$($Borjas$,$ Problem $6-1.$ See also Slides $21-22$ of Lecture $21$ for an analogous example.$)$ 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 only for 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 has a discount rate of $5\%.$ Which career will she pursue?

b$)$ What if she has a discount rate of $15\%?$ Will she choose a different option? Why?

c$)$ For which discount rate $($denoted by r$)$ would Debbie be indifferent between the two career options?

What would her present value be in that case?