Competitive equilibrium with search frictions: A general equilibrium approach

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.Journal of Economic Literature Classification Numbers: D50, D61, D83.

Competitive search equilibrium with multidimensional heterogeneity and two-sided ex-ante investments

“…As we have already noted, in that paper the characteristics of the traders on both sides of the market are exogenous. Also, in Jerez (2014) buyers have di erent valuations depending on the type of seller they trade with (because di erent seller types o er di erent goods), but the valuations of the sellers do not depend on the characteristics of the buyers they trade with.…”

“…the trading technology. Jerez (2014) shows that this price-taking equilibrium notion is a reduced form of the strategic notion used in the literature. The point is made in the context of a related model where all the match-relevant characteristics of the traders are exogenous.…”

“…Whereas this literature uses strategic (game-theoretic) models, here we adopt the Walrasian (price-taking) approach proposed in Jerez (2014). In a nutshell, that paper shows that the Arrow-Debreu competitive equilibrium notion can be extended to environments with search frictions, essentially by replacing market clearing with a trading technology that is not frictionless (e.g.…”

“…The point is made in the context of a related model where all the match-relevant characteristics of the traders are exogenous. Here we extend the Walrasian model in Jerez (2014) to allow for two-sided ex-ante investments which are potentially multidimensional.…”

“…These models impose re nements to pin down the equilibrium beliefs. For a detailed discussion between the relation between the two equilibrium concepts and the two indeterminacies, see Jerez (2014).…”