The Effects of Process R&D in an Asymmetric Duopoly under Cournot and Supply Function Competitions

Saglam, Ismail (2018): The Effects of Process R&D in an Asymmetric Duopoly under Cournot and Supply Function Competitions.

Abstract

In this paper we attempt to explore the welfare effects of (process) R&D in an asymmetric duopoly with a homogeneous product under Cournot and supply function competitions. To this aim, we consider a two-stage perfect-information game where the duopolists compete in stage one in R&D investments and in stage two either in quantities or in supply functions. Calculating the (subgame-perfect Nash) equilibrium of this game numerically for a wide range of initial cost parameters and comparing it to the equilibrium with no R&D, we show that R&D has a positive effect on the welfares of consumers and the society as a whole. While its effect on the profits of the duopolists is also positive under the Cournot competition, it becomes negative under the supply function competition. This latter negative effect is caused by the duopolists' more aggressively investing in R&D under the supply function competition, increasing the industry output, and consequently decreasing the product price, to a harmful level for themselves. Moreover, we show that R&D always widens up the efficiency gap between the duopolists under the supply function competition, while narrowing it down under the Cournot competition.

• Item Type: MPRA Paper
• Language: English
• Keywords: Duopoly; Cournot competition; supply function competition; process R&D
• Subjects: D - Microeconomics > D4 - Market Structure, Pricing, and Design > D43 - Oligopoly and Other Forms of Market Imperfection; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L13 - Oligopoly and Other Imperfect Markets

References

Bertrand J (1883) Theorie mathematique de la richesse sociale. Journal des Savants 67, 499-508.

Cournot A (1838) Recherches sur les Principes Mathematiques de la Theorie des Richesses. Paris: Hachette.

D'Aspremont C and Jacquemin A (1988) Cooperative and noncooperative R&D in duopoly with spillovers. The American Economic Review 78:5, 1133-1137.

Green R (1999) The electricity contract market in England and Wales. 47:1, 107-124.

Hinloopen J and Vandekerckhove J (2009) Dynamic efficiency of Cournot and Bertrand competition: input versus output spillovers. Journal of Economics 98:2, 119-136.

Klemperer PD and Meyer MA (1989) Supply function equilibria in oligopoly under uncertainty. Econometrica 57:6, 1243-1277.

Nash JF (1950) Equilibrium points in n-person games. Proceedings of the National Academy of Sciences 36:1, 48-49.

Qiu LD (1997) On the dynamic efficiency of Bertrand and Cournot equilibria. Journal of Economic Theory 75:1, 213-229.

Saglam I (2018a) The desirability of the supply function competition under demand uncertainty. Economics Bulletin 38:1, 541-549.

Saglam I (2018b) Ranking supply function and Cournot equilibria in a differentiated product duopoly with demand uncertainty. Available at SSRN: https://ssrn.com/abstract=3149142 or http://dx.doi.org/ 10.2139/ssrn.3149142.

Selten R (1965) Spieltheoretische Behandlung eines Oligopolmodells mit Nachfragetragheit. Zeitschrift far die gesamte Staatswissenschaft 121, 301-324; 667-689.

Singh N and Vives X (1984) Price and quantity competition in a differentiated duopoly. Rand Journal of Economics 15:4, 546-554.

Symeonidis G (2003) Comparing Cournot and Bertrand equilibria in a differentiated duopoly with product R&D. International Journal of Industrial Organization 21:1, 39-55.

Vives X (1985) On the efficiency of Bertrand and Cournot equilibria with product differentiation. Journal of Economic Theory 36:1, 166-175.