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The number and type of long-term equilibria. (English) Zbl 1010.91513

Summary: We consider a balanced-growth model with finitely many processes, a uniform rate of profits, and a given composition of final demand. Two types of equilibria are distinguished, “black” and “white”: the color of an equilibrium is defined by the relative sign of two determinants associated with the operated methods, and can be interpreted as a local property of a cross-dual dynamic process. Under standard economic assumptions, and flukes apart, the number of white equilibria exceeds that of black equilibria by one. In particular the total number of long-term equilibria is odd.

MSC:

91B50 General equilibrium theory
91B62 Economic growth models
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[1] Bellino, E. (1997): ?Full-cost Pricing in the Classical Competitive Process: a Model of Convergence to Long-run Equilibrium.?Journal of Economics/Zeitschrift für Nationalökonomie 65: 41-54. · Zbl 0871.90018 · doi:10.1007/BF01239058
[2] Bidard, C. (1984): ?Choix Techniques en Production Jointe.? InLa Production Jointe: Nouveaux Débats, edited by C. Bidard. Paris: Economica.
[3] ? (1990): ?An Algorithmic Theory of the Choice of Techniques.?Economitrica 58: 839-859. · Zbl 0729.90009 · doi:10.2307/2938352
[4] Bidard, C. (1998): ?Le Lemme de Sperner nu.?RAIRO Recherche Operationnelle/Operations Research (forthcoming).
[5] Cottle, R. W., Pang, J.-S., and Stone, R. E. (1992):The Linear Complementarity Problem. Boston: Academic Press.
[6] Dantzig, G. B., and Manne, A. S. (1974): ?A Complementarity Algorithm for an Optimal Capital Path with Invariant Proportions.?Jounal of Economic Theory 9: 312-323. · doi:10.1016/0022-0531(74)90055-6
[7] Debreu, G. (1970): ?Economies with a Finite Set of Equilibria.?Econometrica 38: 387-392. · Zbl 0253.90009 · doi:10.2307/1909545
[8] Dierker, E. (1972): ?Two Remarks on the Number of Equilibria of an Economy.?Econometrica 40: 951-953. · Zbl 0259.90005 · doi:10.2307/1912091
[9] Eaves, B. C. (1971): ?The Linear Complementarity Problem.?Management Science 17: 612-634. · Zbl 0228.15004 · doi:10.1287/mnsc.17.9.612
[10] Erreygers, G. (1990): ?Terre, Rente et Choix de Techniques: Une Étude sur la Théorie Néo-ricardienne.? Ph.D. thesis, University of Paris X, Nanterre, France.
[11] ? (1995): ?On the Uniqueness of Square Cost-minimizing Techniques.?The Manchester School 63: 145-166. · doi:10.1111/j.1467-9957.1995.tb00274.x
[12] Kehoe, T. J. (1980): ?An Index Theorem for General Equilibrium Models with Production.?Econometrica 48: 1211-1232. · Zbl 0436.90017 · doi:10.2307/1912179
[13] Kurz, H. D., and Salvadori, N. (1995):Theory of Production: a Long-period Analysis. Cambridge: Cambridge University Press.
[14] Lippi, M. (1979):I Prezzi di Produzione. Bologna: il Mulino.
[15] Mas-Colell, A. (1991): ?On the Uniqueness of Equilibrium once again.? InEquilibrium Theory and Applications: Proceedings of the Sixth International Symposium in Economic Theory and Econometrics, edited by W. A. Barnett, B. Cornet, C. D’Aspremont, J. Gabszewicz, and A. Mas-Colell. Cambridge: Cambridge University Press. · Zbl 0755.90007
[16] Mas-Colell, A., Whinston, M. D., and Green, J. R. (1995):Microeconomic Theory. Oxford: Oxford University Press.
[17] Morishima, M. (1969): ?Theory of Economic Growth. Oxford: Clarendon Press. · Zbl 0224.90015
[18] Neumann, J. von (1937): ?Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes.?Ergebnisse eines mathematischen Kolloquiums 8: 73-83. · Zbl 0017.03901
[19] Quint, T., and Shubik, M. (1997): ?A Theorem on the Number of Nash Equilibria in a Bimatrix Game.?International Journal of Game Theory 26: 353-359. · Zbl 0880.90141 · doi:10.1007/BF01263276
[20] Salvadori, N. (1982): ?Existence of Cost-minimizing Systems within the Sraffa Framework.?Zeitschrift für Nationalökonomie/Journal of Economics 42: 281-298. · Zbl 0501.90021 · doi:10.1007/BF01282911
[21] ? (1986): ?Land and Choice of Techniques within the Sraffa Framework.?Australian Economic Papers 25: 94-105. · doi:10.1111/j.1467-8454.1986.tb00836.x
[22] Schefold, B. (1978): ?On Counting Equations.?Zeitschrift für Nationalökonomie/Journal of Economics 38: 253-285. · Zbl 0393.90010 · doi:10.1007/BF01289034
[23] ? (1988): ?The Dominant Technique in Joint Production Models.?Cambridge Journal of Economics 12: 97-123.
[24] ? (1989):Mr Sraffa on Joint Production and Other Essays. London: Unwin Hyman.
[25] Sraffa, P. (1960):Production of Commodities by Means of Commodities. Cambridge: Cambridge University Press.
[26] Steedman, I. (1976): ?Positive Profits with Negative Surplus Value: a Reply to Wolfstetter.?Economic Journal 86: 873-876. · doi:10.2307/2231461
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