The Equivalence of Price and Quantity Competition with Incentive Scheme Commitment.pdf

The Equivalence of Price and Quantity Competition with Incentive Scheme Commitment Nolan H. Miller¤ Amit Pazgaly September 7, 1998 Abstract We consider a two stage di¤erentiated products duopoly model (with linear demand and constant marginal cost). In the …rst stage pro…t maxi- mizing owners choose incentive schemes in order to induce their managers to exhibit a certain type of behavior. In the second stage the managers compete either in prices or in quantities. In contrast to Singh and Vives (1984), we show that if the owners have su￠cient power to manipulate the incentives of their managers, the equilibrium outcome is the same regard- less of whether the …rms compete in prices or in quantities. Basing the manager’s objective function on a convex combination of own pro…t and the di¤erence between own pro…t and the rival …rm’s pro…t is su￠cient for the equivalence result to hold. ¤Managerial Economics and Decision Sciences, J.L. Kellogg Graduate School of Management, Northwestern University. yDepartment of Marketing, John M. Olin School of Business, Washington University. The authors thank Bill Sandholm, Daniel Spulber, and Jeroen Swinkels for helpful comments. All errors are our own. Send comments to: pazgal@wuolin.wustl.edu 1. Introduction Singh and Vives (1984) prove the somewhat surprising result that in a di¤eren- tiated products duopoly with constant marginal costs, all else being equal, the equilibrium under price competition di¤ers from the equilibrium under quantity competition. In particular, they show that in Cournot competition1, quantities are lower and prices are higher than in Bertrand competition, regardless of whether the goods are substitutes or complements. This di¤erence stems from the fact that the perceived elasticity of demand when a …rm takes it’s rival’s price as con- stant is larger than the perceived elasticity of demand when a …rm takes it’s rival’s quantity as constant. In other words, the optimal reaction of the manager di¤ers dependin