Question 4) Consider a simple economy with search and unemployment. The matching function is given by M = em(Q, A) = eQ^2/5 A^3/5. The government supplied employment insurance is b = 0.5, the worker productivity is z = 1.3 and the firms' cost of posting a vacancy is k = 0.1 including 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 that Q is the labour force. In DMP model, we consumers make their job search decisions based on the current level of the expected payoff from the job search . Furthermore, the relationship that is derived by maximizing the consumer's utility between Q and is given by Q = N[(v - b)/(z - b)].

a. Compute the equilibrium market tightness j.

b. What is the unemployment rate u? c. What is the vacancy rate v?

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