1. (30 points) Consider the DMP model and a technological change that reduces the costs of recruiting for firms, k. At the same time, there is an increase of the unemployment insurance benefit, b.

The two key equilibrium equations of the DMP model are

??v(Q) = b + em(1, j)(w ? b) = b + em(1, j)a(z ? b) ??

Eqm equations:

where Q is the labor force, b is unemployment insurance benefit, w is the wage rate, e is the efficiency of matching, j = A/Q is job market tightness, A is the number of firms 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, k is the cost of posting a vacancy by the firm, 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 firms, and (v) aggregate output. (The full mark will be given only to answers that com- ment on the changes?simply 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.)

1. (30 points) Consider the DMP model and a technological change that reduces the costs of recruiting for rms, Is. At the same time, there is an increase of the unemployment insurance benet, .5. The two key equilibrium equations of the DMP model are v(Q) = b + em(1,j)(w b) = b + em(1,j)a(z b) Eqm equations: 1 _ k _ k em (3' 1) _ zw _ {la){zb)' where Q is the labor force, I) is unemployment insurance benet, to is the wage rate, 6 is the eiciency of matching, j = 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, I: 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 yaxis 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.)