Cooperative R&D under uncertainty with free entry

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Abstract

This paper analyzes the effects of cooperative R&D arrangements in a model with stochastic R&D and output spillovers. Our main innovation is to allow for free entry in both the R&D race and product market. Moreover, in contrast with the literature, we assume that cooperative R&D arrangements do not have to include all the firms in the industry. We show that sharing of research outcomes is a necessary condition for the profitability of cooperative R&D arrangements with free entry. The profitability of RJV cartels depends on their size. Subsidies may be desirable in cases of larger RJVs since they are the ones which are less likely to be profitable.

Introduction

This paper analyzes the profit and welfare implications of cooperative R&D in an uncertain R&D environment with free entry. An important reason for the desirability of cooperative R&D arrangements is the existence of knowledge spillovers. Both input spillovers (during the R&D process) and output spillovers (after the innovation takes place) may result in inefficiently low amounts of investment. A consistent feature of the literature exploring the effects of cooperative R&D is the assumption that the number of firms participating in both the R&D process and product market is fixed.1 In many R&D intensive industries, it is not realistic to assume that only a limited number of firms can participate in the R&D process. Profit opportunities attract entrepreneurial attention and more participants into the R&D process.2 Moreover, the profitability of cooperative R&D arrangements may depend critically on whether there is free entry and exit in the product market, especially in case of output spillovers. Hence, our goal in this paper is to analyze the effects of cooperative R&D when the number of participants in the R&D process and product market are endogenously determined.

As in Miyagiwa and Ohno (2002), we model R&D as a stochastic process.3 This approach differs in general from the rest of the literature where, following d'Aspremont and Jacquemin (1988), it is common to model R&D as a deterministic process.4 Firms are assumed to participate in a game of three phases, which are denoted as the investment, pre-spillovers, and post-spillovers phases. In the investment stage, firms carry out research either cooperatively or non-cooperatively. We assume that cooperative R&D arrangements do not have to include all the firms in the industry. This assumption is in accordance with industrial practice, but contrasts with the previous literature where it is generally assumed that such arrangements involve all of the firms in the industry.5 We consider an environment with output spillovers and assume that the winner of the race has exclusive access to the innovation for a limited period of time (during the pre-spillovers phase), after which the innovation spills over to all of the firms (in the post-spillovers phase). The duration of the exclusivity represents the speed of output spillovers, which could be affected by the effectiveness of patent and/or trade secret protection. Firms compete in a product market in all three phases. There is free entry and exit in both the product market and the R&D race.

Our results reveal that allowing for entry into the R&D race and product market introduces new strategic, investment and welfare implications of cooperative R&D. Following the literature, we first compare the benchmark case of R&D competition, where firms choose their R&D intensities independently, with R&D cartels, where a fixed number of firms set their investment levels to maximize their joint profits but do not share the research outcomes. We show that with free entry, such cooperative arrangements are never profitable. This result stands in stark contrast to the results in the literature, where R&D cartels are always found to be profitable.

We then consider RJV cartels, where a fixed number of firms choose their investment levels to maximize their joint profits and share their research outcomes.6 We show that the profitability of such cooperative arrangements depends on their size. Specifically, small RJV cartels are more likely to be profitable and have higher per-firm investment levels than R&D competition while large RJV cartels are more likely to be unprofitable and have lower per-firm investment levels than R&D competition. Together with our results on R&D cartels, this implies that sharing of research outcomes is necessary for the profitability of cooperative R&D arrangements with free entry.

While papers which model R&D as a deterministic process always find RJV cartels to be profitable, this is not necessarily true of papers which model R&D as a stochastic process.7 We extend the results in the stochastic R&D literature by showing that when markets are characterized by free entry, the key variable for RJV cartel performance is its size. Hence, our findings can be used to explain why RJVs often do not include all of the firms in an industry and why firms choose to conduct many R&D projects non-cooperatively.

Our analysis further reveals that the impact of cooperative R&D on the aggregate level of innovation depends on whether there are participants in the R&D race who are not part of the cooperative R&D arrangement. Interestingly, if the size of the cartel is such that some outsiders choose to participate in the race, the aggregate rate of innovation remains the same with and without a cooperative R&D arrangement, even if the number of participants in the R&D race changes. Hence, in this case, any welfare gain from R&D cooperation cannot be driven by its impact on the aggregate rate of innovation. Moreover, since R&D cartels are unprofitable, it must be the case that they are welfare-reducing. If the size of the cartel is such that no outsider firm chooses to participate in the R&D race, the aggregate rate of innovation is higher with a cooperative R&D arrangement than without one. In such cases, R&D cartels may be welfare improving because of their positive impact on the aggregate rate of innovation and consumer welfare, and it may be desirable to subsidize them. This result is in contrast with those in the literature, where R&D cartels are generally found to be profitable, so it is never necessary to subsidize them.

Whether there are outsider participants in the R&D race or not, the impact of RJV cartels on consumer welfare is ambiguous. On the one hand, there are more firms in the pre-spillovers product market producing with the new technology under an RJV cartel. On the other hand, an RJV cartel with the new technology may cause more firms with the old technology to exit during this period. That is, the equilibrium number of firms in the pre-spillovers product market is likely to be lower with an RJV cartel. RJV cartels may be socially desirable depending on which of these two effects dominates and there may be a case for subsiding unprofitable RJV cartels when they are welfare improving. This result is in line with the results from the literature where R&D is modelled as a stochastic process. Choi (1993) and Miyagiwa and Ohno (2002) also find room for subsidizing RJV cartels depending on the level of spillovers.8 However, we extend their results with the surprising finding that subsidies may be desirable in case of larger RJVs since they are the ones which are less likely to be profitable.9

The paper proceeds as follows. In Section 2, we present the details of the model. Section 3 presents the product market payoffs which we use in the analysis of R&D competition, R&D cartels, and RJV cartels in 4 R&D competition, 5 R&D cartel, 6 RJV cartel, respectively. Section 7 explores the welfare and policy implications of cooperative R&D under free entry. In Section 8, we extend the analysis by considering the effects of cooperative R&D when there are no outsider participants in the R&D race in equilibrium. We conclude and make suggestions for future research in Section 9. All of the proofs are in the Appendix.

Section snippets

The model

Consider a continuous-time model where firms participate in a game of three phases, which we denote as the investment, pre-spillovers, and post-spillovers phases. Firms compete in a product market in all three phases. In addition, firms compete to be the first to develop a new technology in the investment phase. There is free entry and exit in both the product market and the R&D race.

We assume that the product market is in a long-run equilibrium in which all participants earn zero profits when

Product market competition

In this section, we start the analysis of the model by discussing the product market competition in the three phases of the game: investment, pre-spillovers, and post-spillovers. The discussion in this section is useful in determining the expected payoffs of an R&D race participant in the following sections.

In the investment phase, all firms active in the product market produce using the old technology and earn zero profits. Since firms do not have to participate in the R&D race to be able to

R&D competition

In this section we consider the benchmark case where firms conduct R&D independently. We show that there exists a free-entry equilibrium to the R&D competition game, and characterize the investment choices and the number of firms in this equilibrium.

With a Poisson discovery process and R participants in the R&D race, the probability that there has not been a discovery until time t is given by exp[jRh(xj)t].15

R&D cartel

In this section, we compare the case of R&D competition with the case where a group of C firms form an R&D cartel. The cartel members participate in the R&D race by choosing their investment levels to maximize their joint payoffs, but they do not share their research outcomes. Due to free entry in the R&D race, the cartel participants still face competition from outsider participants in the race.

The joint payoffs of the cartel participants are given byiC(h(xi)Lrxir+jCh(xj)+kCh(xk)S),

RJV cartel

We next consider the case where an exogenously-determined group of J firms form an RJV cartel. The firms make their investment decisions jointly and gain immediate access to the new technology if any one of them wins the race.

The RJV cartel's expected payoff isiJ(h(xi)LJr+ki,kJh(xk)LJrxir+h(xi)+ki,kJh(xk)+lJh(xl)S),where the last term in the denominator stands for the sum of the hazard rates of the outsider participants in the race. LJr represents the present discounted value of the

Welfare and policy implications

We next turn our attention to the welfare and policy implications of cooperative R&D. We define welfare as the sum of consumer welfare and producer surplus. This implies that since firms earn zero profits in equilibrium, welfare under R&D competition is equal toWN=RNh(xN)Ω1r+ω0r+RNh(xN),whereΩ1r=(1erT)ω1+erTωallrstands for the consumer welfare level after the race ends. The superscript 1 denotes the case when only one firm has access to the new technology for duration T. We use ω0, ω1 and ω

Cooperative R&D without R&D race outsiders

In the analysis so far, we have maintained the assumption that some outsiders always find it profitable to enter the R&D race in equilibrium. In this section, we provide some additional insights about cooperative R&D with free entry for the case where no outsiders choose to enter the race. We do this to address the potential concern that cooperation between firms in the R&D race may induce the exit of outsiders and, thus, reduce competition in the R&D race. Our results in this section show that

Conclusion

We have analyzed the effects of cooperative R&D in a model of free entry with a stochastic R&D process and oligopolistic product market. Our findings account for the effects of entry and exit in R&D environments which have been missing from the literature to date. In contrast with the results in the literature, we have shown that R&D cartels are always unprofitable and never affect the aggregate rate of innovation adversely in equilibrium. RJV cartels, on the other hand, can be profitable

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  • Cited by (0)

    We are grateful to Richard Jensen (the editor), two anonymous referees, Georgy Artemov, Joshua Gans, Deborah Minehart, participants of the North American Summer Meetings of the Econometric Society (2007) and the Conference on Innovation and Competition in the New Economy at the University of Milan, Bicocca (2007), and seminar participants at the Australian National University (RSSS), Monash University, and the University of New South Wales for valuable comments. We gratefully acknowledge the financial support of the Faculty of Economics and Commerce at the University of Melbourne.

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