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Question 1 : Search and Unemployment [35 marks] Consider a simple economy with search and unemployment. The matching function is given by M = em(Q, A) = eQ3/11 A8/11 where the government supplied employment insurance is b = 0.562, the worker productivity is z = 1.5, firms' cost of posting a vacancy is k = 0.45, the matching efficiency parameter is e = 0.955 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 W. Furthermore, we assume that the relationship between Q and EW, which can be derived by maximizing the consumer's utility, is given by: EW - b Q =N (1) z - b1. Compute the equilibrium market tightness j, the unemployment rate u, and the vacancy rate 1). [07 marks] 2. Compute the expected payoff from the job search W and deduce the equilibrium number of job searchers Q. [05 marks] 3. How many vacancies are initially posted? How many consumers are employed in this econ- omy? What is the aggregate production? [05 marks] 4. Compute the equilibrium wage. [05 marks] 5. Assume the government sets the wage 10% above its equilibrium value. What will be the unemployment rate and how does it compare to the initial one? [05 marks] 6. Assume the economy is at the equilibrium of Question 1), compute the percentage change in the matching efciency e that is needed to reduce the unemployment rate by 10%. [08 marks]