EFFICIENT UNEMPLOYMENT INSURANCE: A Model of Job Search 4

Existence and Characterization
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Figure 1: An equilibrium maximizes workers’ utility subject to firms earning zero profits. Click Here Higher wages and shorter queues raise utility and lower profits.

Despite the search frictions, capital earns its marginal product and labor keeps the residual output. Since / is concave, (4) defines w* as an increasing function of k*.

Proposition 1 and equation (4) allow us to depict an equilibrium graphically. First, the optimal capital choice and (4) imply that the constraint, firms’ zero profit condition, is an upward sloping curve in {<?, w} space, as shown in Figure 1. Similarly, workers’ indifference curves are upward sloping in {q,w} space. An equilibrium then is a point of tangency between these two indifference curves. Either curve, however, could be non-convex, so uniqueness of the equilibrium is not guaranteed.