There are two types of workers in the labor market. Low skilled workers have a productivity of 500, and high skilled workers have a productivity of 1000. The cost of education for low skilled workers is $150 per year, and the cost of education for high skilled workers is $100 per year. The population share for high skilled workers is 80%.

(1) (10 points) Suppose a firm offers a wage of $500 to workers with less than 4 years of education and $1000 to workers with 4 or more years of education.

(2 points) What is the educational decision for low skilled workers under this wage structure?

(2 points) What is the educational decision for high skilled workers under this wage structure?

(2 points) What is the average wage that the firm pays under this wage structure?

(2 points) What is the average productivity of all workers in the population?

(2 points) Does there exist an equilibrium under this wage structure? If so, is it a

separating equilibrium or a pooling equilibrium?

(2) (10 points) Suppose the firm now offers a wage of $500 to workers with less than 2 years of

education and $900 to workers with 2 or more years of education.

(2 points) What is the educational decision for low skilled workers under this wage

structure?

(2 points) What is the educational decision for high skilled workers under this wage

structure?

(2 points) What is the average wage that the firm pays under this wage structure?

(2 points) What is the average productivity of all workers in the population?

(2 points) Does there exist an equilibrium under this wage structure? If so, is it a

separating equilibrium or a pooling equilibrium?

(3) (10 points) Suppose now the firm offers a wage of $1400 to workers with 6 or more years of

education and $900 to all other workers.

(2 points) What is the educational decision for low skilled workers under this wage

structure?

(2 points) What is the educational decision for high skilled workers under this wage

structure?

(2 points) What is the average wage that the firm pays under this wage structure?

(2 points) What is the average productivity of all workers in the population?

(2 points) Does there exist an equilibrium under this wage structure? If so, is it a

separating equilibrium or a pooling equilibrium?