperation. The coop-erative exploitation of research in new products is usually recommended when positiveexternalities are important, because in this case those beneficial effects outweigh the neg-ative effects associated to less competition. However, our results run against this intuition. Inour model the more important are those positive externalities the more likely is that coopera-tion is not an interesting solution, because the cartel develops a too small number of projects(relative to the competitive outcome).

Our model contradicts also the conventional belief that the more difficult is the task toobtain a new product (reflected in a small individual probability of success or in a large costof the project) the more interesting is allowing cooperation. In contrast, our results showthat competition is more convenient in this case. The explanation is that if the probability ofindividual success is small then the probability of having competition in the product marketis also small. Put in other words, the excessive entry effect, under competition, is small in thiscase, so that competition at the innovation stage is better than cooperation, from the socialpoint of view. The basic argument underlying this explanation is that the excessive entry effectis increasing with the individual probability of success. Therefore this result can be extended toa more general framework. For instance, if the individual probability of success is increasingon individual effort then the excessive entry will be more likely the lower the difficulty of theinnovation task (reflected in some parameter in the relationship between effort and probabilityof success).

Finally there are many elements involved in the debate about the social desirability of coop-eration in the development and exploitation of new products. In particular, our model ignoresrelevant aspects, like the introduction of complementarity of individual research efforts orknowledge externalities within the industry. The consideration of those aspects tend to under-pin the European legislation in favor of RJVs only if other alternative governance mechanismsare not feasible, but otherwise our results would be even reinforced, as explained in theprevious section.

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Acknowledgements

We acknowledge financial support from the Spanish Ministry of Education and Culture underDGES project BEC2000-0172, BBVA under project 02255 (M. González-Maestre) and fromFundación Séneca under project PB/3/FS/02 (D. Peñarrubia). We are grateful to F. Alcalá,L. Corchón, a referee, an anonymous member of the Board and seminar audiences in Bilbao,Murcia, Valencia, ASSET 2003 Annual Conference (Ankara) and XXVIIIth Symposium ofEconomic Analysis (Sevilla) for helpful comments.

References

Barros, P. (1993) Multi-project R&D Competition with Free-entry. Economics of Innovation and New Technology,2(4), 309–317.

Battaggion, M.R. and Garella, P.G. (2001) Joint Venture for a New Product and Antitrust Exemptions. AustralianEconomic Papers, 40(3), 247–262.

Bernstein, J.I. (1989) The Structure of Canadian Inter-industry R&D Spillovers, and the Rates of Return to R&D.Journal-of-Industrial-Economics, 37(3), 315–328.

Bernstein, J.I. and Nadiri, M.I. (1988) Interindustry R&D Spillovers, Rates of Return and Production in High-techIndustries. American Economic Review, 78(2), 429–434.

Breshnahan, T.F. and Greenstein, S. (1999) Technological Competition and the Structure of the Computer Industry.Journal of Industrial Economics, 47(1), 1–40.

Chesbrough, H. (2003) The Governance and Performance of Xerox’s Technology Spin-off Companies. ResearchPolicy, 32(3), 403–421.

Denicolo,V. (2002) Sequential Innovation and the Patent-antitrust Conflict. Oxford Economic Papers, 54(4), 749–768.Fujita, M. and Thisse, J.F. (2003) Does Geographical Agglomeration Foster Economic Growth and Who Gains and

Loses From It? Japanese Economic Review, 54(2), 121–145.Katz, M.L. and Ordover, J.A. (1990) R&D Cooperation and Competition. Brookings Papers on Economic Activity:

Microeconomics, 137–203.Lee, T. and Wilde, L. (1980) Market Structure and Innovation: a Reformulation. Quarterly Journal of Economics,

94(2), 924–436.Loury, G.C. (1979) Market Structure and Innovation. Quarterly Journal of Economics, 93(3), 395–410.Mankiw, N.G. and Whinston, M.D. (1986) Free Entry and Social Inefficiency. Rand Journal of Economics, 17(1),

48–58.Sah, R. and Stiglitz, J. (1987) The Invariance of Market Innovation to the Number of Firms. Rand Journal of

Economics, 18(1), 98–108.Sena, V. (2004) Total Factor Productivity and the Spillover Hypothesis: Some New Evidence. International Journal

of Production Economics (forthcoming).Shapiro, C. (2003) Antitrust Limits to Patent Settlements. Rand Journal of Economics, 34(2), 391–411.Tether, B.S. (2002) Who Co-operates for Innovation, and Why?An EmpiricalAnalysis. Research Policy, 31, 947–967.Yin, X. and Zuscovitch, E. (1995) Research Joint Ventures and R&D Competition under Uncertain Innovation.

Economies et Sociétés, 29(9), 139–161.

APPENDIX A

In this appendix, we provide two alternative justifications to the reduced profit function givenby expression (1):

(i) Let us assume that the patent race is carried out in two different stages: first, each firmundertakes the effort and obtains successfully the invention of the new product with proba-bility z; second, each successful firm tries to obtain the patent for its particular discovering.Assuming that each successful firm has a probability (1 − λ) of obtaining the patent at thesecond stage and that Bertrand competition in the product market follows at the third stage,the profit function of each successful firm, at the second stage is given by

Ri = V (1 − λ)λi−1; i = 2, . . . , n; 0 ≤ λ ≤ 1,

where V is the monopoly profit. Thus the previous expression is equivalent to Eq. (1) bydefining R ≡ V (1 − λ).

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(ii) Let us assume Cournot competition in the product market, after the innovation stage amongthe i successful firms. Under zero production costs and an exponential inverse demandfunction p = be−hQ, where b > 0, h > 0, p is the price and Q is the total quantity sold inthe market, the profits of each firm can be written as

�i = qibe−hQ, (A.1)

where qi is the production of each firm, with i successful firms. The first order conditionsof Cournot equilibrium gives

q∗i = 1

h; p∗ = be−i; �i = b

he−i . (A.2)

Thus profits can be written as

�i = Rλi−1; R = b

he; λ = e−1. (A.3)

APPENDIX B

In this appendix, we show that if the social value of innovation is increasing with the numberof firms, as it happens in case (ii) of Appendix A, then the arguments in favor of competitionversus cooperation are reinforced.

To see this, note that the welfare associated with i successful projects, in case (ii) ofAppendix A, is given by

Si = Sext +∫ i/h

0be−hQdQ = Sext + b

h(1 − e−i ) (B.1)

where Sext is the welfare associated to the direct externalities on the society, which we assumeconstant, and the second term represents the welfare associated to production in the industry(which is the sum of consumers’ surplus and firms’ profits). Thus total welfare is given by

Si = 1 − b

he−i , i > 0, (B.2)

where we have normalized to 1 the welfare level associated to perfect competition (i.e., when i

tends to infinity).Without loss of generality we might assume h = 1 and the value of innovationis given, under competition, by

Si ={

1 − bλi−1 i > 0

0 i = 0,(B.3)

where i is the number of developed projects and λ = e−1.

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The expected welfare under competition is given by

WC(n) = 1 − (1 − z)n − nε − b

λ

[n∑

i=0

(λz)i(1 − z)n−i n!(n − i)!i! − (1 − z)n

]

= 1 −(

1 − b

λ

)(1 − z)n − nε − b

λ(λz + 1 − z)n.

The socially optimal number of projects is obtained from

WC(n0) − WC(n0 − 1) = 0, (B.4)

which implies

ε = z

(1 − b

λ

)(1 − z)n0−1 + bz(λ−1 − 1)(λz + 1 − z)n0−1.

The expected welfare associated to n projects, when developed cooperatively is given by

WM(n) = (1 − b)[1 − (1 − z)n] − nε. (B.5)

Let us define the function

F(λ, b, R, z, ε) = WC(n′) − WM(n∗) = b + ε

zR

[1 − b − z − (1 − z)b

λ

]

−(

1 − b

λ

)(1 − z)1+(ln(ε)−ln(zR))/(ln(λz+1−z))

− ε

[ln(zR) − ln ε

ln(1 − z) ln(λz + 1 − z)ln

(1 + λz

1 − z

)].

By taking the partial derivative with respect to b we get

∂F

∂b= 1 +

( z

λ− 1

) ε

zR+ 1

λ(1 − z)1+[(ln(ε)−ln(zR))/ ln(λz+1−z)] > 0. (B.6)

Note that the first and third terms are positive, and the second is greater than −(1 − z)

×ε/zR > −1, so that it is clear that the greater the inefficiency associated to monopoly, themore likely is that competition is socially better than cooperation.

APPENDIX C

To prove that a ≡ ln(1 − z)/ ln(1 − γ z) is increasing in z, where γ ≡ 1 − λ

∂a

∂z= 1

(ln(1 − γ z)2)2

(− ln(1 − γ z)

1 − γ z+ γ ln(1 − z)

1 − γ z

)

it follows that

∂a

∂z> 0 ←→ γ ln(1 − z)

1 − γ z>

ln(1 − γ z)

1 − γ z� h(z) ≡ (1 − z)γ (1−z)/1−γ z − 1 + γ z > 0.

To show the last inequality note that h(z) tends to 0 as z approaches 0 and

∂h(z)

∂z≡ (1 − z)γ (1−z)/1−γ z ln(1 − z)

−λγ

(1 − γ z)2+ γ > 0, ∀z ∈ (0, 1),

which completes the proof.

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cooperation versus competition in product innovation

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