Question

1. Debbie is about to choose a career path. She has narrowed her options to two alternatives. She can either become a marine biologist or a concert pianist. Debbie lives two periods. In the first, she gets an education. In the second, she works in the labor market. If Debbie becomes a marine biologist, she will spend $15,000 on education in the first period and earn $472,000 in the second period. If she becomes a concert pianist, she will spend $40,000 on education in the first period and then earn $500,000 in the second period.

a. Suppose Debbie can lend and borrow money at a 5 percent rate of interest between the two periods. Which career will she pursue? What if she can lend and borrow money at a 15 percent rate of interest? Will she choose a different option? Why?

b. Suppose musical conservatories raise their tuition so that it now costs Debbie $60,000 to become a concert pianist. What career will Debbie pursue if the interest rate is 5 percent?

Answer 1

Ans.A-Debbie will compare the present value of income for each career choice and choose the career with the largest present value. If the discount rate is 5 percent, PVBiologist = – $15,000 + $472,000/(1.05) = $434,523.81 and PVPianist = – $40,000 + $500,000/(1.05) = $436,190.48. Therefore, she will become a pianist. If the rate of interest is 15 percent, however, the present value calculations become PVBiologist = – $15,000 + $472,000/(1.15) = $395,434.78 and PVPianist = – $40,000 + $500,000/(1.15) = $394,782.61. In this case, Debbie becomes a biologist. As the interest rate increases, the worker discounts future earnings more, lowering the returns from investing in education. A Ans.B-Debbie will compare the present value of being a biologist from part (a) with the present value of becoming a pianist. The relevant present values are: PVBiologist = – $15,000 + $472,000/(1.05) = $434,523.81 and PVPianist = – $60,000 + $500,000/(1.05) = $416,190.48. Debbie will, therefore, become a biologist.