Nash Equilibrium with Markup-pricing Oligopolists

NASH EQUILIBRIUM WITH MARKUP-PRICING OLIGOPOLISTS. Simon Grant Economics Program RSSS, ANU Canberra 0200, Australia John Quiggin Centre for Economic Policy Research RSSS, ANU Canberra 0200, Australia Grant, S. and Quiggin, J. (1994), ‘Nash equilibrium with markup-pricing oligopolists’, Economics Letters 45, 245—51. If business managers formulate strategies in terms of mark-ups, then it is natural to think they will think of their rivals’ actions in these terms. For a market characterized by constant elasticity of demand and supply, the mark-up equilibrium is derived and compared with the traditional monopoly, Cournot and perfectly competitive equilibria. We also compute the ‘revenue as strategy’ equilibria. JEL Classi cation: L10, L13 Economist: As a pro t-maximizing manager, you set price equal to marginal cost. Manager: I have no idea what marginal cost is. I just set my price by adding a markup to my average costs. I don’t worry about maximizing anything. Economist: But what happens if demand for your product weakens ? Manager: I shade my markup down. Economist (scenting victory): And what if demand goes up ? Manager (checking that no consumer advocates are within earshot): I boost my margins a bit. Economist: Aha ! So you do maximize pro ts, after all ! This scene, or something like it, has been played out many times since Hall and Hitch rst interviewed businessmen and found that most of them claimed to follow some form of mark-up pricing. This discovery ignited a erce methodological debate. Friedman (1953) invoked the metaphor of the expert billiards player, implicitly solving complex di erential equations, to argue that businessmen could behave as pro tmaximizers even if they thought in terms of rule-of-thumb markups. 1