7-1. Debbie is about to decide which career path to pursue. 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 annual rate. 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?
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,
PV Biologist $15,000 + $472,000/(1.05) = $434,523.81
PV Pianist– $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
PV Biologist $15,000 + $472,000/(1.15) = $395,434.78
PV Pianist– $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.
(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 discount rate is 5 percent?
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:
PV Biologist $15,000 + $472,000/(1.05) = $434,523.81
PV Pianist– $60,000 + $500,000/(1.05) = $416,190.48.
Debbie will, therefore, become a biologist.
44 7-2. Peter lives for three periods. He is currently considering three alternative education-work
options. He can start working immediately, earning $100,000 in period 1, $110,000 in period 2 (as
his work experience leads to higher productivity), and $90,000 in period 3 (as his skills become
obsolete and physical abilities deteriorate). Alternatively, he can spend $50,000 to attend college in
period 1 and then earn $180,000 in periods 2 and 3. Finally, he can receive a doctorate degree in
period 2 after completing his college education in period 1. This last option will cost him nothing
when he is attending graduate school in the second period as his expenses on tuition and books will
be covered by a research assistantship. After receiving his doctorate, he will become a professor in a
business school and earn $400,000 in period 3. Peter’s discount rate is 20 percent per period. What
education path maximizes Peter’s net present value of his lifetime earnings?
The present discounted values of Peter’s earnings associated with each of the alternatives are
PV =100,000+ 110,000 + 90,000 = $254,167 ,
HS 1.2 1.22
PV COL = −50,000+ 1.2 + 2 = $225,000 ,
PV PhD= −50,000+ + 2 = $227,778 .
Thus, the best option for Peter is to start working upon completely high school.
7-3. Jane has three years of college, Pam has two, and Mary has one. Jane earns $21 per hour, Pam
earns $19, and Mary earns $16. The difference in educational attainment is due completely to
different discount rates. How much can the available information reveal about each woman’s
The returns to increasing one’s education from one to two years of college and then from two to three
years of college are
$19 −$16 $21 −19
r1to2 =18.75% and r2to3= =10.53% .
Having observed their educational choices, we know that Mary’s discount rate is greater than 18.75
percent, Pam’s is between 10.53 percent and 18.75 percent, and Jane’s is less than 10.53 percent.
7-4. Suppose the skills acquired in school depreciate over time, perhaps because technological
change makes the things learned in school obsolete. What happens to a worker’s optimal amount of
schooling if the rate of depreciation increases?
If the rate of depreciation is very high, the payoff to educational investments declines. As a result, a
worker’s optimal amount of schooling will also fall as the benefits of education erode rapidly.
45 7-5. Suppose workers differ in their ability, but have the same discount rate. Is it possible for the
more able workers to choose less schooling?
This result is possible as long as more able workers have lowerinal-rate-of-discountcurves. For
example, if an 18-year-old basketball player can earn $3 million per year by entering the NBA after high
school whereas he would earn $3.25 million per year by entering the NBA after college, the opportunity
cost of college ($3 million per year) may be so great that the player opts to skip college. (A similar story
might explain why Bill Gates dropped out of Harvard.)
7-6. Suppose Carl’s wage-schooling locus is given by
Years of Schooling Earnings
(a) Derive the marginal rate of return schedule. When will Carl quit school if his discount rate is 4
percent? What if the discount rate is 12 percent?
The marginal rate of return is given by the percentage increase in earnings if the worker goes to school
one additional year.
Schooling Earnings MRR
Carl will quit school