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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.

Suggested Citation

  • Antonio Villar Notario, 1994. "Existence and efficiency of equilibrium in economies with increasing returns to scale: An exposition," Working Papers. Serie AD 1994-07, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    • Handle: RePEc:ivi:wpasad:1994-07
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    References listed on IDEAS

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    1. Cornet, B., 1984. "Existence of equilibria in economies with increasing returns," LIDAM Discussion Papers CORE 1984007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Bonnisseau, Jean-Marc & Cornet, Bernard, 1988. "Valuation equilibrium and pareto optimum in non-convex economies," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 293-308, April.
    3. 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.
    4. 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 159-166, June.
    5. Roberts, John & Sonnenschein, Hugo, 1977. "On the Foundations of the Theory of Monopolistic Competition," Econometrica, Econometric Society, vol. 45(1), pages 101-113, January.
    6. 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.
    7. Bonnisseau, Jean-Marc, 1988. "On two existence results of equilibria in economies with increasing returns," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 193-207, April.
    8. 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).
    9. Sharkey, W W, 1979. "Existence of a Core When There Are Increasing Returns," Econometrica, Econometric Society, vol. 47(4), pages 869-876, July.
    10. 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 425-434, June.
    11. 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.
    12. Donald J. Brown & Geoffrey Heal, 1979. "Equity, Efficiency and Increasing Returns," Review of Economic Studies, Oxford University Press, vol. 46(4), pages 571-585.
    13. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    14. 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.
    15. Mas-Colell, Andreu & Silvestre, Joaquim, 1989. "Cost share equilibria: A Lindahlian approach," Journal of Economic Theory, Elsevier, vol. 47(2), pages 239-256, April.
    16. 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.
    17. Vohra, Rajiv, 1992. "Marginal Cost Pricing under Bounded Marginal Returns," Econometrica, Econometric Society, vol. 60(4), pages 859-876, July.
    18. Egbert Dierker, 1986. "When does marginal cost pricing lead to Pareto efficiency?," Journal of Economics, Springer, vol. 46(1), pages 41-66, December.
    19. John S. Chipman, 1970. "External Economies of Scale and Competitive Equilibrium," The Quarterly Journal of Economics, Oxford University Press, vol. 84(3), pages 347-385.
    20. M. Ali Khan & Rajiv Vohra, 1987. "An Extension of the Second Welfare Theorem to Economies with Nonconvexities and Public Goods," The Quarterly Journal of Economics, Oxford University Press, vol. 102(2), pages 223-241.
    21. repec:dau:papers:123456789/5649 is not listed on IDEAS
    22. MacKinnon, James G., 1979. "Computing equilibria with increasing returns," European Economic Review, Elsevier, vol. 12(1), pages 1-16, February.
    23. 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.
    24. 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.
    25. Villar, Antonio, 1994. "Equilibrium with Nonconvex Technologies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(4), pages 629-638, May.
    26. Vohra, Rajiv, 1988. "Optimal regulation under fixed rules for income distribution," Journal of Economic Theory, Elsevier, vol. 45(1), pages 65-84, June.
    27. Calsamiglia, Xavier, 1977. "Decentralized resource allocation and increasing returns," Journal of Economic Theory, Elsevier, vol. 14(2), pages 263-283, April.
    28. 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.
    29. Kamiya, Kazuya, 1988. "Existence and uniqueness of equilibria with increasing returns," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 149-178, April.
    30. 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.
    31. Silvestre, Joaquim, 1978. "Increasing Returns in General Non-Competitive Analysis," Econometrica, Econometric Society, vol. 46(2), pages 397-402, March.
    32. 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 903-922, November.
    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. Dierker, Egbert & Guesnerie, Roger & Neuefeind, Wilhelm, 1985. "General Equilibrium When Some Firms Follow Special Pricing Rules," Econometrica, Econometric Society, vol. 53(6), pages 1369-1393, November.
    35. Dierker, Egbert & Neuefeind, Wilhelm, 1988. "Quantity guided price setting," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 249-259, April.
    36. 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.
    37. 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.
    38. Brown, Donald J. & Heller, Walter P. & Starr, Ross M., 1992. "Two-part marginal cost pricing equilibria: Existence and efficiency," Journal of Economic Theory, Elsevier, vol. 57(1), pages 52-72.
    39. 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.
    40. Guesnerie, Roger, 1975. "Pareto Optimality in Non-Convex Economies," Econometrica, Econometric Society, vol. 43(1), pages 1-29, January.
    41. Cornet, B., 1986. "The second welfare theorem in nonconvex economies," LIDAM Discussion Papers CORE 1986030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    42. Jouini, Elyes, 1989. "A remark on Clarke's normal cone and the marginal cost pricing rule," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 95-101, February.
    43. FitzRoy, Felix R., 1974. "Monopolistic equilibrium, non-convexity and inverse demand," Journal of Economic Theory, Elsevier, vol. 7(1), pages 1-16, January.
    44. 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.
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    Cited by:

    1. Peter J. Hammond & Antonio Villar, 1998. "Efficiency with Non‐Convexities: Extending the “Scandinavian Consensus” Approaches," Scandinavian Journal of Economics, Wiley Blackwell, vol. 100(1), pages 11-32, March.

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    Keywords

    Increasing returns; equilibrium; optimality;

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