Competitive equilibrium with search frictions: A general equilibrium approach

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 the market clearing condition with an exogenous matching function which describes a trading technology that is not frictionless. As is typical in search models, the matching function relates the rationing probabilities of buyers and sellers to the ratio of buyers to sellers in the market. When search frictions vanish, our model is equivalent to the continuous assignment model of Gretsky et al. [20]. We adapt their approach, which uses linear programming techniques and duality theory, to show that a competitive equilibrium exists and is constrained efficient in our 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 ✩ I thank the editor, Christian Hellwig, and several anonymous referees for valuable comments and suggestions which have greatly improved the paper. I am grateful to Joe Ostroy for very helpful comments, and both to him and Louis Makowski for an insightful conversation that inspired this work. I also thank Jan Eeckhout, Onésimo Hernández, Philipp Kircher, Juan Pablo Rincón, Victor Ríos-Rull, Joon Song, and participants at the 2011 SAET Conference at Faro, VIII REDgWorkshop and the departmental seminar at Carlos III. This work started while I was visiting the University of Pennsylvania. I thank the Economics Department, and specially Victor Ríos-Rull, Kenn Burdett and Randy Wright, for their kind hospitality. Financial support from the Spanish DGCYT (projects SEJ2004-07861, SEJ2007-65169, ECO2010-20614 and Ramón y Cajal Program), the Bank of Spain’s Programme of Excellence in Research (2011–2013), and Fundación Ramón Areces (“Economía Pública del Sector Comercial”, IV Concurso Nacional para la adjudicación de Ayudas a la Investigación en Economía) is gratefully acknowledged. Any errors are mine. E-mail address: [email protected]. 1 Fax: +34 91 624 9875. http://dx.doi.org/10.1016/j.jet.2014.07.008 0022-0531/© 2014 Elsevier Inc. All rights reserved. B. Jerez / Journal of Economic Theory 153 (2014) 252–286 253 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 existing algorithms for computing equilibria and taking these models to the data. © 2014 Elsevier Inc. All rights reserved. JEL classification: D50; D61; D83