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Walrasian Equilibrium in an Exchange Economy with Indivisibilities

Author

Listed:
  • Jinpeng Ma

    (Economics, Rutgers University, Camden, NJ 08102)

  • Fusheng Nie

    (Philadelphia Stock Exchange)

Abstract

This paper studies an exchange economy with indivisibilities. Our main goal is to see if a price system can function well in an economy (e.g., an economy with complementary preferences) that does not have a Walrasian equilibrium. We study the price adjustment processes governed by the Euler iterative scheme. We show that in an economy that has a Walrasian equilibrium, our price adjustment processes have a common uniform limit that is unique and converges to a Walrasian equilibrium price vector in finite time. Surprisingly, in an economy that does not have a Walrasian equilibrium, our price adjustment processes also have a common uniform limit that is unique and converges to a market equilibrium price vector in finite time. Moreover, market equilibrium prices coincide with Walrasian equilibrium ones in an economy that has a Walrasian equilibrium. Further, there are no prices other than the Walrasian or market equilibrium ones that have such a property of global stability.

Suggested Citation

  • Jinpeng Ma & Fusheng Nie, 2002. "Walrasian Equilibrium in an Exchange Economy with Indivisibilities," Departmental Working Papers 200207, Rutgers University, Department of Economics.
    • Handle: RePEc:rut:rutres:200207
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    References listed on IDEAS

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    1. Rod Garratt & Todd Keister & Karl Shell, 2004. "Comparing Sunspot Equilibrium And Lottery Equilibrium Allocations: The Finite Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 351-386, May.
    2. van der Laan, Gerard & Talman, Dolf & Yang, Zaifu, 2002. "Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible and Indivisible Commodities and Linear Production Technologies," Journal of Economic Theory, Elsevier, vol. 103(2), pages 411-428, April.
    3. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541, Elsevier.
    4. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-872, August.
    5. Vernon L. Smith, 1962. "An Experimental Study of Competitive Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 70, pages 111-111.
    6. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    7. Garratt, Rod, 1995. "Decentralizing Lottery Allocations in Markets with Indivisible Commodities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 295-313, March.
    8. Donald A. Walker (ed.), 2000. "Equilibrium," Books, Edward Elgar Publishing, volume 0, number 1585.
    9. Paul Milgrom, 2000. "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Journal of Political Economy, University of Chicago Press, vol. 108(2), pages 245-272, April.
    10. Alvin E. Roth & Uriel G. Rothblum, 1999. "Truncation Strategies in Matching Markets--In Search of Advice for Participants," Econometrica, Econometric Society, vol. 67(1), pages 21-44, January.
    11. Garratt, Rod & Keister, Todd & Qin, Cheng-Zhong & Shell, Karl, 2002. "Equilibrium Prices When the Sunspot Variable Is Continuous," Journal of Economic Theory, Elsevier, vol. 107(1), pages 11-38, November.
    12. Prescott, Edward C & Townsend, Robert M, 1984. "Pareto Optima and Competitive Equilibria with Adverse Selection and Moral Hazard," Econometrica, Econometric Society, vol. 52(1), pages 21-45, January.
    13. Vernon L. Smith, 1965. "Experimental Auction Markets and the Walrasian Hypothesis," Journal of Political Economy, University of Chicago Press, vol. 73, pages 387-387.
    14. Ma, Jinpeng, 1998. "Competitive Equilibrium with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 82(2), pages 458-468, October.
    15. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    16. Danilov, Vladimir & Koshevoy, Gleb & Murota, Kazuo, 2001. "Discrete convexity and equilibria in economies with indivisible goods and money," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 251-273, May.
    17. Bikhchandani, Sushil & Mamer, John W., 1997. "Competitive Equilibrium in an Exchange Economy with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 74(2), pages 385-413, June.
    18. Roth, Alvin E & Vande Vate, John H, 1991. "Incentives in Two-Sided Matching with Random Stable Mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 31-44, January.
    19. Paul R. Milgrom, 1985. "Auction Theory," Cowles Foundation Discussion Papers 779, Cowles Foundation for Research in Economics, Yale University.
    20. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
    21. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    22. Garratt, Rod & Qin, Cheng-Zhong, 1997. "On a Market for Coalitions with Indivisible Agents and Lotteries," Journal of Economic Theory, Elsevier, vol. 77(1), pages 81-101, November.
    23. Yang, Zaifu, 2000. "Equilibrium in an exchange economy with multiple indivisible commodities and money," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 353-365, April.
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    Cited by:

    1. Jinpeng Ma & Qiongling Li, 2016. "Convergence of price processes under two dynamic double auctions," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 1-44, December.
    2. Xiaojing Xu & Jinpeng Ma & Xiaoping Xie, 2019. "Price Convergence under a Probabilistic Double Auction," Computational Economics, Springer;Society for Computational Economics, vol. 54(3), pages 1113-1155, October.
    3. W D A Bryant, 2009. "General Equilibrium:Theory and Evidence," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6875, December.
    4. Paul Oslington, 2012. "General Equilibrium: Theory and Evidence," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 446-448, September.
    5. Xiaojing Xu & Jinpeng Ma & Xiaoping Xie, 2017. "Convergence of Markovian price processes in a financial market transaction model," Operational Research, Springer, vol. 17(1), pages 239-273, April.

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    More about this item

    Keywords

    Walrasian;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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