3. Quantifying the effect of unemployment benefits on unemployment. Consider a version of the labor market model of Pissarides (1985) in which the matching functionM(u, v) isuv/(u+v) and the discount factoris 1.

a.Derive an expression for the worker's job-finding probability,p(), and for the firm's job-filling probability,q().

b.Express the equilibrium market tightnessin terms of the parameters of the model,k, and.

c.Express the equilibrium unemploymentuin terms of the parameters of the model.

w=(e+b)+(qm) 1N

Draw the locus of (w,N) that satisfies the labor supply and no-shirking conditions and identify theequilibrium of the economy.

d.Lety= 1,b= 0.75,= 0.025,= 0.5 andk= 0.5. Compute the equilibrium market tightnessand the equilibrium unemploymentu.

e.If the unemployment benefit decreases fromb= 0.75 to 0.5, what happens to the equilibrium market tightnessand to the equilibrium unemploymentu? Explain your findings.