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On the efficiency of Bertrand and Cournot equilibria with product differentiation. (English) Zbl 0596.90017
Summary: In a differentiated products setting with n varieties it is shown, under certain regularity conditions, that if the demand structure is symmetric and Bertrand and Cournot equilibria are unique then prices and profits are larger and quantities smaller in Cournot than in Bertrand competition and, as n grows, both equilibria converge to the efficient outcome at a rate of at least 1/n. If Bertrand reaction functions slope upwards and are continuous then, even with an asymmetric demand structure, given any Cournot equilibrium price vector one can find a Bertrand equilibrium with lower prices. In particular, if the Bertrand equilibrium is unique then it has lower prices than any Cournot equilibrium.

91B50 General equilibrium theory
Full Text: DOI
[1] Bertrand, J, Book reviews of “théorie mathématique de la richesse sociale“ and of “researches sur LES principes mathématiques de la théorie des richesses,”, J. savants, 499-508, (1983)
[2] Chamberlin, E.H, The theory of monopolistic competition, (1956), Harvard Univ. Press Cambridge, Massachusetts
[3] Cheng, L, Bertrand equilibrium is more competitive than Cournot equilibrium: the case of differentiated products, (1984), University of Florida, mimeo
[4] Cournot, A, Researches into the mathematical principles of the theory of wealth, (1960), Kelley New York, English edition of Cournot (1983), translated by N. T. Bacon · JFM 28.0211.07
[5] Deneckere, R; Davidson, C, Coalition formation in noncooperative oligopoly models, Michigan state university working paper series no. 8302, (1983)
[6] Dixit, A; Stiglitz, J, Monopolistic competition and optimum product diversity, Amer. econom. rev., 67, 297-308, (1977)
[7] Friedman, J.W, Oligopoly and the theory of games, (1977), North-Holland Amsterdam · Zbl 0385.90001
[8] Hart, O, Monopolistic competition in the spirit of chamberlin: (1) A general model; (2) special results, () · Zbl 0586.90012
[9] Hathaway, N.J; Rickard, J.A, Equilibria of price-setting and quantity setting duopolies, Econom. lett., 3, 133-137, (1979)
[10] McKenzie, L.W, Matrices with dominant diagonals and economic theory, 1959, ()
[11] Novshek, W, Cournot equilibrium with free entry, Restuds, 47, 473-486, (1980) · Zbl 0433.90007
[12] \scK. Okuguchi, Price-adjusting and quantity adjusting oligopoly equilibria, undated manuscript. · Zbl 0379.90028
[13] Roberts, J; Sonnenschein, H, On the foundations of the theory of monopolistic competition, Econometrica, 45, 101-113, (1977) · Zbl 0352.90019
[14] Ruffin, R, Cournot oligopoly and competitive behavior, Restuds, 38, 493-502, (1971) · Zbl 0246.90006
[15] Shapley, L.S, A duopoly model with price competition, Econometrica, 25, 354-355, (1957)
[16] Shubik, M, Market structure and behavior, (1971), Harvard Univ. Press Cambridge, Massachusetts, (with R. Levitan) · Zbl 0228.90057
[17] Singh, N; Vives, X, Price and quantity competition in a differentiated duopoly, The rand journal of economics, 15, 4, 546-554, (1984)
[18] Spence, M, Product selection, fixed costs and monopolistic competition, Rev. econom. stud., 43, 217-253, (1976) · Zbl 0362.90013
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