4. Vacancy costs and the labor market. Consider the search-theoretic model of the labor market of Diamond (1982), Mortensen (1982) and Pissarides (1985).

a.The equilibrium tightness of the labor market,, solves the following equationk=q()(1)(yb).

1[1p()]

Plot the left and the right hand side of the above equation as functions ofand identify.

b.Using the same graph as before, identify the effect of an incraese in the vacancy costkon the equilibrium tightness of the labor market. Interpret your finding.

c.The equilibrium unemployment,u, and the equilibrium vacancies,v, solve simultaneously the following system of equations

u=,v=u. +p(v/u)

Plot the solutions to these two equations in a graph that hasuon the horizontal axis andvon the vertical axis (i.e. plot the Beveridge curve and the market tightness curve). Identifyuandv.

d.Using the same graph as before, illustrate the effect of an increase in the vacancy costkon the equilibrium unemployment and vacancies. Interpret your findings.

e.Should the government intervene to lower unemployment in response to an increase ink?