Question ] Consider the following matching model of the labour market. Let u denote the unemployment rate, v denote the vacancy rate, and O denote "labour market tightness": O=v/w . The matching function is given by: M = Mu (1-e-*) (1) where M > 0 is a parameter, and e = 2.7183. The number of separations, as a fraction of the labour force, is given by: S = (1-H)s (2) where se (0,1) is a parameter, representing the separation rate. In any steady state, the number of matches must equal the number of separations: S =M (3) a) (10 marks) Given the parameter values M =0.9,s = 0.05, derive the Beveridge curve for this labour market, expressing a as a function of 0. Now, from the firms' optimization problem, suppose the equilibrium value of O is given by: 0' =0.5+.0ly-c-r-$-s+M (4) where y > 0 is the output per matched worker, c> 0 is the cost of vacancy creation, " >0 is the discount rate, and $ 6 (0,1) represents workers' bargaining power. b) (10 marks) Given the values y=110, c=1, r=0.05, $=0.5, s=0.05, M =0.9, and using your results from Question (a), along with equation (4), compute the equilibrium values of 0', u' , and v. c) (10 marks) How do your answers to Question (b) change if of increases to =0.67 Illustrate this change, using a Beveridge curve diagram and explain, briefly