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R&D spillovers and information exchange
Economics Letters 61 (1998) 121–123
R&D spillovers and information exchange a b, Klaus Kultti , Tuomas Takalo * a
Department of Economics and Management Science, Helsinki School of Economics and Business Administration, Helsinki, Finland b Department of Economics, University of Helsinki, P.O. Box 54, 00014 Helsinki, Finland Received 31 October 1997; accepted 25 June 1998
Abstract We show that the spillover of R&D can be endogenised in a sense that even without spillovers firms have an incentive to exchange the R&D information after the investment costs are sunk. 1998 Elsevier Science S.A. All rights reserved. Keywords: Spillovers; R&D investments JEL classification: L13; O32
1. Introduction In the mushrooming literature following d’Aspremont and Jacquemin (1988) spillovers are usually modelled as an automatic result of firms’ investment in R&D. In the standard version the firms engage in Cournot-competition with an additional feature that before production the firms may invest in cost reducing R&D activities. These activities are characterised by spillovers; one firm’s investment reduces the other firms’ costs, too. The spillover is not perfect but there is a spillover parameter which is between zero and unity. The purpose of this note is to offer an explanation for the spillover parameter. We show that the model of d’Aspremont and Jacquemin (1988) is outcomewise equivalent with the following model. The firms make decisions in three stages; in the first stage they invest in cost reducing R&D like in d’Aspremont and Jacquemin (1988). There are no spillovers but the firms reap the full value of their investment. In the second stage the firms play a game where they may exchange their R&D results if both agree. We assume that the firms can make full use only of the R&D that they have conducted themselves. The value of other firms’ R&D results is captured by a parameter that is between zero and unity. When it is the same as the spillover parameter in the original model these two models yield the same outcome. The firms always have an incentive to exchange the research information after the R&D investments are made, which may to some extent explain patent pooling and ex-post cross-licensing agreements. Next we present the original model, and then we show that the three stage model yields the same results. *Corresponding author. Tel.: 1358-9-1918908; Fax: 1358-9-1918877; E-mail: [email protected]. 0165-1765 / 98 / $ – see front matter 1998 Elsevier Science S.A. All rights reserved. PII: S0165-1765( 98 )00152-9
K. Kultti, T. Takalo / Economics Letters 61 (1998) 121 – 123
122
2. The result
2.1. The model of d’ Aspremont and Jacquemin There are two identical firms i and j, and the inverse market demand function p 5 a 2 Q where Q 5 qi 1 q j . In the first stage the firms invest x i , x j in R&D, and in the second stage they choose production qi , q j . Unit costs of firm i’s production are c i 5 A 2 x i 2 b x j ; the degree of spillover is captured by b [ (0, 1), i.e. investment into R&D by firm j decreases also the costs of firm i. The R&D costs are assumed quadratic, and the profits of firm i can be expressed as x 2i ] pi 5 (a 2 Q)qi 2 (A 2 x i 2 b x j )qi 2 g 2
(1)
where g .0 is an efficiency parameter. One solves for optimal quantity and R&D investment in a standard manner assuming that firms make their choices non-cooperatively. In equilibrium these are 3g (a 2 A) q *i 5 ]]]]]]] 9g 2 2(2 2 b )(1 1 b )
(2)
2(2 2 b )(a 2 A) x i* 5 ]]]]]]] 9g 2 2(2 2 b )(1 1 b )
(3)
Inserting Eq. (2) and Eq. (3) into Eq. (1) one gets the profits a 2 A 1 2x * 2 x * x* p 5F]]]]]]G 2 g ] 3 2 2
2
i
j
i
i
(4)
2.2. The model with exchange of information We consider a three-stage game. In the first stage the firms invest non-cooperatively in R&D and the second stage involves the decision to exchange information. In the last stage the firms decide about quantities in a Cournot-manner. The model is the same as in d’Aspremont and Jacquemin (1988) except for two features; we assume that there are no spillovers, and there is the second stage game in which the firms decide whether to exchange the research information. In the second stage the firms play a simultaneous move game in which they can choose ‘‘yes’’ or ‘‘no’’. If both choose ‘‘yes’’ they exchange R&D information. In all other cases they do not exchange the information. If firm i gets firm j’s information its costs are reduced by bi x j , and similarly for firm j. Otherwise firm j’s R&D expenditures do not affect firm i’s costs. If both firms say ‘‘yes’’ in equilibrium their profits are as in d’Aspremont and Jacquemin (1988) since the spillover parameter is assumed to be the same, and the firms foresee the exchange of information that they naturally incorporate in their investment decision. Our equilibrium concept is a Nash-equilibrium in undominated strategies. Proposition. The firms always exchange information if the degree of spillover is symmetric, i.e. bi 5 bj 5 b.
K. Kultti, T. Takalo / Economics Letters 61 (1998) 121 – 123
123
Proof: Consider the case with possibly different betas. The unit costs in case of information exchange are c i 5 A2x i 2 bi x j and c j 5 A2x j 2 bj x i . The profits of firm i as a result of this exchange are given by
F
a 2 A 1 x i (2 2 bj ) 1 x j (2bi 2 1) pi 5 ]]]]]]]]]] 3
G 2 g ]x2 2
2 i
(5)
Without information exchange the profits of firm i are a 2 A 1 2x 2 x x p 5F]]]]]G 2 g ] 3 2 i
i
j
2
2 i
(6)
At the second stage R&D costs are already sunk, and comparing Eq. (6) to Eq. (5) we see that, ‘‘yes’’ is a weakly dominant strategy, if and only if x i bj x j bi $ ]] 2
(7)
But this holds trivially since x i 5x j when bi 5 bj 5 b. QED. It is obvious from Eq. (7) that the degree of spillover need not be symmetric; it is a dominant strategy for either firm to choose ‘yes’ as long as it receives in return at least half of the amount of spillover it gives up. The result that firms have an incentive to exchange information after the R&D costs are sunk holds also in other models of R&D like Kamien et al. (1992).
Acknowledgements ¨ Tuomas Saarenheimo, Rune Stenbacka, Mihkel Tombak, and the FPPE We thank J–P Niinimaki, Microeconomics and Industrial Organization seminar participants for helpful comments. Financial support by Yrjo¨ Jahnsson Foundation is gratefully acknowledged. Takalo thanks the Department of Economics at the University of Warwick that he was visiting while preparing this note for hospitality.
References d’Aspremont, C., Jacquemin, A., 1988. Cooperative and noncooperative R&D in duopoly with spillovers. American Economic Review 78, 1133–1137. Kamien, M., Muller, E., Zang, I., 1992. Research joint ventures and R&D cartels. American Economic Review 82, 1293–1306.
R&D spillovers and information exchange a b, Klaus Kultti , Tuomas Takalo * a
Department of Economics and Management Science, Helsinki School of Economics and Business Administration, Helsinki, Finland b Department of Economics, University of Helsinki, P.O. Box 54, 00014 Helsinki, Finland Received 31 October 1997; accepted 25 June 1998
Abstract We show that the spillover of R&D can be endogenised in a sense that even without spillovers firms have an incentive to exchange the R&D information after the investment costs are sunk. 1998 Elsevier Science S.A. All rights reserved. Keywords: Spillovers; R&D investments JEL classification: L13; O32
1. Introduction In the mushrooming literature following d’Aspremont and Jacquemin (1988) spillovers are usually modelled as an automatic result of firms’ investment in R&D. In the standard version the firms engage in Cournot-competition with an additional feature that before production the firms may invest in cost reducing R&D activities. These activities are characterised by spillovers; one firm’s investment reduces the other firms’ costs, too. The spillover is not perfect but there is a spillover parameter which is between zero and unity. The purpose of this note is to offer an explanation for the spillover parameter. We show that the model of d’Aspremont and Jacquemin (1988) is outcomewise equivalent with the following model. The firms make decisions in three stages; in the first stage they invest in cost reducing R&D like in d’Aspremont and Jacquemin (1988). There are no spillovers but the firms reap the full value of their investment. In the second stage the firms play a game where they may exchange their R&D results if both agree. We assume that the firms can make full use only of the R&D that they have conducted themselves. The value of other firms’ R&D results is captured by a parameter that is between zero and unity. When it is the same as the spillover parameter in the original model these two models yield the same outcome. The firms always have an incentive to exchange the research information after the R&D investments are made, which may to some extent explain patent pooling and ex-post cross-licensing agreements. Next we present the original model, and then we show that the three stage model yields the same results. *Corresponding author. Tel.: 1358-9-1918908; Fax: 1358-9-1918877; E-mail: [email protected]. 0165-1765 / 98 / $ – see front matter 1998 Elsevier Science S.A. All rights reserved. PII: S0165-1765( 98 )00152-9
K. Kultti, T. Takalo / Economics Letters 61 (1998) 121 – 123
122
2. The result
2.1. The model of d’ Aspremont and Jacquemin There are two identical firms i and j, and the inverse market demand function p 5 a 2 Q where Q 5 qi 1 q j . In the first stage the firms invest x i , x j in R&D, and in the second stage they choose production qi , q j . Unit costs of firm i’s production are c i 5 A 2 x i 2 b x j ; the degree of spillover is captured by b [ (0, 1), i.e. investment into R&D by firm j decreases also the costs of firm i. The R&D costs are assumed quadratic, and the profits of firm i can be expressed as x 2i ] pi 5 (a 2 Q)qi 2 (A 2 x i 2 b x j )qi 2 g 2
(1)
where g .0 is an efficiency parameter. One solves for optimal quantity and R&D investment in a standard manner assuming that firms make their choices non-cooperatively. In equilibrium these are 3g (a 2 A) q *i 5 ]]]]]]] 9g 2 2(2 2 b )(1 1 b )
(2)
2(2 2 b )(a 2 A) x i* 5 ]]]]]]] 9g 2 2(2 2 b )(1 1 b )
(3)
Inserting Eq. (2) and Eq. (3) into Eq. (1) one gets the profits a 2 A 1 2x * 2 x * x* p 5F]]]]]]G 2 g ] 3 2 2
2
i
j
i
i
(4)
2.2. The model with exchange of information We consider a three-stage game. In the first stage the firms invest non-cooperatively in R&D and the second stage involves the decision to exchange information. In the last stage the firms decide about quantities in a Cournot-manner. The model is the same as in d’Aspremont and Jacquemin (1988) except for two features; we assume that there are no spillovers, and there is the second stage game in which the firms decide whether to exchange the research information. In the second stage the firms play a simultaneous move game in which they can choose ‘‘yes’’ or ‘‘no’’. If both choose ‘‘yes’’ they exchange R&D information. In all other cases they do not exchange the information. If firm i gets firm j’s information its costs are reduced by bi x j , and similarly for firm j. Otherwise firm j’s R&D expenditures do not affect firm i’s costs. If both firms say ‘‘yes’’ in equilibrium their profits are as in d’Aspremont and Jacquemin (1988) since the spillover parameter is assumed to be the same, and the firms foresee the exchange of information that they naturally incorporate in their investment decision. Our equilibrium concept is a Nash-equilibrium in undominated strategies. Proposition. The firms always exchange information if the degree of spillover is symmetric, i.e. bi 5 bj 5 b.
K. Kultti, T. Takalo / Economics Letters 61 (1998) 121 – 123
123
Proof: Consider the case with possibly different betas. The unit costs in case of information exchange are c i 5 A2x i 2 bi x j and c j 5 A2x j 2 bj x i . The profits of firm i as a result of this exchange are given by
F
a 2 A 1 x i (2 2 bj ) 1 x j (2bi 2 1) pi 5 ]]]]]]]]]] 3
G 2 g ]x2 2
2 i
(5)
Without information exchange the profits of firm i are a 2 A 1 2x 2 x x p 5F]]]]]G 2 g ] 3 2 i
i
j
2
2 i
(6)
At the second stage R&D costs are already sunk, and comparing Eq. (6) to Eq. (5) we see that, ‘‘yes’’ is a weakly dominant strategy, if and only if x i bj x j bi $ ]] 2
(7)
But this holds trivially since x i 5x j when bi 5 bj 5 b. QED. It is obvious from Eq. (7) that the degree of spillover need not be symmetric; it is a dominant strategy for either firm to choose ‘yes’ as long as it receives in return at least half of the amount of spillover it gives up. The result that firms have an incentive to exchange information after the R&D costs are sunk holds also in other models of R&D like Kamien et al. (1992).
Acknowledgements ¨ Tuomas Saarenheimo, Rune Stenbacka, Mihkel Tombak, and the FPPE We thank J–P Niinimaki, Microeconomics and Industrial Organization seminar participants for helpful comments. Financial support by Yrjo¨ Jahnsson Foundation is gratefully acknowledged. Takalo thanks the Department of Economics at the University of Warwick that he was visiting while preparing this note for hospitality.
References d’Aspremont, C., Jacquemin, A., 1988. Cooperative and noncooperative R&D in duopoly with spillovers. American Economic Review 78, 1133–1137. Kamien, M., Muller, E., Zang, I., 1992. Research joint ventures and R&D cartels. American Economic Review 82, 1293–1306.