On the Efficiency of Matching and Related Models of Search and Unemployment
Arthur J. Hosios
The Review of Economic Studies
Vol. 57, No. 2 (Apr., 1990), pp. 279-298
Published by: Oxford University Press
Stable URL: http://www.jstor.org/stable/2297382
Abstract: This paper describes a simple framework for evaluating the allocative performance of economies characterized by trading frictions and unemployment. This framework integrates the normative results of earlier Diamond-Mortensen-Pissarides bilateral matching-bargaining models of trade coordination and price-setting, and consists of a set of general conditions for constrained Pareto efficient resource allocation that are applicable to conventional natural rate models. To illustrate, several conventional models of the labour market are reformulated as matching- bargaining problems and analyzed using this framework.
Hosios (1990) derives the conditions which the matching function and surplus-sharing rule must satisfy to be internalized. Intuitively, how the externalities of congestion in the labor market, represented by the matching function ($m(u,v)$), and the way the surplus (economic profits) is shared has to exactly balance. In the literature, these conditions are known as the Hosios' Condition.
Hosios' Conditions + Pareto Efficiency
imply
Agent's social contributions = Private Gains
These conditions are:
Entry/Exit Externalities:
Entry to be efficient requires that unattached agents of each type received their social marginal profit. Which is equivalent to say that the share of unemployed workers and vacant firms in the surplus of the match is equal to the elasticity of matching function with respect to the search input (unemployed workers and vacant firms):
Entry/Exit Externalities:
Entry to be efficient requires that unattached agents of each type received their social marginal profit. Which is equivalent to say that the share of unemployed workers and vacant firms in the surplus of the match is equal to the elasticity of matching function with respect to the search input (unemployed workers and vacant firms):
$m_{u}=\gamma \frac{m(u,v)}{u}$
$m_{v}=(1-\gamma) \frac{m(u,v)}{v}$
Job Acceptance:
Sharing rule and the matching technology must satisfy:
$m_{u}+m_{v}=\gamma \frac{m(u,v)}{u}+(1-\gamma) \frac{m(u,v)}{v}$
Search/Recruitment externality:
To be efficient has to equate the marginal social and private benefits for matching of search and recruitment.
