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Implementing Arrow-Debreu equilibria by trading infinitely-lived securities

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  • Kevin X.D. Huang
  • Jan Werner

Abstract

We show that Arrow-Debreu equilibria with countably additive prices in infinite-time economy under uncertainty can be implemented by trading infinitely-lived securities in complete sequential markets under two different portfolio feasibility constraints: wealth constraint, and essentially bounded portfolios. Sequential equilibria with no price bubbles implement Arrow-Debreu equilibria, while those with price bubbles implement Arrow-Debreu equilibria with transfers. Transfers are equal to price bubbles on initial portfolio holdings. Price bubbles arise in sequential equilibrium under the wealth constraint if some securities are in zero supply or negative prices are permitted, but cannot arise with essentially bounded portfolios.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Kansas City in its series Research Working Paper with number RWP 02-08.

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Date of creation: 2002
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Handle: RePEc:fip:fedkrw:rwp02-08

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Keywords: Prices ; Equilibrium (Economics);

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  1. Florenzano, M. & Gourdel, P., 1994. "Incomplete Markets in Infinite Horizon: Debt Constraints Versus Node Prices," Papiers d'Economie Mathématique et Applications 94.76, Université Panthéon-Sorbonne (Paris 1).
  2. Levine, David K. & Zame, William R., 1996. "Debt constraints and equilibrium in infinite horizon economies with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 103-131.
  3. Kevin X.D. Huang & Jan Werner, 2000. "Asset price bubbles in Arrow-Debreu and sequential equilibrium," Economic Theory, Springer, vol. 15(2), pages 253-278.
  4. Magill, Michael & Quinzii, Martine, 1996. "Incomplete markets over an infinite horizon: Long-lived securities and speculative bubbles," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 133-170.
  5. Magill, M. & Quinzii, M., 1992. "Infinite Horizon Incomplete Markets," Papers 413a, California Davis - Institute of Governmental Affairs.
  6. Montrucchio, Luigi & Privileggi, Fabio, 2001. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," Journal of Economic Theory, Elsevier, vol. 101(1), pages 158-188, November.
  7. L. Wade, 1988. "Review," Public Choice, Springer, vol. 58(1), pages 99-100, July.
  8. Kandori, Michihiro, 1988. "Equivalent Equilibria," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(3), pages 401-17, August.
  9. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
  10. Aliprantis, Charalambos D & Brown, Donald J & Burkinshaw, Owen, 1987. "Edgeworth Equilibria," Econometrica, Econometric Society, vol. 55(5), pages 1109-37, September.
  11. Duffie, J Darrell & Huang, Chi-fu, 1985. "Implementing Arrow-Debreu Equilibria by Continuous Trading of Few Long-lived Securities," Econometrica, Econometric Society, vol. 53(6), pages 1337-56, November.
  12. Kocherlakota, N.R., 1990. "Bubbles and Constraints on Debt Accumulation," Working Papers 90-29, University of Iowa, Department of Economics.
  13. Tirole, Jean, 1982. "On the Possibility of Speculation under Rational Expectations," Econometrica, Econometric Society, vol. 50(5), pages 1163-81, September.
  14. Peleg, Bezalel & Yaari, Menahem E, 1970. "Markets with Countably Many Commodities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(3), pages 369-77, October.
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Cited by:
  1. Marco Bassetto & Thomas J. Sargent, 2005. "Politics and efficiency of separating capital and ordinary Government budgets," Working Paper Series WP-05-07, Federal Reserve Bank of Chicago.
  2. BLOISE, Gaetano & DRÈZE, Jacques & POLEMARCHAKIS, Heracles, 2002. "Money and indeterminacy over an infinite horizon," CORE Discussion Papers 2002021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Patarick Leoni, 2006. "Market Power, Survival and Accuracy of Predictions in Financial Markets," Economics, Finance and Accounting Department Working Paper Series n1701106, Department of Economics, Finance and Accounting, National University of Ireland - Maynooth.

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