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Existence and efficiency of equilibrium in economies with increasing returns to scale: An exposition

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  • Antonio Villar Notario

    (Instituto Valenciano de Investigaciones Económicas)

Abstract

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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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-1994-07.pdf
File Function: Fisrt version / Primera version, 1994
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Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 1994-07.

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Length: 75 pages
Date of creation: May 1994
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:1994-07
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Keywords: Increasing returns; equilibrium; optimality;

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  1. Dierker, E. & Neuefeind, W., 1987. "Quantity guided price setting," CORE Discussion Papers 1987043, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  6. John Roberts & Hugo Sonnenschein, 1976. "On the Foundations of the Theory of Monopolistic Competition," Discussion Papers 169, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. 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.
  8. 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.
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  10. Cornet, B., 1986. "The second welfare theorem in nonconvex economies," CORE Discussion Papers 1986030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  13. Mirman, Leonard J. & Tauman, Yair & Zang, Israel, 1986. "Ramsey prices, average cost prices and price sustainability," International Journal of Industrial Organization, Elsevier, vol. 4(2), pages 123-140, June.
  14. Vohra, Rajiv, 1992. "Marginal Cost Pricing under Bounded Marginal Returns," Econometrica, Econometric Society, vol. 60(4), pages 859-76, July.
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  16. Greenberg, Joseph & Shitovitz, Benyamin, 1984. "Aumann-Shapley prices as a scarf social equilibrium," Journal of Economic Theory, Elsevier, vol. 34(2), pages 380-382, December.
  17. 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).
  18. Mas-Colell, Andreu & Silvestre, Joaquim, 1989. "Cost share equilibria: A Lindahlian approach," Journal of Economic Theory, Elsevier, vol. 47(2), pages 239-256, April.
  19. Quinzii, Martine, 1982. "An existence theorem for the core of a productive economy with increasing returns," Journal of Economic Theory, Elsevier, vol. 28(1), pages 32-50, October.
  20. Vohra, Rajiv, 1988. "Optimal regulation under fixed rules for income distribution," Journal of Economic Theory, Elsevier, vol. 45(1), pages 65-84, June.
  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. 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.
  23. Donald J. Brown & Geoffrey M. Heal, 1983. "The Optimality of Regulated Pricing: A General Equilibrium Analysis," Cowles Foundation Discussion Papers 684, Cowles Foundation for Research in Economics, Yale University.
  24. 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.
  25. Guesnerie, Roger, 1975. "Pareto Optimality in Non-Convex Economies," Econometrica, Econometric Society, vol. 43(1), pages 1-29, January.
  26. Benassy, Jean-Pascal, 1991. "Monopolistic competition," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 37, pages 1997-2045 Elsevier.
  27. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  28. Villar, Antonio, 1994. "Equilibrium with Nonconvex Technologies," Economic Theory, Springer, vol. 4(4), pages 629-38, May.
  29. 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.
  30. 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.
  31. Calsamiglia, Xavier, 1977. "Decentralized resource allocation and increasing returns," Journal of Economic Theory, Elsevier, vol. 14(2), pages 263-283, April.
  32. Chipman, John S, 1970. "External Economies of Scale and Competitive Equilibrium," The Quarterly Journal of Economics, MIT Press, vol. 84(3), pages 347-85, August.
  33. Sharkey, William W., 1989. "Game theoretic modeling of increasing returns to scale," Games and Economic Behavior, Elsevier, vol. 1(4), pages 370-431, December.
  34. Cornet, B., 1984. "Existence of equilibria in economies with increasing returns," CORE Discussion Papers 1984007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  35. 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).
  36. 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.
  37. MacKinnon, James G., 1979. "Computing equilibria with increasing returns," European Economic Review, Elsevier, vol. 12(1), pages 1-16, February.
  38. 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).
  39. Dierker, Egbert & Guesnerie, Roger & Neuefeind, Wilhelm, 1985. "General Equilibrium When Some Firms Follow Special Pricing Rules," Econometrica, Econometric Society, vol. 53(6), pages 1369-93, November.
  40. Ichiishi, Tatsuro & Quinzii, Martine, 1983. "Decentralization for the Core of a Production Economy with Increasing Returns," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(2), pages 397-412, June.
  41. 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.
  42. Brown, Donald J & Heal, Geoffrey, 1979. "Equity, Efficiency, and Increasing Returns," Review of Economic Studies, Wiley Blackwell, vol. 46(4), pages 571-85, October.
  43. Kamiya, Kazuya, 1988. "Existence and uniqueness of equilibria with increasing returns," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 149-178, April.
  44. repec:cup:cbooks:9780521424585 is not listed on IDEAS
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Cited by:

  1. Peter J. Hammond & Antonio Villar, . "Efficiency with Non-Convexities: Extending the "Scandinavian Consensus" Approaches," Working Papers 97036, Stanford University, Department of Economics.

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