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Construction of Stationary Markov Equilibria in a Strategic Market Game

This paper studies stationary noncooperative equilibria in an economy with fiat money, one nondurable commodity, countably many time periods, no credit or futures market, and a measure space of agents -- who may differ in their preferences and in the distributions of their (random) endowments. These agents are immortal, and hold fiat money as a means of hedging against the random fluctuations in their endowments of the commodity. In the aggregate, these fluctuations offset each other, and equilibrium prices are constant. We carry out an equilibrium analysis that focuses on distribution of wealth, on consumption, and on price formation. A careful analysis of the one-agent, infinite-horizon optimization problem, and of the invariant measure for the associated optimally controlled Markov chain, leads by aggregation to a stationary noncooperative or competitive equilibrium. This consists of a price for the commodity and of a distribution of wealth across agents which, under appropriate simple strategies for the agents, stay fixed from period to period and preserve the basic quantities of the model. We hope that, in future work, we shall be able to address additional features of the model treated here, such as borrowing and lending at appropriate (endogenously determined) interest rates, the endogenous production of the commodity, overlapping generations of agents, and bankruptcy and treatment of creditors.

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File URL: http://cowles.econ.yale.edu/P/cd/d10a/d1033.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1033.

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Length: 44 pages
Date of creation: Oct 1992
Date of revision:
Publication status: Published in Mathematics of Operations Research (November 1994), 19(4): 975-1006
Handle: RePEc:cwl:cwldpp:1033
Note: CFP 884.
Contact details of provider: Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/

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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
  2. Deaton, A., 1989. "Saving And Liquidity Constraints," Papers 153, Princeton, Woodrow Wilson School - Public and International Affairs.
  3. Hakansson, Nils H, 1970. "Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions," Econometrica, Econometric Society, vol. 38(5), pages 587-607, September.
  4. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  5. Martin Shubik & Ward Whitt, 1973. "Fiat Money in an Economy with One Nondurable Good and No Credit (A Noncooperative Sequential Game)," Cowles Foundation Discussion Papers 355, Cowles Foundation for Research in Economics, Yale University.
  6. Mendelssohn, Roy & Sobel, Matthew J., 1980. "Capital accumulation and the optimization of renewable resource models," Journal of Economic Theory, Elsevier, vol. 23(2), pages 243-260, October.
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