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Price level uniformity in a random matching model with perfectly patient traders

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Edward J. Green
Ruilin Zhou

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Abstract

This paper shows that one of the defining features of Walrasian equilibrium---law of one price---characterizes equilibrium in a non-Walrasian environment of (1) random trade matching without double coincidence of wants, and (2) strategic, price-setting conduct. Money is modeled as perfectly divisible and there is no constraint on agents' money inventories. In such an environment with discounting, the endogenous heterogeneity of money balances among agents implies differences in marginal valuation of money between distinct pairs of traders, which raises the question whether decentralized trade would typically involve price dispersion. We investigate the limiting case in which agents are patient, in the sense that they have overtaking-criterion preferences over random expected-utility streams. We show that in this case the ``law of one price'' holds exactly. That is, in a stationary Markov monetary equilibrium, all transactions endogenously must occur at a single price despite the decentralized organization of exchange. The result is in the same spirit as the work of Gale (1986a, b) on bargaining and competition, although the model differs from Gale's in some significant respects.

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Paper provided by Federal Reserve Bank of Chicago in its series Working Paper Series with number WP-01-17.

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Date of creation: 2001
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Handle: RePEc:fip:fedhwp:wp-01-17

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Keywords: Prices ; Money;

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  1. Camera, Gabriele & Corbae, Dean, 1999. "Money and Price Dispersion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(4), pages 985-1008, November.
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  2. Edward J. Green & Ruilin Zhou, 2000. "Dynamic monetary equilibrium in a random-matching economy," Working Paper Series WP-00-1, Federal Reserve Bank of Chicago. [Downloadable!]
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  3. Gale, Douglas M, 1986. "Bargaining and Competition Part I: Characterization," Econometrica, Econometric Society, vol. 54(4), pages 785-806, July. [Downloadable!] (restricted)
  4. Gale, Douglas M, 1986. "Bargaining and Competition Part II: Existence," Econometrica, Econometric Society, vol. 54(4), pages 807-18, July. [Downloadable!] (restricted)
  5. Itzhak Gilboa & Akihiko Matsui, 1990. "A Model of Random Matching," Discussion Papers 887, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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