l. (30 points) Consider the DMP model and a technological change that reduces the costs of recruiting for rms, 1:. At the same time, there is an increase of the unemployment insurance benet, I). The two key equilibrium equations of the DH]? model are 0(6)) : b + em(1,j)(w b) = b + em(1,j)a(z b) Eqm equations: . l _ It _ 4 em (3-11) zw _ (ham-b)\" where Q is the labor force, I) is unemployment insurance benet, a; is the wage rate, (3 is the efciency of matching, 3' = A / Q is job market tightness, A is the number of rms posting vacancies, M' is the number of successful matches given by M : em(Q, A), m(-, -) is the matching function which is Constant Returns to Scale in Q and A, a. is the share of total match surplus that is allocated to the worker, is is the cost of posting a vacancy by the rm, and z is a worker's productivity. (a) (10 points) Show the diagrams for all possible scenarios, clearly labelling axes, and showing all the relevant. values on the X-axis and y-axis before and after the change. (b) (20 points) Discuss economics behind the possible effects of changes on i) labor market tightness; ii) unemployment rate; iii) labor force; (iv) the number of rms, and (v) aggregate output. (The full mark will be given only to answers that com- ment on the changessimply stating direction of the change will be not enough. Your answer should acknowledge that various scenarios are possible, that is, if a change is ambiguous you should clearly state so and explain why.)