Cooperative R&D between vertically related firms with spillovers

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Abstract

This paper analyzes the effects of cooperative R&D in two vertically related duopolies, which are two final-good manufacturers and two input suppliers, with horizontal and vertical spillovers. Vertical R&D cartels yield a larger social welfare than non-cooperative R&D and, if the horizontal spillover rate between the input suppliers is not sufficiently high, than horizontal R&D cartels. Technological improvement is accelerated by forming vertical research joint ventures (RJVs), whether or not their member firms' R&D decisions are coordinated. Vertical RJV cartels yield the largest social welfare when the vertically related firms can coordinate their R&D decisions and/or share useful knowledge fully.

Introduction

The purpose of this paper is to investigate the effects of cooperative R&D in two vertically related duopolies with horizontal and vertical spillovers.

The theoretical studies on R&D cooperation among firms have mainly addressed many issues in the economics of horizontal cooperative R&D.1 In particular, d'Aspremont and Jacquemin (1988) and Kamien et al. (1992) are pioneering works on horizontal cooperative R&D with horizontal spillovers. Their works have been generalized and extended by many economists.2 By contrast, vertical cooperative R&D has not received much attention in the theoretical literature until recently.3

This paper focuses on a case where a final-good manufacturer and an input supplier cooperate in their R&D activities in the presence of horizontal and vertical spillovers. It is often pointed out that the close linkages between final-good manufacturers and input suppliers are important for successful innovation (see von Hippel, 1988, Riggs and von Hippel, 1994, Lee, 1996). For input suppliers, knowing final-good manufacturers' needs is useful for the development and production of the parts and materials they use. The information on new parts and materials also allows their users to adopt them promptly. Therefore, when a final-good manufacturer purchases an input from its supplier, one would expect that R&D spillovers occur between these firms. Such vertical spillovers should be taken into consideration along with horizontal spillovers in order to obtain a well-balanced evaluation of the effects of cooperative R&D.

There are benefits and risks of organizing vertical cooperative R&D. A final-good manufacturer and an input supplier can internalize a vertical R&D externality by coordinating their R&D decisions, and eliminate duplication of research efforts by sharing knowledge useful to their R&D investments. On the other hand, the member firms of a vertical cooperative R&D project fear that their non-member rivals free ride on their R&D investments through horizontal spillovers and through the input dealings with other members.

We consider two vertically related duopolies with R&D input spillovers, as assumed in Kamien et al. (1992). There are two upstream firms (called U-firms) selling a homogeneous input to two downstream firms (called D-firms) in the market. Each D-firm purchases an equal amount of the input from both U-firms to produce a homogeneous final good. The firms compete in three stages. In the first stage, the firms strategically precommit themselves to cost-reducing R&D expenditure levels. In the second, U-firms choose their output levels in Cournot fashion. In the third, D-firms choose their output levels in the same fashion. Symmetric R&D spillovers occur between D-firms and between U-firms. Due to the symmetric market transaction, knowledge is assumed to spill over at the same rate from D-firms to U-firms and from U-firms to D-firms.4

In such a situation, we consider three vertical cooperative R&D modes: vertical R&D cartels, vertical non-cooperative RJVs, and vertical RJV cartels. Their distinctions are as follows. When a D-firm and a U-firm coordinate only their R&D decisions, they form a vertical R&D cartel. A vertical non-cooperative RJV is formed when a D-firm and a U-firm share only their knowledge useful to R&D investments. When a D-firm and a U-firm not only coordinate their R&D decisions but also share their useful knowledge fully, they form a vertical RJV cartel. We assume that a D-firm and a U-firm impose no restrictions on the input dealings with their rivals even if they agree to coordinate their R&D decisions and/or share all their useful knowledge.5

In the first part of this paper, we compare vertical R&D cartels with non-cooperative R&D and horizontal R&D cartels, and obtain two main findings. First, irrespective of the sizes of spillovers, vertical R&D cartels attain a higher technological improvement and a larger social welfare than non-cooperative R&D. This contrasts with the results of the comparison between a horizontal R&D cartel and non-cooperative R&D obtained by d'Aspremont and Jacquemin, 1988, Kamien et al., 1992, Suzumura, 1992, and Yi (1996). They showed that only with high horizontal spillover rate, a horizontal R&D cartel attains a higher technological improvement and a larger social welfare. Second, vertical R&D cartels yield a larger social welfare than horizontal R&D cartels if the horizontal spillover rate between U-firms is not sufficiently high.

The reason why vertical R&D cartels lead to a higher technological improvement than non-cooperative R&D is explained as follows. Since the cost-reducing R&D expenditure by a D-firm (resp. U-firm) not only expands the demand (resp. supply) for the input but also reduces the production costs of U-firms (resp. D-firms) through vertical spillover, it always produces profit-increasing effects on U-firms (resp. D-firms). Under vertical R&D cartels, the firms can internalize such vertical externalities and carry out a larger R&D expenditure than under non-cooperative R&D. As a result, technological improvement is higher under vertical R&D cartels than under non-cooperative R&D.

A higher R&D incentive under a vertical R&D cartel may be harmful from the point of view of social welfare, as well as from that of the producers' surplus, depending on the sizes of spillovers. R&D expenditures produce a business-stealing effect by making a strategic commitment to higher output levels and also a free-riding effect of reducing the production costs of other firms through spillovers. With high spillover rates, an increase in R&D expenditures under a vertical R&D cartel alleviates not only the inefficiency from underproduction due to duopolistic pricing but also that from underinvestment due to free-riding. With low spillover rates, on the other hand, it alleviates the inefficiency from underproduction but aggravates the unprofitability from overinvestment occurring due to business-stealing. In this case, it produces a positive impact on social welfare, since the former effect dominates the latter. Thus, vertical R&D cartels yield a larger social welfare than non-cooperative R&D, because they enable the firms to carry out a larger R&D expenditure. Under vertical R&D cartels, it need not be the case that all firms undertake a larger R&D expenditure than under horizontal R&D cartels. If the horizontal spillover rate between U-firms is not sufficiently high, however, vertical R&D cartels lead to larger total R&D expenditures of D-firms and U-firms than horizontal R&D cartels, so that the former yields a larger social welfare.

In the second part of this paper, we compare four vertical R&D organization modes: non-cooperative R&D, vertical R&D cartels, vertical non-cooperative RJVs, and vertical RJV cartels. Two main findings are obtained regarding vertical RJVs. First, technological improvement and social welfare increase by forming vertical RJVs, whether or not their member firms' R&D decisions are coordinated. This is in contrast to the result for horizontal RJVs obtained by Kamien et al. (1992). They showed that technological improvement and social welfare increase by forming a horizontal RJV only if its member firms coordinate their R&D decisions. Second, among the vertical R&D organization modes, vertical RJV cartels attain the highest technological improvement and the largest social welfare but do not necessarily yield the largest joint profits of D-firms and U-firms. Kamien et al. (1992) showed that a horizontal RJV cartel dominates the other horizontal R&D organization modes (that is, non-cooperative R&D, a horizontal R&D cartel, and a horizontal non-cooperative RJV) in terms of technological improvement, firms' profits, and social welfare. Thus, the results for horizontal RJV cartels obtained by them do not necessarily carry over to vertical RJV cartels, as far as firms' profits are concerned.

Vertical RJVs have two opposite effects on R&D incentives. The D-firm (resp. U-firm) participating in a vertical RJV strengthens its incentive to invest by obtaining useful knowledge from the other member. On the other hand, it weakens its R&D incentive by providing its useful knowledge to the other member, which induces an increased supply (resp. demand) for the input and thus promotes its rival's production. Nonetheless, since the former direct effect on R&D incentive of vertical knowledge-sharing dominates the latter indirect one, vertical RJVs accelerate technological improvement. The R&D expenditure by a member firm of a vertical RJV generates a profit-increasing effect on the other member. Under vertical RJV cartels, the firms can internalize such vertical externalities and carry out a larger R&D expenditure than under vertical non-cooperative RJVs. As a result, vertical RJV cartels attain the highest technological improvement among the vertical organization modes.

Under vertical RJVs, the firms strategically overinvest from the point of view of their joint profits when spillover rates are low. This is the reason why vertical RJV cartels do not necessarily yield the largest joint profits among the vertical R&D organization modes. For the same reason as in the case of vertical R&D cartels, however, an increase in R&D expenditures under a vertical RJV improves social welfare even though it reduces joint profits. Therefore, from the results for technological improvement attained under vertical RJVs, social welfare increases by forming vertical RJVs, and vertical RJV cartels yield the largest social welfare among the vertical R&D organization modes.

This paper is closely related to Atallah (2002), which focused on vertical spillovers and vertical R&D cartels. Atallah (2002) studied how changes in vertical and horizontal spillover rates affect the R&D expenditures and social welfare under four R&D organization modes (that is, non-cooperative R&D, horizontal R&D cartels, vertical R&D cartels, and simultaneous horizontal and vertical R&D cartels),6 and also compared the total R&D expenditures of D-firms and U-firms under them. There are, however, three major differences between Atallah (2002) and this paper. First, this paper sets out a more general model with respect to the specification of how spillovers affect the cost of production. Besides the special forms of the cost functions, Atallah's (2002) model treats R&D spillovers not as input spillovers à la Kamien et al. (1992) but as output spillovers à la d'Aspremont and Jacquemin (1988), whose plausibility has been critically questioned by Amir (2000). Further, it presumes that the horizontal spillover rates in the downstream and upstream industries are exactly the same. The two-way vertical spillover rates, from U-firms to D-firms and vice versa, are also assumed to be identical. Second, this paper compares the total R&D expenditures between vertical and horizontal R&D cartels in a broader dimension. Atallah (2002) found that vertical R&D cartels lead to larger total R&D expenditures than horizontal R&D cartels if the horizontal spillover rates in the downstream and upstream industries are equal and not sufficiently high. This paper, by contrast, allowing their divergence between industries, shows that the same result holds if the horizontal spillover rate in the upstream industry is not sufficiently high, regardless of that in the downstream industry (Lemma 1 below). Third, Atallah (2002) neither conducted welfare comparisons between different R&D organization modes nor considered the effects of vertical RJVs.

The remainder of the paper is organized as follows. We present the basic model for analyzing vertical R&D cartels in Section 2 and characterize the equilibria in Section 3. In Section 4, the equilibrium outcomes under vertical R&D cartels are compared with those under horizontal R&D cartels as well as those under non-cooperative R&D. In Section 5, two types of vertical RJVs are examined and the equilibrium outcomes under four vertical R&D organization modes are compared. Concluding remarks are given in Section 6. All proofs are presented in the appendices.

Section snippets

The basic model

Consider two vertically related industries. There are two identical firms in each industry. Two firms in the downstream (resp. upstream) industry are called D-firms (resp. U-firms) 1 and 2. U-firms sell a homogeneous input to D-firms at price Pu, and D-firms produce a homogeneous final good using the input and then sell it to consumers at price Pd. D-firms use one unit of the input to produce one unit of the final good. We assume that each D-firm purchases an equal amount of the input from both

Equilibria

We use subgame perfection as the equilibrium concept and solve the game by backward induction.

Comparison of equilibrium effective R&D investments

To start with, let us compare the equilibrium effective R&D investments under vertical R&D cartels with those realized in the other cases.

Proposition 1

(i) The equilibrium effective R&D investments are larger under vertical R&D cartels than under non-cooperative R&D. (ii) The equilibrium effective R&D investments are larger under vertical R&D cartels than under horizontal R&D cartels if hu<4/5 and vu=0.

Proof

See Appendix C.

Recall that each firm's R&D expenditure always produces profit-increasing effects on the

Vertical research joint ventures

In this section, we consider two types of vertical RJVs. One is a vertical non-cooperative RJV, in which D-firm i and U-firm i (i=1,2) share all their useful knowledge to avoid duplication of R&D activities but do not coordinate their R&D decisions. The other is a vertical RJV cartel, in which D-firm i and U-firm i (i=1,2) share their useful knowledge completely and also coordinate their R&D decisions. We compare four possible vertical R&D organization modes: non-cooperative R&D, vertical R&D

Concluding remarks

This paper considers the effects of cooperative R&D in two vertically related Cournot duopolies with horizontal and vertical spillovers. We obtain four main findings. First, vertical R&D cartels attain a higher technological improvement and a larger social welfare than non-cooperative R&D. Second, vertical R&D cartels yield a larger social welfare than horizontal R&D cartels if the horizontal spillover rate between input suppliers is not sufficiently high. Third, technological improvement and

Acknowledgements

I am grateful to two anonymous referees, Stephen Martin, and Hideki Konishi for their valuable and constructive suggestions. I would also like to thank Toshihiro Matsumura, Jun Wako, Taichi Ezawa, and Tetsuo Wada for their helpful comments on an earlier version of this paper. Of course, any remaining errors are my responsibility.

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