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Competitive equilibrium with search frictions : a general equilibrium approach

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  • Belén Jerez

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Abstract

When the trading process is characterized by search frictions, traders may be rationed so markets need not clear. We build a general equilibrium model with transferable utility where the uncertainty arising from rationing is incorporated in the definition of a commodity, in the spirit of the Arrow-Debreu theory. Prices of commodities then depend not only on their physical characteristics, but also on the probability that their trade is rationed. The standard definition of competitive equilibrium is extended by replacing market clearing with a matching condition which describes a trading technology that is not frictionless. This condition relates the rationing probabilities of buyers and sellers to ratio of buyers to sellers in the market via an exogenous matching function with constant returns, as in standard search-theoretic models. When search frictions vanish, our model is equivalent to the competitive assignment model of Gretsky, Ostroy and Zame (1992). We adopt their approach, which uses linear programming techniques and duality theory, to derive the welfare and existence theorems in our search environment. Our competitive equilibrium notion is equivalent to that of directed (or competitive) search. The strength of our formulation and the linear programming approach is that they allow us to generalize the constrained efficiency and existence results in the directed search literature to a much broader class of economies. Our framework also opens the door to the use of linear programming algorithms for computing equilibria

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Bibliographic Info

Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we1235.

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Date of creation: Dec 2012
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Handle: RePEc:cte:werepe:we1235

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Keywords: Search frictions; Transferable utility; Competitive equilibriumm; Matching function; Linear programming and duality; Directed search;

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References

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  1. Shouyong Shi, 2006. "Directed Search for Equilibrium Wage-Tenure Contracts," Working Papers tecipa-260, University of Toronto, Department of Economics.
  2. Jerez, Belen, 2003. "A dual characterization of incentive efficiency," Journal of Economic Theory, Elsevier, Elsevier, vol. 112(1), pages 1-34, September.
  3. Guido Menzio & Shouyong Shi, 2011. "Efficient Search on the Job and the Business Cycle," Working Papers tecipa-437, University of Toronto, Department of Economics.
  4. Gretsky, Neil E. & Ostroy, Joseph M. & Zame, William R., 1999. "Perfect Competition in the Continuous Assignment Model," Journal of Economic Theory, Elsevier, Elsevier, vol. 88(1), pages 60-118, September.
  5. Hart, Sergiu & Hildenbrand, Werner & Kohlberg, Elon, 1974. "On equilibrium allocations as distributions on the commodity space," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 159-166, August.
  6. Douglas Gale, 1996. "Equilibria and Pareto optima of markets with adverse selection (*)," Economic Theory, Springer, Springer, vol. 7(2), pages 207-235.
  7. Guido Menzio & Shouyong Shi, 2010. "Directed Search on the Job, Heterogeneity, and Aggregate Fluctuations," Working Papers tecipa-390, University of Toronto, Department of Economics.
  8. Kenneth Burdett & Shouyong Shi & Randall Wright, 2001. "Pricing and Matching with Frictions," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 109(5), pages 1060-1085, October.
  9. Robert Shimer, 2005. "The Assignment of Workers to Jobs in an Economy with Coordination Frictions," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 113(5), pages 996-1025, October.
  10. Neil E. Gretsky & Joseph M. Ostroy & William R. Zame, 1990. "The Nonatomic Assignment Model," UCLA Economics Working Papers, UCLA Department of Economics 605, UCLA Department of Economics.
  11. Joon Song, 2007. "Futures Market: Contractual Arrangement to Restrain Moral Hazard in Teams," Economics Discussion Papers, University of Essex, Department of Economics 633, University of Essex, Department of Economics.
  12. Michael Peters, 1995. "On the Equivalence of Walrasian and Non-Walrasian Equilibria in Contract Markets: The case of Complete Contracts," GE, Growth, Math methods, EconWPA 9507001, EconWPA.
  13. Jan Eeckhout & Philipp Kircher, 2008. "Sorting and Decentralized Price Competition," PIER Working Paper Archive 08-020, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  14. Pissarides, Christopher A, 1985. "Short-run Equilibrium Dynamics of Unemployment Vacancies, and Real Wages," American Economic Review, American Economic Association, American Economic Association, vol. 75(4), pages 676-90, September.
  15. Belén Jerez, 2010. "Competitive equilibrium with search frictions: Arrow-Debreu meets Diamond-Mortensen-Pisarides," Economics Working Papers we1039, Universidad Carlos III, Departamento de Economía.
  16. Moen, Espen R, 1997. "Competitive Search Equilibrium," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 105(2), pages 385-411, April.
  17. Michael Peters, 1998. "Limits of Exact Equilibria for Capacity Constrained Sellers with costlySearch," Working Papers peters-98-01, University of Toronto, Department of Economics.
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