3. In a competitive economy with many firms there are two types of workers that look ex ante identical. Low productive workers (type Ls) have an outside option of 0 (dollar or util), a utility function of w=w, -2e,, where s, is utility, w, is the wage received and e, is the education obtained. An L-type worker has a productivity of O. A high-type worker (H-type) has an outside option of 0, a utility function of w-e, where is utility, w, is the wage received and e the level of education obtained. An H-type worker has a productivity of 2. For the firms the workers look identical. However, firms can observe the level of education a worker has obtained. The timing of the game is as follows: workers decide how much education to receive; firms then observe the level of education of a worker and make a wage offer; worker can accept the offer (and work for the firm) or reject the offer and receive their outside option. a. What are the incentive compatibility constraints for the L-type worker and the H-type worker respectively? Explain your equations. b. Construct a separating equilibrium in which employers can distinguish between high and low- type workers. What are the firm beliefs in your equilibrium? Use a diagram to help explain your answer. For what level of education would the high-type workers decline to get any education? Explain your answer. c. Now assume that the L-type worker has a utility function of u = 2w₁ -2e₁. Can you derive a new separating equilibrium with high and low type workers getting different levels of education (and wages)? Explain your answer.
3. In a competitive economy with many firms there are two types of workers that look ex ante identical. Low productive workers (type Ls) have an outside option of 0 (dollar or util), a utility function of w=w, -2e,, where s, is utility, w, is the wage received and e, is the education obtained. An L-type worker has a productivity of O. A high-type worker (H-type) has an outside option of 0, a utility function of w-e, where is utility, w, is the wage received and e the level of education obtained. An H-type worker has a productivity of 2. For the firms the workers look identical. However, firms can observe the level of education a worker has obtained. The timing of the game is as follows: workers decide how much education to receive; firms then observe the level of education of a worker and make a wage offer; worker can accept the offer (and work for the firm) or reject the offer and receive their outside option. a. What are the incentive compatibility constraints for the L-type worker and the H-type worker respectively? Explain your equations. b. Construct a separating equilibrium in which employers can distinguish between high and low- type workers. What are the firm beliefs in your equilibrium? Use a diagram to help explain your answer. For what level of education would the high-type workers decline to get any education? Explain your answer. c. Now assume that the L-type worker has a utility function of u = 2w₁ -2e₁. Can you derive a new separating equilibrium with high and low type workers getting different levels of education (and wages)? Explain your answer.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:3. In a competitive economy with many firms there are two types of workers that look ex ante
identical. Low productive workers (type Ls) have an outside option of 0 (dollar or util), a utility
function of "=w₁-2e,, where , is utility, w, is the wage received and e, is the education
obtained. An L-type worker has a productivity of O. A high-type worker (H-type) has an outside
option of 0, a utility function of w-e, where is utility, w, is the wage received and
e the level of education obtained. An H-type worker has a productivity of 2.
For the firms the workers look identical. However, firms can observe the level of education a
worker has obtained.
The timing of the game is as follows: workers decide how much education to receive; firms then
observe the level of education of a worker and make a wage offer; worker can accept the offer
(and work for the firm) or reject the offer and receive their outside option.
a. What are the incentive compatibility constraints for the L-type worker and the H-type worker
respectively? Explain your equations.
b. Construct a separating equilibrium in which employers can distinguish between high and low-
type workers. What are the firm beliefs in your equilibrium? Use a diagram to help explain your
answer. For what level of education would the high-type workers decline to get any education?
Explain your answer.
c. Now assume that the L-type worker has a utility function of u, =2w, -2e₁. Can you derive a
new separating equilibrium with high and low type workers getting different levels of education
(and wages)? Explain your answer.
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