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Competitive equilibrium with search frictions : a general equilibrium approach

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  • Jerez, Belén

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

Suggested Citation

  • Jerez, Belén, 2012. "Competitive equilibrium with search frictions : a general equilibrium approach," UC3M Working papers. Economics we1235, Universidad Carlos III de Madrid. Departamento de Economía.
  • Handle: RePEc:cte:werepe:we1235
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    1. 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.
    2. Guido Menzio & Shouyong Shi, 2011. "Efficient Search on the Job and the Business Cycle," Journal of Political Economy, University of Chicago Press, vol. 119(3), pages 468-510.
    3. Joon Song, 2012. "Futures market: contractual arrangement to restrain moral hazard in teams," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(1), pages 163-189, September.
    4. Acemoglu, Daron & Shimer, Robert, 1999. "Holdups and Efficiency with Search Frictions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(4), pages 827-849, November.
    5. Peters, Michael, 2000. "Limits of Exact Equilibria for Capacity Constrained Sellers with Costly Search," Journal of Economic Theory, Elsevier, vol. 95(2), pages 139-168, December.
    6. Ivar Ekeland & James J. Heckman & Lars Nesheim, 2004. "Identification and Estimation of Hedonic Models," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages 60-109, February.
    7. Shouyong Shi, 2009. "Directed Search for Equilibrium Wage-Tenure Contracts," Econometrica, Econometric Society, vol. 77(2), pages 561-584, March.
    8. Dale T. Mortensen, 1982. "The Matching Process as a Noncooperative Bargaining Game," NBER Chapters, in: The Economics of Information and Uncertainty, pages 233-258, National Bureau of Economic Research, Inc.
    9. Daron Acemoglu & Robert Shimer, 1999. "Efficient Unemployment Insurance," Journal of Political Economy, University of Chicago Press, vol. 107(5), pages 893-928, October.
    10. J. Gabriel & Raquiel López-Martínez & Onésimo Hernández-Lerma, 2001. "The lagrange approach to infinite linear programs," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 293-314, December.
    11. Jerez, Belen, 2003. "A dual characterization of incentive efficiency," Journal of Economic Theory, Elsevier, vol. 112(1), pages 1-34, September.
    12. Diamond, Peter A, 1981. "Mobility Costs, Frictional Unemployment, and Efficiency," Journal of Political Economy, University of Chicago Press, vol. 89(4), pages 798-812, August.
    13. Michael Peters, 1997. "On the Equivalence of Walrasian and Non-Walrasian Equilibria in Contract Markets: The Case of Complete Contracts," Review of Economic Studies, Oxford University Press, vol. 64(2), pages 241-264.
    14. Guido Menzio & Shouyong Shi, 2010. "Directed Search on the Job, Heterogeneity, and Aggregate Fluctuations," American Economic Review, American Economic Association, vol. 100(2), pages 327-332, May.
    15. Gretsky, Neil E & Ostroy, Joseph M & Zame, William R, 1992. "The Nonatomic Assignment Model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 103-127, January.
    16. Alfred Galichon & Bernard Salanié, 2010. "Matching with Trade-offs: Revealed Preferences over Competiting Characteristics," Working Papers hal-00473173, HAL.
    17. Ivar Ekeland, 2010. "Existence, uniqueness and efficiency of equilibrium in hedonic markets with multidimensional types," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 275-315, February.
    18. Kenneth Burdett & Shouyong Shi & Randall Wright, 2001. "Pricing and Matching with Frictions," Journal of Political Economy, University of Chicago Press, vol. 109(5), pages 1060-1085, October.
    19. Veronica Guerrieri & Robert Shimer & Randall Wright, 2010. "Adverse Selection in Competitive Search Equilibrium," Econometrica, Econometric Society, vol. 78(6), pages 1823-1862, November.
    20. Espen R. Moen & Åsa Rosén, 2011. "Incentives in Competitive Search Equilibrium," Review of Economic Studies, Oxford University Press, vol. 78(2), pages 733-761.
    21. Dale T. Mortensen & Randall Wright, 2002. "Competitive Pricing and Efficiency in Search Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(1), pages 1-20, February.
    22. Pierre-André Chiappori & Robert McCann & Lars Nesheim, 2010. "Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 317-354, February.
    23. Pissarides, Christopher A, 1984. "Search Intensity, Job Advertising, and Efficiency," Journal of Labor Economics, University of Chicago Press, vol. 2(1), pages 128-143, January.
    24. Douglas Gale, 1996. "Equilibria and Pareto optima of markets with adverse selection (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 207-235.
    25. Peters, Michael, 1991. "Ex Ante Price Offers in Matching Games Non-steady States," Econometrica, Econometric Society, vol. 59(5), pages 1425-1454, September.
    26. Mortensen, Dale T, 1982. "Property Rights and Efficiency in Mating, Racing, and Related Games," American Economic Review, American Economic Association, vol. 72(5), pages 968-979, December.
    27. Jan Eeckhout & Philipp Kircher, 2010. "Sorting and Decentralized Price Competition," Econometrica, Econometric Society, vol. 78(2), pages 539-574, March.
    28. Moen, Espen R, 1997. "Competitive Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 385-411, April.
    29. Pietro Garibaldi & Espen R. Moen, 2010. "Job to Job Movements in a Simple Search Model," American Economic Review, American Economic Association, vol. 100(2), pages 343-347, May.
    30. Mas-Colell, Andreu, 1975. "A model of equilibrium with differentiated commodities," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 263-295.
    31. K. J. Arrow, 1964. "The Role of Securities in the Optimal Allocation of Risk-bearing," Review of Economic Studies, Oxford University Press, vol. 31(2), pages 91-96.
    32. Decker, Colin & Lieb, Elliott H. & McCann, Robert J. & Stephens, Benjamin K., 2013. "Unique equilibria and substitution effects in a stochastic model of the marriage market," Journal of Economic Theory, Elsevier, vol. 148(2), pages 778-792.
    33. Pissarides, Christopher A, 1985. "Short-run Equilibrium Dynamics of Unemployment Vacancies, and Real Wages," American Economic Review, American Economic Association, vol. 75(4), pages 676-690, September.
    34. Guido Menzio & Shouyong Shi, 2008. "Efficient Search on the Job and the Business Cycle," PIER Working Paper Archive 08-029, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    35. repec:hal:spmain:info:hdl:2441/1293p84sf58s482v2dpn0gsd67 is not listed on IDEAS
    36. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898, Elsevier.
    37. James D. Montgomery, 1991. "Equilibrium Wage Dispersion and Interindustry Wage Differentials," The Quarterly Journal of Economics, Oxford University Press, vol. 106(1), pages 163-179.
    38. Jerez, Belén, 2010. "Competitive equilibrium with search frictions: Arrow-Debreu meets Diamond-Mortensen-Pisarides," UC3M Working papers. Economics we1039, Universidad Carlos III de Madrid. Departamento de Economía.
    39. Shi, Shouyong, 2001. "Frictional Assignment. I. Efficiency," Journal of Economic Theory, Elsevier, vol. 98(2), pages 232-260, June.
    40. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc0c7apsi is not listed on IDEAS
    41. Robert Shimer, 2005. "The Assignment of Workers to Jobs in an Economy with Coordination Frictions," Journal of Political Economy, University of Chicago Press, vol. 113(5), pages 996-1025, October.
    42. Arthur J. Hosios, 1990. "On The Efficiency of Matching and Related Models of Search and Unemployment," Review of Economic Studies, Oxford University Press, vol. 57(2), pages 279-298.
    43. Peter A. Diamond, 1982. "Wage Determination and Efficiency in Search Equilibrium," Review of Economic Studies, Oxford University Press, vol. 49(2), pages 217-227.
    44. repec:dau:papers:123456789/6486 is not listed on IDEAS
    45. Gretsky, Neil E. & Ostroy, Joseph M. & Zame, William R., 1999. "Perfect Competition in the Continuous Assignment Model," Journal of Economic Theory, Elsevier, vol. 88(1), pages 60-118, September.
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    Cited by:

    1. Jerez, Belén, 2022. "Competitive search with two-sided risk aversion," UC3M Working papers. Economics 34383, Universidad Carlos III de Madrid. Departamento de Economía.
    2. Jerez, Belén, 2017. "Competitive search equilibrium with multidimensional heterogeneity and two-sided ex-ante investments," Journal of Economic Theory, Elsevier, vol. 172(C), pages 202-219.
    3. Jerez, Belén, 2023. "Competitive search with two-sided risk aversion," European Economic Review, Elsevier, vol. 157(C).
    4. Randall Wright & Philipp Kircher & Benoit Julîen & Veronica Guerrieri, 2017. "Directed Search: A Guided Tour," NBER Working Papers 23884, National Bureau of Economic Research, Inc.
    5. Antonia Díaz & Belén Jerez & Juan Pablo Rincón-Zapatero, 2023. "Housing Prices and Credit Constraints in Competitive Search," The Economic Journal, Royal Economic Society, vol. 134(657), pages 220-270.
    6. Jan Eeckhout & Alireza Sepahsalari, 2020. "The Effect of Wealth on Worker Productivity," Bristol Economics Discussion Papers 20/731, School of Economics, University of Bristol, UK.
    7. Hector Chade & Jan Eeckhout & Lones Smith, 2017. "Sorting through Search and Matching Models in Economics," Journal of Economic Literature, American Economic Association, vol. 55(2), pages 493-544, June.
    8. Gabrovski, Miroslav & Kospentaris, Ioannis, 2021. "Intermediation in over-the-counter markets with price transparency," Journal of Economic Theory, Elsevier, vol. 198(C).
    9. Jan Eeckhout, 2013. "Unemployment Risk and the Distribution of Assets," 2013 Meeting Papers 337, Society for Economic Dynamics.

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    More about this item

    Keywords

    Competitive equilibrium;

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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