Equilibrium prices in the Bertrand and Cournot oligopolies
type: Item
instance of: scholarly article
title: Equilibrium prices in the Bertrand and Cournot oligopolies
zbMATH Open document ID: 0631.90009
DOI: 10.1016/0022-0531(87)90106-2
author: K. Okuguchi
published in: Journal of Economic Theory
publication date: 1987-01-01T00:00:00Z
review text: 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 \textit{L. Cheng}, ``Comparing Bertrand and Cournot equilibria: A geometric approach'' [Rand J. Econ. 16, 146-152 (1985)], \textit{N. J. Hathaway} and \textit{J. A. Rickard}, ``Equilibria of price-setting and quantity-setting duopolies'' [Econ. Letters 3, 133-137 (1979)], \textit{N. Singh} and \textit{X. Vives}, ``Price and quantity competition in a differential duopoly'' [Rand J. Econ. 15, 546-554 (1984)], and \textit{X. Vives} [J. Econ. Theory 36, 166-175 (1985; Zbl 0596.90017)].
Mathematics Subject Classification ID: 91B24
Mathematics Subject Classification ID: 91B50
Mathematics Subject Classification ID: 91A40
zbMATH DE Number: 4027134
zbMATH Keywords: Cournot oligopoly
zbMATH Keywords: Bertrand oligopoly
zbMATH Keywords: equilibrium prices
zbMATH Keywords: product differentiation
reviewed by: Dan Kovenock
MaRDI profile type: Publication
full work available at URL: 0022-0531(87)90106-2
OpenAlex ID: W1986824963
cites work: Spectral localization of operators in Banach spaces
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cites work: Expectations and stability in oligopoly models
cites work: The stability of price adjusting oligopoly with conjectural variations
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cites work: On the efficiency of Bertrand and Cournot equilibria with product differentiation
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description: scientific article; zbMATH DE number 4027134