Technology policy and the organization of R&D

Journal of Economic Behavior & Organization Vol. 36 (1998) 503±520

Technology policy and the organization of R&D Rune Stenbackaa,*, Mihkel M. Tombakb b

a Swedish School of Economics, P.O. Box 479, 00101 Helsinki, Finland Helsinki School of Economics, Runeberginkatu 14±16, SF±00100, Helsinki, Finland

Received 24 February 1997; accepted 2 December 1997

Abstract In this study we examine how technology policy in the form of R&D subsidies and encouragement of research joint ventures (RJVs) affects the investment incentives of firms in various types of imperfectly competitive markets. We find that joint ventures yield lower research intensities in the absence of subsidies. In the presence of optimal subsidy policy higher expected welfare is obtained with RJVs, but the optimal policy may also involve a more costly subsidy program. The analysis also identifies possible difficulties in implementing socially optimal policies arising from private incentives conflicting with the public interest. # 1998 Elsevier Science B.V. All rights reserved JEL classi®cation: O38; O31; O32 Keywords: Research joint ventures; R&D subsidies

1. Introduction There is strong theoretical support as well as empirical evidence for the view that private rates of return from investments in research and development are generally lower than their social returns. As a result, modern industrial economies exercise substantial public intervention intended to encourage technological progress. Technology policy makers have a number of means of encouraging such investment, including subsidies, modifications of competition policy to allow for cooperation, laws protecting intellectual property, and institutions for the diffusion of new knowledge. In this study, we examine how subsidies and encouragement of research joint ventures affects the investment incentives in various imperfectly competitive markets. * Corresponding author. Tel: +358 94 313 3433; fax: +358 94 313 3382; e-mail: [email protected] 0167-2681/98/$19.00 # 1998 Elsevier Science B.V. All rights reserved PII S 0 1 6 7 - 2 6 8 1 ( 9 8 ) 0 0 1 0 8 - 5

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In the last few decades a number of countries have modified their technology policies, changing the emphasis from one policy tool to another. In 1950s and 1960s many countries pursued a policy of creating `national champions' in key industries. In the 1980s the emphasis seems to have changed to encouraging interfirm cooperation in research and development. Substantial public support has been directed towards cooperative R&D in areas such as microelectronics in both Europe (Rothwell, 1989) and Japan (Audretsch, 1989). A prominent American example of a government supported research joint venture is SEMATECH which initially received 50% of its funding from the federal government (Economist, 1994). In this study, we present a number of relevant considerations for evaluating a shift in technology policy towards encouraging cooperative research joint ventures (RJVs). Recently, there has been considerable interest in the economics of cooperative R&D. Jacquemin (1988) reviews the main costs and benefits of such cooperation to both the public and private sectors. d'Aspremont and Jacquemin (1988) examine a two-stage duopoly model in which firms are initially engaged in cost-reducing innovation and at the second stage the firms are Cournot competitors. They find that for sufficiently large spillovers cooperative R&D yields greater technological advance than noncooperative investments. Kamien et al. (1992) also examine R&D investments in process innovation. They study such investments under a variety of organizational forms ranging from R&D competition to cartelized research joint ventures. They demonstrate that the profit and welfare consequences of an RJV are dependent on the way it is organized. A remarkable conclusion of their analysis is that cartelized RJVs yield the highest investments, the highest firm profits and the highest total welfare. Our results contrast with those of Kamien et al. as we find that in the absence of subsidies R&D competition can yield equilibrium investment levels higher than those under joint ventures, since we focus on innovation without an incumbent technology and without spillovers under R&D competition. For a good review of the issues in R&D cooperation we refer to DeBondt (1997), and to Katz and Ordover (1990) where some of the problems associated with R&D subsidies are pointed out. The contributions mentioned above focused on the allowance of interfirm cooperation in the absence of other policy tools. The literature examining R&D subsidies is rather sparse despite their extensive use as a policy tool. Spence (1984) finds that subsidies can be effective in markets where technological spillovers are high. Spencer and Brander (1983) examine the strategic use of R&D subsidies by a policy maker in a game of international competition and Bagwell and Staiger (1994) have subsequently extended their analysis to include uncertainty in the R&D processes. In this literature subsidies have been examined in isolation from other policy tools, and only in the context of R&D competition. Policy makers, however, have several policy tools at their disposal and make use of these in combination. Romano (1989) examines the interaction between patent policy and subsidies in the cases of monopoly and perfect competition. Leahy and Neary (1995) examine the interactions between subsidies for R&D with different R&D organization and subsidies for output. In a different context, focusing on the interaction between innovators and imitators, Kanniainen and Stenbacka (1995) characterized the optimal combination of patent and subsidy policies indicating the effect of social costs due to distortions created by subsidies. In our study we examine the effects of combining subsidies and R&D

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cooperation in imperfectly competitive markets and thereby characterize the interaction between these policies. We analyze a two-stage model where firms choose research investments in the second stage. In the first stage policy makers commit themselves to a subsidy rate. Furthermore they decide on a policy of whether to allow (or even encourage) either cartelized or competitive research joint ventures. In addition, in the context of R&D competition, policy makers must decide whether a technological leader (a `national champion') is desirable. Using R&D competition as a benchmark we find that organizing the research activities in the form of a joint venture would typically imply a more costly optimal subsidy program, but in the absence of distortion costs this program would generate higher expected social benefits. Consequently, the policy maker would prefer a joint venture to R&D competition as long as the optimal subsidy program can be financed without causing substantial deadweight losses to the economy. With attention restricted to the joint ventures we find that the policy maker would prefer cartelization. However, this produces a policy dilemma because we establish that in the presence of an optimal subsidy program the firms would prefer RJV competition to an RJV cartel. Further, we find in our model that the incentives of firms to form a joint venture depend on the nature of competition in the product market stage. If restricted to R&D competition, the policy maker would prefer a Stackelberg regime where one firm acts as a technological leader. Again the policy maker would be confronted by private incentives conflicting with the public interest because, at the optimal subsidy rates, the leading firm would not want to make a credible commitment to a research intensity. Our study first describes the models and the asumptions used in the analysis. In Section 3 we characterize the socially optimal investment and identify its dependence on how the research activities are organized in the industry. In Section 4 we focus on the subsidy policies which will generate the social optimum. In Section 5 we illustrate the results with an example. In the final section we summarize. 2. The models We develop a two-stage model. In the first stage, the policy maker commits himself to a technology policy based on a certain institutional framework (defined below). In the second stage, firms choose investments in new product innovation conditional on the prevailing technology policy. The industry is modelled as a duopoly where firms choose the probability (p) of success in research directly and where the corresponding costs (c(p)) are an increasing and convex function of the probability of success (c0 (p)>0, c00 (p)>0). We assume that for a given laboratory these costs are independent of how the research is organized within the industry. We focus on sufficiently complex research projects so that the costs of achieving certain success are both privately and socially prohibitively high1 regardless of how the research activity is organized. More specifically we assume that in a duopoly it holds that c0 …1=2† > W2d , where Wd is the total welfare level 1

Realistically, in such research and development it is impossible, at any cost, to guarantee success.

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under duopoly production. This means that the marginal cost of increasing the probability from 1/2 is so large, as to be neither socially nor privately worthwhile. We classify the organization of the research activity into two types: R&D competition and R&D cooperation. We further subdivide the former into regimes of simultaneous and sequential decision making. We consider two types of cooperation in which firms share research results. Using the terminology introduced by Kamien et al. (1992) these two types of research joint ventures are RJV competition and RJV cartels. In RJV competition firms set the R&D budget noncooperatively while in cartelized RJVs the investments are determined so as to maximize industry profits, assuming noncooperative behavior in the post-discovery product market. We focus on a duopoly2 engaged in R&D. If only one firm is successful it achieves a monopoly payoff of m under R&D competition. If both firms complete the R&D successfully they obtain the duopoly profit d each. We assume that m>2d0. For example, d could denote the profit associated with either Cournot competition or Bertrand competition with differentiated products. There is no incumbent technology (or profits are normalized to the level of the incumbent technology) so that if neither firm is successful there are no revenues. In R&D cooperation both participating firms obtain duopoly profits d if either (or both) of the partners are successful. Thus our model offers a general characterization of the product market competition. Our analysis is not restricted to cost-reducing innovation as in the models of d'Aspremont and Jacquemin (1988) and Kamien et al. (1992). In the analysis of technology policy we assume that the policy maker maximizes expected total welfare (pi, pj). This is a function of the welfare generated by monopoly or duopoly production. Let Wm denote the total welfare level generated by monopoly production when only one firm has succeeded in innovating so that Wmˆm‡CSm, where CSm is the consumer surplus with monopoly production. Analogously, when both the firms have access to the new technology, total welfare is Wd ˆ2d ‡ CSd, where CSd is the consumer surplus under duopoly production. We assume that Wm 0: @pi @pj We now proceed to delineate the goal of technology policy by characterizing the socially optimal investments in our models. 3. Socially optimal R&D investments The problem of determining socially optimal investments will serve as the basis for the subsequent analysis of the issue of how to design technology policy so as to obtain the social optimum. The financing of the technology policy, however, could cause distortions to the economy (for example, of the type identified by Dixit and Grossman, 1986). We 2 The restriction to a duopoly does not allow for an examination of the issue of endogenous research joint venture formation. For analysis of such an extension we refer to Kamien and Zang (1993) and Greenlee (1994).

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subsequently focus on the size of the optimal subsidy programs since those subsidies could involve a social cost related to the size of those programs. In general, it is likely that there are two types of social costs associated with the public investment subsidies. First, distortions will be created whenever lump-sum taxation is precluded. Second, a subsidy policy requires monitoring as long as the private incentives to invest are weaker than those of the policy maker. However, we find no reason to believe that these types of social costs connected with public subsidy policies would differ across different forms of organizing R&D activities. Thus, since our analysis has its focus primarily on the impact of the organization of R&D on the efficiency of subsidy programs it would be justified to assume no systematic difference in the social costs of raising the funds necessary to sustain the subsidy program across different organizational forms. As in Laffont (1996), we assume that the distortion costs are proportional to the size of the subsidy program, with the factor of proportionality denoted by 0. We derive the socially optimal R&D intensities both with and without cooperation and then specify subsidy levels by which those optimal intensities can be achieved. The socially optimal probabilities are calculated without institutional restrictions. We demonstrate how higher welfare levels can be achieved through cooperative R&D in the absence of possible distortions created by subsidies. 3.1. Social optimum with R&D competition As a benchmark case we now examine the hypothetical situation where the government controls the R&D intensities of the two laboratories. Both the firms are engaged in R&D competition so that when only one firm is successful it will enjoy monopoly rents. The policy maker decides on the probabilities pi and pj so as to maximize …pi ; pj † ˆ ‰pi …1 ÿ pj † ‡ pj …1 ÿ pi †ŠWm ‡ pi pj Wd ÿ …1 ‡ si †c…pi † ÿ …1 ‡ sj †c…pj †; which simplifies to …pi ; pj † ˆ …pi ‡ pj †Wm ‡ pi pj …Wd ÿ 2Wm † ÿ …1 ‡ si †c…pi † ÿ …1 ‡ sj †c…pj †:

(1)

Optimization of (1) (subject to pi, pj1) yields a system of first order conditions which are symmetric with identical cost functions and subsidy levels. The socially optimal p are characterized by3 probabilities ~pi ˆ ~pj ˆ ~ c0 …~ p† ˆ

Wm ‡ ~ p…Wd ÿ 2Wm † : …1 ‡ s†

(2)

We can see from (2) that cost functions with higher marginal costs would decrease the socially optimal R&D intensity. Also, from (2) we see how the distortion costs will reduce the socially optimal investments. Furthermore, as our socially optimal probability is (by assumption) less than 1/2 this optimal investment increases with an increase in Wm and/or Wd. We will compare this research intensity to that of the socially optimal research level under joint ventures in Section 3.2. 3

The sufficiency conditions hold for convex cost functions and Wd<2Wm.

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3.2. Social optimum with research joint ventures Consider now the hypothetical situation where the policy maker decides on the R&D intensities given that the industry is organized as an RJV. In such a case the possibility of monopoly production is eliminated since a successful innovation will be distributed to both participating firms. We assume that the RJV partners are equally efficient. The problem for the policy maker is then to choose probabilities so as to maximize †c…pi † ÿ …1 ‡ sRJV †c…pj †: …pi ; pj † ˆ …pi ‡ pj ÿ pi pj †Wd ÿ …1 ‡ sRJV i j

(3)

The first order conditions for each firm are again symmetric when firms face identical cost functions and subsidy levels and the socially optimal per firm research intensity ~pRJV ˆ ~pRJV ˆ ~pRJV is given by4 i j c0 …~ pRJV † ˆ

Wd …1 ÿ ~pRJV † : …1 ‡ sRJV †

(4)

Again, we see that cost functions with smaller marginal costs increase the socially optimal probability. Further, increased distortions generated by the subsidy program will decrease the socially optimal investment. Also, a greater welfare level under duopoly production increases the socially optimal investment. Comparison of the first order conditions for the socially optimal research intensity with R&D competition to that of an RJV yields the following proposition. Proposition 1: Research joint ventures induce larger socially optimal research intensities than R&D competition for uniform levels of subsidies (sRJV ˆ s). Proof: The R.H.S. of (2) and (4) are linear and downward sloping itn p. Comparing (2) p ˆ ~pRJV ˆ 1=2. The slope of the R.H.S. with (4) one can see that ~ pˆ~ pRJV if and only if ~ RJV of (2) is …ÿWd †=…1 ‡ s † which is less than the slope of the R.H.S. of (4) which is …Wd ÿ 2Wm †=…1 ‡ s†. First order conditions (2) and (4) are as illustrated in Fig. 1 for s or  equal to zero. The comparison is then determined by whether the marginal cost function intersects the R.H.S. of (2) or (4) at a p larger than or less than 1/2. Since we have assumed R&D costs to be similar and such that c0 …1=2† > W2d the proposition holds. & Q.E.D. Proposition 1 implies that it is socially beneficial to have a higher probability of success with joint ventures than under R&D competition once the research task is sufficiently complex. This is due to the fact that with a joint venture society is certain that an innovation will be diffused to both firms and that there will be duopoly instead of monopoly production. Thus it is worthwhile for society to invest more with a joint venture. As can be seen directly from Fig. 1, the difference in investment levels between

4

Again, sufficiency conditions require convexity of the cost function.

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Fig. 1. First order conditions for socially optimal R&D intensities for s or ˆ0.

RJVs and R&D competition increases with the difference in welfare levels Wd and Wm. With this ordering of R&D intensities we find that total expected welfare is always higher with research collaboration. This is shown in the following corollary. Corollary 1: At the social optimum and with a uniform subsidy level a research joint venture generates a greater total expected welfare than R&D competition. Proof: To compare the total welfare levels we substitute the socially optimal probability under R&D competition into both (1) and (3). This yields the difference RJV

…~ p† ÿ …~ p† ˆ 2~ p…1 ÿ ~ p†…Wd ÿ Wm † > 0:

p. Since ~pRJV is the solution to the From Proposition 1 we know that ~ pRJV > ~ RJV RJV RJV …~ p †> …~p† and the proposition follows. & maximization problem (3), Q.E.D. Provided that the policy maker can implement the socially optimal R&D intensities with the same distortion to the economy, Corollary 1 shows that there is an incentive to encourage the firms to form joint ventures.5 The potential for the welfare gain with an RJV comes from it always diffusing an innovation into duopoly production. Thus a joint venture allows society to better exploit the fruits of an innovation as production would take place under conditions of competition. Organizing the research activities within an RJV, as we shall see in the next section, will have consequences for optimal technology policy.

5

As an anonymous referee has pointed out, this may not generalize to particular versions of patent races.

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4. Optimal subsidy policies In this section we focus on subsidy policy and demonstrate how the subsidy rate affects private R&D incentives. We first compute the privately determined equilibrium investments as a function of the subsidy rates. We then find the subsidy rates which will induce firms to provide the socially optimal R&D intensities computed in the previous section. That is, we find the subgame perfect subsidy rates under the regimes of R&D competition with both simultaneous and sequential decision making, and R&D collaboration organized as both RJV competition and RJV cartelization. 4.1. R&D competition In this section we examine two firms which choose investments noncooperatively and which do not share the results of their research. We distinguish between the cases where firms make those choices simultaneously and sequentially. With sequential decision making one firm is assigned the role of `technology champion' and behaves as a Stackelberg leader with respect to investments. 4.1.1. Simultaneous R&D decisions We now consider firms choosing their investments simultaneously. In this game the policy maker has announced subsidy rates si and sj such that the effective costs of R&D for firms i and j are (1ÿ si) c (pi) and (1 ÿ sj) c (pj), respectively. Firm i chooses its probability of success pi in order to maximize  i ˆ pi …1 ÿ pj †m ‡ pi pj d ÿ …1 ÿ si †c…pi †:

(5)

With probability pi (1ÿpj) firm i is the only successful innovator and attains monopoly rents m. With probability pi pj both firms are successful in innovating and gain duopoly rents. The reaction function for firm i is6 c0 …pi † ˆ

1 ‰m ÿ pj …m ÿ d †Š: …1 ÿ si †

(6)

This reaction function shows that R&D intensities in this model are strategic substitutes. These reaction functions are illustrated in Fig. 2. It can also be seen from (6) that an increase in one's subsidy rate results in the firm's reaction function shifting out. The effect of such a shift on the equilibrium innovation efforts is illustrated in Fig. 2. Analytically, the comparative statics with respect to subsidy rates are @pi …1 ÿ sj †c}…pj †c0 …pi † ˆ >0 @si …1 ÿ sj †…1 ÿ si †c}…pi †c}…pj † ÿ …m ÿ d †2 and

@pj ÿ…m ÿ d †c0 …pi † ˆ < 0: @si …1 ÿ sj †…1 ÿ si †c}…pi †c}…pj † ÿ …m ÿ d †2

6 The first order conditions expressed as the reaction functions are sufficient if c}…pi † > 0 and we assume that the stability condition …1 ÿ sj †…1 ÿ si †c}…pi †c}…pj † ÿ …m ÿ d †2 > 0 holds.

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Fig. 2. Reaction functions under R&D competition

In other words, an increased subsidy rate for any one firm increases that firm's investment and decreases that of the rival firm but at a lower rate. Thus strategic interaction somewhat diminishes the impact of a subsidy to one firm on overall industry innovation. We will compare the equilibrium probability defined by (6) to that of the other regimes as well as to the socially optimal probability. 4.1.2. Sequential R&D decisions We now examine the case where investments are chosen sequentially. As previously, we assume that the policy maker commits himself to irreversible subsidy rates prior to the investment decisions of the firms. There is a technological leader (L) with the ability to commit itself to an R&D intensity pL. The follower (F) considers pL as fixed. In other words, we consider a Stackelberg game with respect to the investments. This regime may have its origin in institutions which facilitate irreversible investment decisions (such as government conditions for subsidies) and the diffusion of information thereof. In this case the firms' payoffs are identical in form to (5) so that the reaction function for the follower is given by (6) except that the firm indices are replaced with either L or F. As already mentioned, this reaction function is downward sloping. Thus, for given subsidy levels the R&D intensity for the leader is greater than that of a duopolist with simultaneous decisions. Consequently, the following relationship holds for uniform subsidies (7) pL > pi > pF : This same relationship between the leader's and follower's R&D intensities has also been demonstrated in a different context by Grossman and Shapiro (1987).7 In terms of 7 The particular context in which they found this phenomenon was with the simultaneous choice of R&D intensities in a two stage race. Success in the first stage of their model yielded an intermediate result prerequisite for the ultimate success of the research. The leading firm in the Grossman and Shapiro model is then that which has succeeded in the first stage while its rival has not.

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comparative statics, again we found that the innovation efforts are increasing in one's own subsidy rate and decreasing in the rival's subsidy rate. 4.2. Research joint ventures In this section we examine two types of RJVs described in Kamien et al. (1992). First, we study symmetric RJV competition (case NJ) where the participating firms each noncooperatively decide on their contribution to the joint venture. Secondly, we examine cartelized RJVs where participants coordinate their investment levels so as to maximize the sum of overall profits. Any results are distributed to all joint venture participants. That is, if any participating firm is successful in innovating, both the partners receive a payoff of d . In order to retain comparability to the R&D competition case, we assume that the joint venture partners would retain their separate laboratories. Thus we focus on the information sharing capability of RJVs as opposed to their ability to centralize research activity (note that for convex cost functions such a centralized organization could be less cost efficient than separate laboratories). This way of organizing research collaboration is frequently observed. For example, Odagiri and Goto (1993) report on the RJVs formed under the Mining and Manufacturing Industry Technology Research Association Act of Japan during the period 1961±1987 and found that in 85 out of 87 joint ventures the R and D is conducted in separate laboratories. The probability of success of the joint venture would be pi ‡ pj less the chance of simultaneous success in both laboratories pi pj . For both types of research collaboration we assume that the policy maker treats the participating firms equally. 4.2.1. Case NJ With RJV competition the problem of the firm is to choose its investment in order to maximize NJ  NJ i ˆ …pi ‡ pj ÿ pi pj †d ÿ …1 ÿ s †c…pi † With symmetric firms it can be easily shown that the equilibrium probabilities are characterized by d …1 ÿ pNJ † : (8) c0 …pNJ † ˆ …1 ÿ sNJ † We will compare this equilibrium with that of the cartelized RJV. 4.2.2. Case CJ With a cartelized RJV the problem of the cartel is to choose probabilities …pi ; pj † so as to maximize 2 CJ ˆ 2…pi ‡ pj ÿ pi pj †d ÿ …1 ÿ sCJ †c…pi † ÿ …1 ÿ sCJ †c…pj † with identical cost functions straightforward optimization yields the optimal investment levels c0 …pCJ † ˆ

2d …1 ÿ pCJ † : …1 ÿ sCJ †

(9)

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Comparing (4) with (8) and (9) it is evident that without subsidies ~pRJV is greater than pNJ or pCJ. It is also apparent that the RJV cartel would invest more than the competitive RJV unless there were a large subsidy rate differential. This is due to the `free rider' problem associated with an RJV partner's noncooperatively determined contribution of R&D input (Kamien et al., 1992). That is, in the NJ case there is a disincentive to invest in R&D since a firm obtains all the benefits of the other firm's investment. Proposition 2: For uniform subsidies the equilibrium research intensities satisfy pi > pCJ > pNJ Proof: Compare (6), (9) and (8) with identical subsidy rates (see Fig. 3). Note that they are linear and downward sloping in p. At pˆ0 the R.H.S. of (6), (9) and (8) are m =…1 ÿ s†, 2d =…1 ÿ s†, and d =…1 ÿ s†, respectively. At pˆ1/2 they are …m ‡ d †=‰2…1 ÿ s†Š, d =…1 ÿ s†, and d =‰2…1 ÿ s†Š, respectively. In other words, the R.H.S. of (6) is always greater than the R.H.S. of (9) which is always greater than the R.H.S. of (8). As the marginal cost functions are the same this implies the ordering of the research intensities stated above. & Q.E.D. Proposition 2 implies that R&D competition induces higher investments than RJVs. This result differs from the model of Kamien et al. (1992). In accordance with them we find that an RJV cartel would lead to higher investments than RJV competition. Our results differ since in our model firms have a greater profit incentive under R&D competition. This larger profit incentive comes from the firm's opportunity to achieve monopoly rents …m †. In contrast, joint ventures diminish the investments since the partners agree to share the results of the research and hence with RJVs there is no possibility of obtaining m . Furthermore, for the cost reducing process innovations

Fig. 3. First order conditions for individually optimal R&D intensities (for sˆ0).

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considered by Kamien et al. the absence of success in R&D still entailed profits. Our models capture both the processes and product innovation in the absence of an incumbent technology (or with the payoffs from the incumbent technology normalized to zero). That is, there are no rents unless the R&D is successful. Neither do we include an exogeneous rate of spillover between rival firms. Hence, in our models the profit incentives are greater with R&D competition. 4.3. Comparisons of optimal subsidy rates We now examine the problem of how to use subsidy policies to implement the socially optimal investment level determined in Section 3. To find these optimal subsidy levels we equate the marginal costs at pi ; pj ; pL , and pF to the marginal cost at ~p. The calculation of these optimal subsidies leads to the following proposition. Proposition 3: Optimal subsidy levels satisfy sL < si ˆ sj ˆ sF < 1 Proof: The optimal subsidy policy will implement the socially optimal probability ~p and must satisfy (2). From the reaction function (6) the optimal subsidy rate is then determined by 1 ÿ si m ÿ pj …m ÿ d † ˆ : (10)  …1 ‡ si † Wm ‡ ~ p…Wd ÿ 2Wm † As ~p < 1=2 both the numerator and the denominator of the R.H.S. in (10) are positive. Note that these expressions differ only in the research intensities of the rival firm. Consequently, si is increasing in pj . An optimal policy would bring each pj to level ~p and hence si ˆ sj . Given ordering (7), which holds for uniform subsidies, it follows that sL < si . Furthermore, once the policy maker has announced the subsidy rates which implement the socially optimal R&D level for the leader, the follower's optimal subsidy rate would be identical to that of the simultaneous decision makers. & Q.E.D. Without subsidies we know that pL > pF . Furthermore, a subsidy directed to the leader will increase its research intensity while decreasing the intensity of the follower. Thus, to raise the probabilities of both the firms to the socially optimal level the follower must be subsidized at a higher rate. The subsidy rate to the follower is equal to the optimal subsidy rate directed to simultaneous duopolists, because at the optimal subsidy rate the research intensity of the rival (the leader) is ~ p and the reaction functions are identical. An interesting implication of Proposition 3 is that government assistance in the form of a subsidy program should be targeted towards technological followers. Neary (1994) has recently explored the implications of two other forms of asymmetry between the firms in the context of strategic trade policy. His analysis was focused on the asymmetry between the private and social costs of subsidy programs as well as on asymmetries due to different home and foreign costs of production. Neary finds that in such a context the government should provide more help to the relatively profitable firms than to the unprofitable ones.

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The cost to the public is …1 ‡ †sc…~ p† and since the probability in each case is the same, this cost is ordered by the subsidy rate. Consequently, the socially optimal intensity is less expensive to implement with sequential decision making. An implication of Proposition 3 is that the policy maker would have an incentive to design institutions which would sustain sequential investment decisions. Unfortunately, the private incentives do not correspond with the public ones in this regard. Since the cost function is the same, the leading firm would bear a higher proportion of the costs and yet achieve no competitive advantage, the ultimate probabilities of success being the same. Since the leading firm will then want to avoid making a credible commitment if offered a lower subsidy rate than the follower, this would constitute a policy dilemma as it would be difficult to implement the sequential decision making regime with the optimal subsidy rates. One conceivable way of implementing the Stackelberg regime could involve public ownership of the leading firm. We now characterize the optimal subsidy programs with RJVs. Equating the marginal costs at pNJ in (8) and pCJ in (9) to the marginal cost at ~pRJV in (4) one can compute the optimal subsidies to satisfy 1 ÿ sCJ 2d ˆ …1 ‡ sCJ † Wd

(11)

1 ÿ sNJ d ˆ : NJ …1 ‡ s † Wd

(12)

and

It follows directly from these expressions that the optimal subsidy rates for RJV's always satisfy 0 < sCJ < sNJ < 1. Recall that in the absence of subsidies (a uniform subsidy of zero) we have p<~ pRJV . The optimal subsidy for RJVs, sNJ or sCJ, will raise the pNJ < pCJ < pi < ~ RJV probability of success to ~ pRJV and thereby the corresponding welfare level to ~ . The optimal subsidy under R&D competition raises the research intensity by less, from pi to ~p, yielding a lower welfare level (when ˆ0). However, we shall see that the increase in welfare resulting from the optimal subsidy policy towards an RJV takes place at the expense of a more costly subsidy program. To see that the subsidy would be lower under R&D competition compare (10) with (11) and (12). Note that the denominator in (10) is less than that of (11) and (12) since Wm ‡ ~p…Wd ÿ 2Wm † < Wm < Wd . Also, the numerator in (10) is the probability weighted average of the profits under monopoly and the profits under duopoly and hence it is p < 1 so that si < sNJ . Clearly, at pi ˆ 0 the optimal subsidy always larger than d when ~ given by (10) is less than that under CJ since the numerator of the R.H.S. in (10) is then m which is greater than the numerator of the R.H.S. in (11). As the marginal investment costs decrease, however, pi increases and si increases and may surpass the subsidy rate of the cartelized RJV. We show the conditions for this in the parametric example of the next section. We summarize our analysis of optimal subsidy rates in the following proposition.

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Proposition 4: The optimal subsidy rates (i) always have the ordering sCJ < sNJ and (ii) satisfy m …1 ÿ ~ p† ‡ ~ pd Wm ‡ ~p…Wd ÿ 2Wm † : > si < sCJ < SNJ if 2d Wd …1 ÿ ~pRJV † Under R&D competition the cost to the public of the optimal subsidy program would be …1 ‡ †sc…~p†. If the subsidy rate were lower with R&D competition than under RJV, the cost to the public of the optimal subsidy program would be lower with R&D competition since ~p < ~pRJV . The condition for the subsidy rate to be lower under R&D competition is given in Proposition 4. The R.H.S. of this condition is the ratio of the marginal social benefit of additional investments in research under R&D competition to that of joint ventures. This ratio is always less than 1 in our model. On the L.H.S. we have the ratio of the socially optimal probability weighted average of the monopoly and duopoly rents to twice the duopoly rents. This is the ratio of marginal private benefits of additional investments in research. For low ~p this ratio is greater than 1. For ~ p ˆ 1=2 whether this ratio is greater than 1 would depend on the difference between monopoly and duopoly rents. Consequently, for sufficiently low ~p the relationship between the public costs of optimal subsidy programs under R&D competition and RJVs depends on the nature of product market competition. As we have shown in Corollary 1, optimal subsidy policy will generate a greater expected welfare with joint ventures provided that the optimal policy can be implemented without distortions to the economy. If one assumes that the marginal social cost of raising public revenues is an increasing function of the amount of funds required, the social cost of implementing optimal subsidies are higher with RJVs. Since such distortions would offset the expected welfare gain from forming a joint venture, substantial social costs associated with the financing of subsidies could reverse the argument in Corollary 1 for promoting RJVs. As in the previous section, the cost to the public sector of the subsidy program implementing the socially optimal research intensity with RJVs is …1 ‡ †sc…~pRJV †. Hence, it is less costly to the public sector to achieve the social optimum under case CJ than under case NJ. Again, we can identify a policy dilemma as the private incentives differ from those of the policy maker. With the optimal subsidy rates in force the firms achieve payoffs which yield the difference d CJ > 0:  NJ i ÿ i ˆ Wd Consequently, the firms do not have an incentive to form an RJV cartel. Under both cases NJ and CJ the firms receive the same expected profit. Firms prefer NJ simply because the subsidy rate is higher. Let us now turn to the question of whether the firms want to form a joint venture at all. For this purpose we now examine a parametric example with quadratic cost functions. 5. An Example In this section we compute the equilibrium and optimal research intensities, the optimal subsidy rates, and the payoffs for a parametric example where the costs are

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Table 1 Optimal and equilibrium R&D intensities Wm K ÿ Wd ‡ 2Wm Wd ~pRJV ˆ K ‡ Wd m ……1 ÿ sj †K ÿ m ‡ d pi ˆ …1 ÿ si †…1 ÿ sj †K 2 ÿ …m ÿ d †2 ~p ˆ

pL ˆ pNJ pCJ

m ‰…1 ÿ sF †K ÿ …m ÿ d †Š

…1 ÿ sL †…1 ÿ sF †K 2 ÿ 2…m ÿ d †2 d ˆ …1 ÿ sNJ †K ‡ d 2d ˆ …1 ÿ sNJ †K ‡ 2d

quadratic and there are no distortion costs. We assume c…pi † ˆ 12 Kp2i where K>Wd so that our assumption c0 …12† > …1=2†Wd is satisfied. We then illustrate in the presence of optimal subsidy policy how the firms' incentives to form a joint venture depend on the nature of the product market competition (Bertrand or Cournot). Because K > Wd and Wd < 2Wm verifying that ~pRJV > ~p for the quadratic cost function is straightforward (see Table 1). We observe that pi is less than 1. Further, it can be seen that pi is an increasing function of m and d and a decreasing function of K. From this expression one can show that an increased subsidy rate for any one firm increases that firm's probability and decreases that of the rival firm. We find the Stackelberg equilibrium probability for the leader is identical to the expression for the equilibrium probabilities in the simultaneous game with the exception of the second term in the denominator so that pL > pi .Comparing sCJ with si we find the optimal subsidy rate of firms in the CJ case is larger than that of the simultaneous R&D competition case if 2Wm Kd < Wd ‰m …K ‡ Wm ÿ Wd † ‡ d Wm Š; which can be rewritten as

 K > Wd

 Wd m ÿ Wm …m ‡ d † : Wd m ÿ 2d Wm

We are able to see that the latter inequality always holds since the term within the square brackets is always less than one and K > Wd . Consequently, si < sCJ < sNJ < 1. Let us now turn to the question of whether the firms want to form an RJV at all. For this purpose we rewrite the expected payoffs for the case of quadratic costs under the R&D competition and NJ regimes with optimal subsidy rates as ~ p p~RJV 3K ‡ 2Wd d p†m ‡ ~ pd Š and  NJ : i ˆ ‰…1 ÿ ~ i ˆ 2 K ‡ Wd 2

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From this formulation we see that the incentives of the firms to form a competitive RJV depend on the degree of product market competition as well as on the complexity of the research project once the policy maker implements an optimal subsidy policy. Since ~pRJV > ~p, the firms would clearly prefer to form a competitive RJV if p†m ‡ ~ pd . This condition implies a restriction on d …3K ‡ 2Wd †=…K ‡ Wd † > …1 ÿ ~ the difference between m and d and thus on the degree of competition in the product market. Bertrand competition between symmetric firms with a homogeneous product is a simple example where R&D competition would be preferred. In this case d is zero and R&D competition is the only situation in which there is a possibility of attaining monopoly rents. With Cournot competition in the case of linear inverse demand with an intercept of a and a slope of 1 and with the marginal costs of production equal to zero, however, we find that firms would prefer to form a competitive RJV. In this case, profits, consumer surplus and total welfare are, m ˆ a2 =4, CSm ˆ a2 =8, Wm ˆ 3a2 =8 for the monopoly and d ˆ a2 =9, CSd ˆ 2a2 =9, Wd ˆ 4a2 =9 for the duopoly. When K ˆ a2 and in the absence of subsidies, the equilibrium R&D investment is pi  0:219 with R&D competition while the success probability is pNJ ˆ 0:1 with RJV competition. The welfare maximizing probabilities of success are ~p ˆ 27=94 and ~pRJV ˆ 4=13 which are achieved with subsidies of si ˆ 29=108 and sNJ ˆ 3=4. The public cost of the optimal subsidy program is substantially greater with the RJV. The firm's expected payoffs in 2 2  2 2 each regime are then  NJ i ˆ 70a =1521  0:046a and i ˆ 2133a =70688  0:030a . These examples illustrate that the question of whether the firms prefer RJV competition or R&D competition depends on the degree of product market competition. This contrasts with the results from the model of Kamien et al. (1992) which showed that under both Cournot and Bertrand competition firms prefer RJV cartels. Again, this difference is due to three factors: (i) the absence of an incumbent technology in our model, (ii) the presence of fixed spillovers in their model of R&D competition, and (iii) our consideration of optimal subsidy policy. The first two factors tend to favor R&D competition. As we see in the above example the third factor can make RJV competition more appealing to the firm. 6. Conclusions and discussion In this study we analyze a two-stage model in which firms choose research investments in the second stage while in the first stage policy makers choose subsidy rates and a regulatory framework. We initially examine the problem of what the expected welfare maximizing research intensities would be under a variety of ways of organizing research and development. These forms of organization include duopolisitic R&D competition with both simultaneous and sequential decision making, a joint venture where participants choose their investments noncooperatively, and a cartelized RJV. Our analysis shows that the policy maker would prefer an RJV to R&D competition as the expected total welfare level achieved would be greater with sufficiently low distortions to the economy created by subsidies. Consequently, we find a rationale for supporting research joint ventures.

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Subsequently we examine the second stage problem of firms choosing innovation efforts with costs subsidized at a given rate. We find that for sufficiently low subsidy rates the industry investment will be lower in a joint venture arrangement than under R&D competition. The investment is also found to be greater with an RJV cartel than with RJV competition. Under R&D competition a technological (Stackelberg) leader would select a greater research intensity than it would if it were to decide on the investment level simultaneously with its rival. The commitment of the leader to a higher investment implies that the follower will choose a lower research intensity than in the Nash equilibrium with simultaneous decisions. We then study the problem of designing an optimal technology policy. Policy makers decide on a rate at which to subsidize the research expenditures of firms which will implement the socially optimal research intensities. They also determine which type of competition policy to apply. We investigate the competition policy problem of whether to allow for (or even encourage) research joint ventures of either the cartelized or competitive type. We find that an RJV would typically imply a more costly subsidy program, so that substantial social costs associated with the financing of subsidies could reverse the arguments for promoting RJVs. With attention restricted to joint ventures we find that the policy maker would prefer the cartelized RJV. However, this entails a dilemma in that with an optimal subsidy program the firms would prefer RJV competition to an RJV cartel since the optimal subsidy rate is larger. Further, we find that the incentives of the firms to form a joint venture depend on the nature of the duopoly competition taking place at the product market stage. That is, with more intense product market competition (as in cases approaching Bertrand competition in a homogenous market) firms would prefer R&D competition to forming a joint venture. If restricted to R&D competition, the policy maker would prefer a Stackelberg regime where one firm is chosen to be a technological leader. Again, however, the policy maker would be confronted by private incentives conflicting with the public interest as firms would not want to make credible commitments to research intensities at the optimal subsidy rates. An interesting modification of our study would be to examine technology policies in the context of international competition. In this case, the stage of technology policy would involve a game between policy makers setting subsidy rates as well as competition policy. Such an extension would introduce the interaction between several technology policy makers and could provide a framework for an analysis of the potential gains from international coordination of technology policy. Another potentially interesting dimension would be to introduce patents in combination with the policy tools already examined in our analysis. Clearly, an increased patent length or breadth would increase m and decrease d . However, the introduction of patents into the set of policy options would require a dynamic model. The introduction of patent policy will provide further interaction effects between policy tools. Our present study has identified significant interaction effects between competition policy and R&D subsidy policy. Acknowledgements The authors would like to thank the seminar participants in conferences at EEA in Istanbul, OECD in Porvoo, Finland, Wissenschaftszentrum in Berlin and the International

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Conference in Industrial Economics at Universidad Carlos III de Madrid for their comments. The authors acknowledge financial support from the Academy of Finland. References Audretsch, D., 1989. Joint R&D and industrial policy in Japan. In: Link, A., Tassey, G. (Eds.), Cooperative R&D: The Industry±University±Government Relationship. Kluwer Academic Publishers, London. d'Aspremont, C., Jacquemin, A., 1988. Cooperative and noncooperative R&D in duopoly with spillovers. American Economic Review 78, 1133±1137. Bagwell, K., Staiger, R., 1994. The sensitivity of strategic and corrective R&D policy in oligopolistic industries. Journal of International Economics 36, 133±150. DeBondt, R., 1997. Spillovers and innovative activities. International Journal of Industrial Organization 15(1), 1±28. Dixit, A., Grossman, G., 1986. Targeted export promotion with several oligopolisitic industries. Journal of International Economics 21, 233±249. Economist, 1994. Uncle Sam's helping hand. pp. 77±79. Greenlee, P., 1994. Endogenous Formation of Competitive Research Joint Ventures. Northwestern University, MEDS Department Working Paper. Grossman, E., Shapiro, C., 1987. Dynamic R&D competition. Economic Journal 97, 372±387. Jacquemin, A., 1988. Cooperative agreements in R&D and European antitrust policy. European Economic Review 32, 551±560. Kamien, M., Muller, E., Zang, I., 1992. Research joint ventures and R&D cartels. American Economic Review 82(5), 1293±1306. Kamien, M., Zang, I., 1993. Competing Research joint ventures. Journal of Economics and Management Strategy 2(1), 23±40. Kanniainen, V., Stenbacka, R., 1995. Towards a Theory of Socially Valuable Imitation with Implications for Technology Policy. Economic Policy Research Unit, Copenhagen Business School Working Paper No. 1995-3. Katz, M., Ordover, J., 1990. R&D Cooperation and Competition. Brookings Papers on Economic Activity, Microeconomics, pp. 137±191. Laffont, J.-J., 1996. Industrial policy and politics. International Journal of Industrial Organization 14, 1±27. Leahy, D., Neary, P., 1995. Public Policy towards R&D in Oligopolistic Industries. CEPR Working Paper No. 1243. Neary, P., 1994. Cost asymmetries in international subsidy games: should governments help winners or losers?. Journal of International Economics 37, 197±218. Odagiri, H., Goto, A., 1993. The Japanese System of Innovation: Past, Present and Future. In: Nelson, R. (Ed.), National Innovation Systems: A Comparative Analysis. Oxford University Press, Oxford, UK. Romano, R., 1989. Aspects of R&D subsidization. The Quarterly Journal of Economics 104, 863±873. Rothwell, R., 1989. Technology policy and collaborative research in Europe. In: Link, A., Tassey, G. (Eds.), Cooperative R&D: The Industry±University±Government Relationship. Kluwer Academic Publishers, London. Spence, M., 1984. Cost reduction, competition, and industry performance. Econometrica 52, 101±121. Spencer, B., Brander, J., 1983. International R&D rivalry and industrial strategy. Review of Economic Studies L, 707±722.