Consider a simple economy with search and unemployment. The matching function is given by

M = em(Q, A) = eQ^2/5 A^3/5,

where the government supplied employment insurance is b = 0.5, the worker productivity is z = 1.3, firms' cost of posting a vacancy is k = 0.1, the matching efficiency parameter is e = 0.4191 and the worker's bargaining power factor is a = 0.5. The working age population is N = 1000 and we denote by Q the labour force. As standard in DMP model, we assume that consumers make their job search decisions based on the current level of the expected payoff from the job search . Furthermore, we assume that the relationship between Q and , which can be derived by maximizing the consumer's utility, is given by:

Q= N (v-b/z-b )

1. Compute the equilibrium market tightness j.

2. What is the unemployment rate u?

3. What is the vacancy rate v?

4. Compute the expected payoff from the job search and deduce the equilibrium number of job searchers Q.

5. How many vacancies are posted initially in the economy?

6. How many workers are involved in the production process? What is the aggregate production?

7. Compute the equilibrium wage

8. Assume the government sets the wage 20% above its equilibrium value. Find the new unemployment rate. Compare it to the initial one.