Problem 1 (Search and Unemployment) [ 40 marks ] Consider a simple economy with search unemployment. The matching function is given by M = egg-WAVE. 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 meancy. 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 payo' a consumer obtains from searching for work.J EV. Further.J we assume that the relationship between Q and EV, which can be derived by maximizing the consumer's utility is given by: (EV 41)) Q=N( zb