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Equilibrium prices in the Bertrand and Cournot oligopolies. (English) Zbl 0631.90009
This paper compares the equilibrium prices of Bertrand and Cournot oligopolies with product differentiation. Conditions are derived enabling the comparison of Bertrand and Cournot equilibrium prices, under linear or nonlinear cost and demand functions, on the basis of a theorem on non- negative solvability of a linear system of equations. The second order partial derivatives of the profit functions for the Bertrand oligopoly play a key role in deriving the results. Closely related work includes L. Cheng, “Comparing Bertrand and Cournot equilibria: A geometric approach” [Rand J. Econ. 16, 146-152 (1985)], N. J. Hathaway and J. A. Rickard, “Equilibria of price-setting and quantity-setting duopolies” [Econ. Letters 3, 133-137 (1979)], N. Singh and X. Vives, “Price and quantity competition in a differential duopoly” [Rand J. Econ. 15, 546-554 (1984)], and X. Vives [J. Econ. Theory 36, 166-175 (1985; Zbl 0596.90017)].
Reviewer: D.Kovenock

MSC:
91B24 Microeconomic theory (price theory and economic markets)
91B50 General equilibrium theory
91A40 Other game-theoretic models
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