Taxes, Subsidies and Equilibrium Unemployment

Abstract

This paper considers the effects of wage taxes, employment subsidies and unemployment benefits in a simple model of equilibrium search. Unemployment is determined by the equality of job matchings and job separations, job vacancies are determined by a zero-profit condition and wages by a Nash bargain between the meeting firm and worker. I show that marginal wage taxes influence the firm's and worker's equilibrium sharing rule, whereas employment subsidies and unemployment benefits influence only the surplus shared. Hence, tax-financed subsidies reduce wages and raise employment and vacancies, whereas tax-financed unemployment benefits raise wages and reduce employment and vacancies. In this paper we consider the effects of wage taxes, employment subsidies and unemployment benefits on equilibrium search unemployment, in a model where wages are determined competitively by the meeting firm and worker. Discussions about the desirability of taxes and subsidies and their effect on employment and wages abound in the labour economics literature. Yet, the only tax or subsidy that has been systematically discussed in a competitive-search framework is a lump-sum unemployment benefit. The reason for this might be that the structure of the model is such that it is ideally suited to the study of unemployment benefits, whereas traditional supply and demand analysis could arguably cope with other kinds of taxes. This might be true in some cases, but if it is at all appropriate to think of equilibrium unemployment as coming out of an essentially competitive framework, when the process which brings together jobs and workers is characterized by frictions, traditional supply and demand analysis may not be rich enough to give us all the answers we need.1 The model of this paper is a simple equilibrium model with endogenous unemployment, supply of jobs (i.e. demand for labour) and real wages. Unemployment exists because unemployed workers and unfilled jobs cannot find each other instantaneously. In the interval of time required to match all workers and jobs some existing job-worker pairs break up, providing a new flow into unemployment. Thus unemployment can never be eliminated; in equilibrium flows into and flows out of unemployment are equal. Wages are set endogenously by generalized Nash bargains between the individual firm and worker. The equilibrium wage rate is shown to depend on all the parameters of the model and to be determined simultaneously with equilibrium unemployment. The driving force in the model, which provides the link between wages and unemployment, is the rate of job vacancies. The total number of jobs is determined by zero-profit conditions, because of constant returns to scale. The number of jobs taken up each period depends positively on the number of job vacancies, because a typical unemployed worker will have a better chance of locating a job when there are more vacancies. If the real wage rate falls the expected profits from a job rise. Firms open up more vacancies to take advantage of this, and so more jobs are taken up. But as vacancies rise and