Problem 1 (Search and Unemployment) [ 40 marks ] Consider a simple econOmy with search unemployment. The matching fimdion is given by M = eQ1/2A1/2. Let b = 0.58, z = 1.5, k = 0.45, e = 0.945 and a = 0.5, where k is the cost of creating a vacancy. The working age population is N = 1000, and labour force denote by Q. As standard in DMP model, we assume that consumers make their job search based on the expected payoff a consumer obtains from searching for work, EV. Further, we assume that the relationship between Q and EV, which can be derived by maximizing the consumer's utility is given by: Q = N (mlha) 1. Calculate the market tightness 3'. Show your calculation in details. 2. What is the unemployment rate? 3. What is the vacancy rate? 4. Compute the expected payo' from the job search, EV, and solve for the equilibrium number of job searchers, Q. 5. How many vacancies are posted in the ec0nomy? How many consumers are employed in this economy? What is the aggregate production? 6. COmpute the equilibrium wage. 7. Assume that the governement sets the wage 10% above its equilibrium value. What will be the unemployment rate and how does it compare to the initial one? Using diagrams explain how labour market tightness, j, and labour force, Q are affected in the high wage equilibrium