Complementarities and Substitutabilities in Matching Models

In a standard search and matching model the labor market presents frictions while in the competitive product market the demand is infinitely elastic. To have a more realistic framework, some macroeconomic models abandon the assumption of infinite elasticity and consider a two-tier productive scheme in the goods market. In this paper, it is shown that, under some reasonable assumptions about the final goods production function (for instance Cobb-Douglas technology) the unique equilibrium of this kind of model features no production and full unemployment, making them useless for any policy analysis. A comparison between the two frameworks shows that a standard matching model overestimates the impact in terms of employment of any policy intervention in the sector where such a policy has been promoted, while at the same time it ignores the effects that emerge in other sectors of the economy.