(This abstract was borrowed from another version of this item.)"> (This abstract was borrowed from another version of this item.)">
[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/iec/inveco/v18y1994i2p205-243.html
   My bibliography  Save this article

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

Author

Listed:
  • Antonio Villar

    (Universidad de Alicante and IVIE)

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Antonio Villar, 1994. "Existence and efficiency of equilibrium in economics with increasing returns to scale: an exposition," Investigaciones Economicas, Fundación SEPI, vol. 18(2), pages 205-243, May.
    • Handle: RePEc:iec:inveco:v:18:y:1994:i:2:p:205-243
    as

    Download full text from publisher

    File URL: https://www.fundacionsepi.es/investigacion/revistas/paperArchive/May1994/v18i2a1.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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," The Review of Economic Studies, Review of Economic Studies Ltd, 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, President and Fellows of Harvard College, vol. 84(3), pages 347-385.
    20. Takashi Negishi, 1961. "Monopolistic Competition and General Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 28(3), pages 196-201.
    21. 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, President and Fellows of Harvard College, vol. 102(2), pages 223-241.
    22. repec:dau:papers:123456789/5649 is not listed on IDEAS
    23. MacKinnon, James G., 1979. "Computing equilibria with increasing returns," European Economic Review, Elsevier, vol. 12(1), pages 1-16, February.
    24. 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.
    25. 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.
    26. 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.
    27. Vohra, Rajiv, 1988. "Optimal regulation under fixed rules for income distribution," Journal of Economic Theory, Elsevier, vol. 45(1), pages 65-84, June.
    28. Paulina Beato, 1982. "The Existence of Marginal Cost Pricing Equilibria with Increasing Returns," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 97(4), pages 669-688.
    29. Leonard J. Mirman & Yair Tauman, 1982. "Demand Compatible Equitable Cost Sharing Prices," Mathematics of Operations Research, INFORMS, vol. 7(1), pages 40-56, February.
    30. Calsamiglia, Xavier, 1977. "Decentralized resource allocation and increasing returns," Journal of Economic Theory, Elsevier, vol. 14(2), pages 263-283, April.
    31. Leonard J. Mirman & Dov Samet & Yair Tauman, 1983. "An Axiomatic Approach to the Allocation of a Fixed Cost Through Prices," Bell Journal of Economics, The RAND Corporation, vol. 14(1), pages 139-151, Spring.
    32. 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.
    33. Kamiya, Kazuya, 1988. "Existence and uniqueness of equilibria with increasing returns," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 149-178, April.
    34. 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.
    35. Louis J. Billera & David C. Heath, 1982. "Allocation of Shared Costs: A Set of Axioms Yielding A Unique Procedure," Mathematics of Operations Research, INFORMS, vol. 7(1), pages 32-39, February.
    36. Silvestre, Joaquim, 1978. "Increasing Returns in General Non-Competitive Analysis," Econometrica, Econometric Society, vol. 46(2), pages 397-402, March.
    37. 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.
    38. Sharkey, William W., 1989. "Game theoretic modeling of increasing returns to scale," Games and Economic Behavior, Elsevier, vol. 1(4), pages 370-431, December.
    39. Rajiv Vohra, 1990. "On the Inefficiency of Two-Part Tariffs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(3), pages 415-438.
    40. 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.
    41. Dierker, Egbert & Neuefeind, Wilhelm, 1988. "Quantity guided price setting," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 249-259, April.
    42. 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.
    43. 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.
    44. 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.
    45. 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.
    46. Guesnerie, Roger, 1975. "Pareto Optimality in Non-Convex Economies," Econometrica, Econometric Society, vol. 43(1), pages 1-29, January.
    47. 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).
    48. 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.
    49. Beato, Paulina & Mas-Colell, Andreu, 1985. "On marginal cost pricing with given tax-subsidy rules," Journal of Economic Theory, Elsevier, vol. 37(2), pages 356-365, December.
    50. FitzRoy, Felix R., 1974. "Monopolistic equilibrium, non-convexity and inverse demand," Journal of Economic Theory, Elsevier, vol. 7(1), pages 1-16, January.
    51. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.
    2. Hichem Ben-El-Mechaiekh & Philippe Bich & Monique Florenzano, 2009. "General equilibrium and fixed-point theory: a partial survey," PSE-Ecole d'économie de Paris (Postprint) hal-00755998, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. J. M. Bonnisseau & A. Jamin, 2008. "Equilibria with Increasing Returns: Sufficient Conditions on Bounded Production Allocations," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(6), pages 1033-1068, December.
    2. Tian, Guoqiang, 2009. "Implementation in economies with non-convex production technologies unknown to the designer," Games and Economic Behavior, Elsevier, vol. 66(1), pages 526-545, May.
    3. Jean-Marc Bonnisseau, 2000. "The Marginal Pricing Rule in Economies with Infinitely Many Commodities," Econometric Society World Congress 2000 Contributed Papers 0262, Econometric Society.
    4. 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.
    5. Hichem Ben-El-Mechaiekh & Philippe Bich & Monique Florenzano, 2009. "General equilibrium and fixed-point theory: a partial survey," PSE-Ecole d'économie de Paris (Postprint) hal-00755998, HAL.
    6. Murty, Sushama, 2010. "Externalities and fundamental nonconvexities: A reconciliation of approaches to general equilibrium externality modeling and implications for decentralization," Journal of Economic Theory, Elsevier, vol. 145(1), pages 331-353, January.
    7. Tian, Guoqiang, 2005. "Implementation in production economies with increasing returns," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 309-325, May.
    8. Moriguchi, Chiaki, 1996. "Two-part marginal cost pricing in a pure fixed cost economy," Journal of Mathematical Economics, Elsevier, vol. 26(3), pages 363-385.
    9. Antonio Villar Notario, 2000. "On The Efficiency Of Market Equilibrium In Production Economies," Working Papers. Serie AD 2000-17, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    10. Jean-Marc Bonnisseau & Matías Fuentes, 2020. "Market Failures and Equilibria in Banach Lattices: New Tangent and Normal Cones," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 338-367, February.
    11. van den Elzen, Antoon & Kremers, Hans, 2006. "An adjustment process for nonconvex production economies," Journal of Mathematical Economics, Elsevier, vol. 42(1), pages 1-13, February.
    12. Bonnisseau, J.-M. & Cornet, B., 2008. "Existence of equilibria with a tight marginal pricing rule," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 613-624, July.
    13. Dehez, Pierre & Dreze, Jacques H. & Suzuki, Takashi, 2003. "Imperfect competition a la Negishi, also with fixed costs," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 219-237, June.
    14. Guoqiang Tian, 2016. "On the existence of price equilibrium in economies with excess demand functions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 5-16, April.
    15. Paul Oslington, 2012. "General Equilibrium: Theory and Evidence," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 446-448, September.
    16. Sushama Murty, 2014. "Necessary and sufficient conditions for an environmental Kuznets curve with some illustrative examples," Discussion Papers 1407, University of Exeter, Department of Economics.
    17. Jean-Marc Bonnisseau & Bernard Cornet & Marc-Olivier Czarnecki, 2007. "The marginal pricing rule revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(3), pages 579-589, December.
    18. Guesnerie, R., 1995. "The genealogy of modern theoretical public economics: From first best to second best," European Economic Review, Elsevier, vol. 39(3-4), pages 353-381, April.
    19. Egbert Dierker, 1986. "When does marginal cost pricing lead to Pareto efficiency?," Journal of Economics, Springer, vol. 46(1), pages 41-66, December.
    20. W D A Bryant, 2009. "General Equilibrium:Theory and Evidence," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6875, August.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:iec:inveco:v:18:y:1994:i:2:p:205-243. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Isabel Sánchez-Seco (email available below). General contact details of provider: https://www.fundacionsepi.es/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.