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Indeterminacy of Cournot–Walras equilibrium with incomplete markets

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  • Michael Zierhut

    (Humboldt University)

Abstract

This paper studies a sole proprietorship economy with imperfect competition in a transferable utility setting. While consumers behave as price takers, producers issue real assets strategically to maximize their own utility. Even when complete markets are technologically feasible, equilibria with incomplete markets are robust, and they appear in large numbers: There is a continuum of equilibria with different asset spans that can be welfare-ranked. This real indeterminacy does not vanish as the number of producers goes to infinity. Therefore, the self-interest of producers restricts economic outcomes but does not determine them.

Suggested Citation

  • Michael Zierhut, 2021. "Indeterminacy of Cournot–Walras equilibrium with incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 81-114, February.
  • Handle: RePEc:spr:joecth:v:71:y:2021:i:1:d:10.1007_s00199-020-01248-2
    DOI: 10.1007/s00199-020-01248-2
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    1. Jaskold Gabszewicz, Jean & Vial, Jean-Philippe, 1972. "Oligopoly "A la cournot" in a general equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 4(3), pages 381-400, June.
    2. Dierker, Egbert & Dierker, Hildegard, 2010. "Welfare and efficiency in incomplete market economies with a single firm," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 652-665, September.
    3. Philip J. Reny, 2016. "Introduction to the symposium on discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 423-429, March.
    4. Mas-Colell, Andreu, 1991. "Indeterminacy in Incomplete Market Economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 45-61, January.
    5. Geanakoplos, John & Mas-Colell, Andreu, 1989. "Real indeterminacy with financial assets," Journal of Economic Theory, Elsevier, vol. 47(1), pages 22-38, February.
    6. Camelia Bejan, 2008. "The objective of a privately owned firm under imperfect competition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(1), pages 99-118, October.
    7. Birgit Grodal & Egbert Dierker, 1999. "The price normalization problem in imperfect competition and the objective of the firm," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(2), pages 257-284.
    8. Werner, Jan, 1990. "Structure of financial markets and real indeterminacy of equilibria," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 217-232.
    9. Stefano Demichelis & Klaus Ritzberger, 2011. "A general equilibrium analysis of corporate control and the stock market," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(2), pages 221-254, February.
    10. Michael Zierhut, 2017. "Constrained efficiency versus unanimity in incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(1), pages 23-45, June.
    11. Shirai, Koji, 2010. "An existence theorem for Cournot-Walras equilibria in a monopolistically competitive economy," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1093-1102, November.
    12. Husseini, S. Y. & Lasry, J. -M. & Magill, M. J. P., 1990. "Existence of equilibrium with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 39-67.
    13. Marta Faias, 2008. "Approximate equilibrium in pure strategies for a two-stage game of asset creation," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 31(2), pages 117-136, November.
    14. Balasko, Yves & Cass, David, 1989. "The Structure of Financial Equilibrium with Exogenous Yields: The Case of Incomplete Markets," Econometrica, Econometric Society, vol. 57(1), pages 135-162, January.
    15. Novshek, William & Sonnenschein, Hugo, 1978. "Cournot and Walras equilibrium," Journal of Economic Theory, Elsevier, vol. 19(2), pages 223-266, December.
    16. Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December.
    17. Klaus Ritzberger & Frank Milne, 2002. "Strategic pricing of equity issues," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 271-294.
    18. Andrés Carvajal & Marzena Rostek & Marek Weretka, 2012. "Competition in Financial Innovation," Econometrica, Econometric Society, vol. 80(5), pages 1895-1936, September.
    19. Novshek, William & Sonnenschein, Hugo, 1983. "Walrasian equilibria as limits of noncooperative equilibria. Part II: Pure strategies," Journal of Economic Theory, Elsevier, vol. 30(1), pages 171-187, June.
    20. Hirsch, M. D. & Magill, M. & Mas-Colell, A., 1990. "A geometric approach to a class of equilibrium existence theorems," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 95-106.
    21. Zierhut, Michael, 2019. "Nonexistence of constrained efficient production plans," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 127-136.
    22. Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June.
    23. Roberts, Kevin, 1980. "The limit points of monopolistic competition," Journal of Economic Theory, Elsevier, vol. 22(2), pages 256-278, April.
    24. Allen, Beth, 1994. "Randomization and the limit points of monopolistic competition," Journal of Mathematical Economics, Elsevier, vol. 23(3), pages 205-218, May.
    25. Nagata, Ryo, 1998. "The degree of indeterminacy of equilibria with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 109-123, January.
    26. Dierker, Egbert, 1972. "Two Remarks on the Number of Equilibria of an Economy," Econometrica, Econometric Society, vol. 40(5), pages 951-953, September.
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    Cited by:

    1. Hervé Crès & Mich Tvede, 2023. "Corporate self-regulation of imperfect competition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 1181-1205, May.

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    More about this item

    Keywords

    Incomplete markets with production; Imperfect competition; Discontinuous games; Real indeterminacy; Endogenously incomplete markets;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

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