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Existence and efficiency of equilibrium in economics with increasing returns to scale: an exposition

  • Antonio Villar

    (Universidad de Alicante and IVIE)

The purpose of this paper is to offer an exposition of the results on the existence and optimality of equilibria when production sets are not assumed to be convex, in a general equilibrium framework. We aim at providing a formal and systematic account of the main results available, rather than survey the literature. Besides presenting an abstract model, where firms' behavior is described by general pricing rules, we analyze the family of Loss-free Pricing Rules (focusing on Profit Maximization, both constrained and unconstrained, and Average Cost Pricing), and the Marginal Pricing Rule and other regulation policies. Then, we discuss the efficiency problem, referring to both the first and second welfare theorems.

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Article provided by Fundación SEPI in its journal Investigaciones Economicas.

Volume (Year): 18 (1994)
Issue (Month): 2 (May)
Pages: 205-243

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Handle: RePEc:iec:inveco:v:18:y:1994:i:2:p:205-243
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  1. Dehez, Pierre & Dreze, Jacques, 1988. "Competitive equilibria with quantity-taking producers and increasing returns to scale," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 209-230, April.
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  4. Jouini, Elyes, 1988. "A remark on Clarke's normal cone and the marginal cost pricing rule," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 309-315, April.
  5. Dierker,Egbert & Neuefeind,Wilhelm, 1987. "Quantity guided price setting," Discussion Paper Serie A 129, University of Bonn, Germany.
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  7. Bonnisseau, Jean-Marc & Cornet, Bernard, 1988. "Existence of equilibria when firms follow bounded losses pricing rules," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 119-147, April.
  8. Brown, Donald J. & Heal, Geoffrey M. & Ali Khan, M. & Vohra, Rajiv, 1986. "On a general existence theorem for marginal cost pricing equilibria," Journal of Economic Theory, Elsevier, vol. 38(2), pages 371-379, April.
  9. Leonard J. Mirman & Yair Tauman & Israel Zang, 1983. "Ramsey Prices, Average Cost Prices and Price Sustainability," Discussion Papers 561, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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  11. Dehez, Pierre & Dreze, Jacques, 1988. "Distributive production sets and equilibria with increasing returns," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 231-248, April.
  12. Edlin, Aaron S & Epelbaum, Mario, 1993. "Two-Part Marginal Cost Pricing Equilibria with n Firms: Sufficient Conditions for Existence and Optimality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(4), pages 903-22, November.
  13. Donald J. Brown & Geoffrey M. Heal, 1978. "Equity, Efficiency and Increasing Returns," Cowles Foundation Discussion Papers 504, Cowles Foundation for Research in Economics, Yale University.
  14. Mas-Colell, Andreu & Silvestre, Joaquim, 1989. "Cost share equilibria: A Lindahlian approach," Journal of Economic Theory, Elsevier, vol. 47(2), pages 239-256, April.
  15. Khan, M Ali & Vohra, Rajiv, 1987. "An Extension of the Second Welfare Theorem to Economies with Nonconvexities and Public Goods," The Quarterly Journal of Economics, MIT Press, vol. 102(2), pages 223-41, May.
  16. Bonnisseau, Jean-Marc & Cornet, Bernard, 1990. "Existence of Marginal Cost Pricing Equilibria: The Nonsmooth Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 685-708, August.
  17. Sharkey, William W., 1989. "Game theoretic modeling of increasing returns to scale," Games and Economic Behavior, Elsevier, vol. 1(4), pages 370-431, December.
  18. Samet, Dov & Tauman, Yair, 1982. "The Determination of Marginal Cost Prices under a Set of Axioms," Econometrica, Econometric Society, vol. 50(4), pages 895-909, July.
  19. Villar, Antonio, 1994. "Equilibrium with Nonconvex Technologies," Economic Theory, Springer, vol. 4(4), pages 629-38, May.
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  21. Jouini, Elyès, 1988. "A remark on Clarke's normal cone and the marginal cost pricing rule," Economics Papers from University Paris Dauphine 123456789/5649, Paris Dauphine University.
  22. Antonio Villar Notario, 1994. "Existence and optimality of social equilibrium with many convex and nonconvex firms," Working Papers. Serie AD 1994-12, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  23. Guesnerie, Roger, 1975. "Pareto Optimality in Non-Convex Economies," Econometrica, Econometric Society, vol. 43(1), pages 1-29, January.
  24. Bonnisseau, J.-M. & Cornet, B., 1986. "Valuation equilibrium and Pareto optimum in nonconvex economies," CORE Discussion Papers 1986036, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  25. Brown, Donald J., 1991. "Equilibrium analysis with non-convex technologies," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 36, pages 1963-1995 Elsevier.
  26. Herrero, Carmen & Villar, Antonio, 1988. "General Equilibrium in a Non-linear Leontief Framework," The Manchester School of Economic & Social Studies, University of Manchester, vol. 56(2), pages 159-66, June.
  27. BONNISSEAU, Jean-Marc, . "On two existence results of equilibria in economies with increasing returns," CORE Discussion Papers RP -815, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  28. Vohra, Rajiv, 1988. "Optimal regulation under fixed rules for income distribution," Journal of Economic Theory, Elsevier, vol. 45(1), pages 65-84, June.
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  30. Roberts, John & Sonnenschein, Hugo, 1977. "On the Foundations of the Theory of Monopolistic Competition," Econometrica, Econometric Society, vol. 45(1), pages 101-13, January.
  31. Silvestre, Joaquim, 1977. "General Monopolistic Equilibrium under Non-Convexities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 425-34, June.
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  35. Vohra, Rajiv, 1992. "Marginal Cost Pricing under Bounded Marginal Returns," Econometrica, Econometric Society, vol. 60(4), pages 859-76, July.
  36. MacKinnon, James G., 1979. "Computing equilibria with increasing returns," European Economic Review, Elsevier, vol. 12(1), pages 1-16, February.
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  41. repec:cup:cbooks:9780521424585 is not listed on IDEAS
  42. repec:cup:cbooks:9780521335614 is not listed on IDEAS
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