Schooling choice under perfect information. Suppose that an individual is deciding whether or not to complete high school.

Schooling choice under perfect information. Suppose that an individual is deciding whether or not to

complete high school. If she leaves school after only 11 years, she will earn $13,000 today (period 0) and

$16,000 tomorrow (period 1). On the other hand, if she completes high school, or leaves school after 12

years, she will earn $30,000 tomorrow.

a. Suppose that she has access to credit markets. If the interest rate is 3 percent:

i. What is the present value of the wage benefit of education in the second period?

ii. What is the opportunity cost of staying enrolled in school?

iii. What is her optimal level of schooling?

b. Suppose now that she does not have access to credit markets, and her discount rate is 10

percent.

i. What is her marginal rate of return to schooling?

ii. What is her optimal level of schooling? [Hint: use discount rate in calculation as you

would use the interest rate when there is access to credit markets.]

iii. If her discount rate were 6 percent instead of 10 percent, would she be more patient or

less patient? Explain.

c. Compulsory schooling laws establish the ages at which children must be enrolled in school.

Suppose that our individual lives in a state where she can’t leave school until she reaches age 18.

i. Assuming that she has no access to credit markets, do you think that such a policy affect

her decision about completing high school? Explain.

ii. Assume once again that she can borrow. Does such a policy affect her educational choice?

Explain.

iii. Compulsory schooling laws force some people to invest more in education than they

otherwise would. Why might the state pursue such a policy?

Signaling. Jane and Catrina are both deciding whether to complete college. Catrina likes school, andhas the cost function C (S)Catrina = 25,000S , but Jane thinks that schooling is painful and has the costfunction C (S) Jane = 30,000S , where S represents years of college. Jane and Catrina will eventually beemployed at the same firm, which cannot observe productivity.a. Given the assumptions of the signaling model, which individual (Jane or Catrina) is higherproductivity?b. Suppose that this firm offered everyone, regardless of schooling, earnings equal to $500,000 (inpresent value).2i. How many years of college will Jane choose to get? How many years of college willCatrina decide to get?ii. Is this a pooling or separating equilibrium? Explain.c. Now suppose that this firm offers employees with at least 4 years of college ( S ≥ 4 ) earningsequal to $600,000 (in present value) and employees with less than 4 years of college ( S < 4 )earnings equal to $400,000 (in present value).i. How many years of college will Jane choose to get? How many years of college willCatrina decide to get?ii. Is this a pooling or separating equilibrium? Explain.d. Now suppose that this firm offers employees with at least a professional degree ( S ≥ 7 ) earningsequal to $600,000 (in present value) and employees with less than a professional degree ( S < 7 )earnings equal to $400,000 (in present value).i. How many years of college will Jane choose to get? How many years of college willCatrina decide to get?ii. Is this a pooling or separating equilibrium? Explain.