1. (40 Points) Consider our search model of unemployment. LetVudenote the value of an unemployed worker,Ve(w) the value of an employed worker with a job offerw,H(w) the fraction of job offers abovew,sthe separation rate,pthe job offer rate, andUthe unemployment rate. Unemployed workers receive some benefitbwhen unemployed (which lasts until the unemployed worker starts working). Assume all workers are identical.

(a) (10 Points) Assume that at datetthe unemployment rate isUt. State an equation that dictates the evolution over time of the unemployment rate (i.e.,Ut+1as a

function ofUt). Solve for the steady-state unemployment rate in this economy as a function of the reservation wagewand exogenous parameters.

(b) (10 Points) Suppose that the government decreases unemployment benefits tob0< band uses the savings to lower taxes paid by employed workers. Determine the effects on the reservation wage and on the steady-state unemployment rate in the model.

(c) (20 Points) Suppose that the government introduces a proportional payroll tax on wage costs, such that firms must pay the governmentfor every dollar paid in wages. How do you think firms would react to this within the context of the model? How will their response affect the reservation wage? Can you predict what happens to steady-state unemployment without making any further assumptions? The average unemployment rate in European countries, where payroll taxes are relatively high, is generally higher than in the U.S. What assumptions do you need to make in order to make the model's predictions consistent with this observation?