# ECO101H1 Chapter Notes - Chapter 7: Marginal Revenue, Capital Accumulation, Marginal Product

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44

CHAPTER 7

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,

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.

(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:

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.

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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

167,254$

2.1

000,90

2.1

000,110

000,100 2=++=

HS

PV ,

000,225$

2.1

000,180

2.1

000,180

000,50 2=++−=

COL

PV ,

and

778,227$

2.1

000,400

2.1

0

000,50 2=++−=

PhD

PV .

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

discount rate?

The returns to increasing one’s education from one to two years of college and then from two to three

years of college are

%75.18

16$

16$19$

21 =

−

=

to

r and %53.10

19$

19$21$

32 =

−

=

to

r.

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.

## Document Summary

Pvpianist = ,000 + ,000/(1. 05) = ,190. 48. 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. In the second, she works in the labor market. If debbie becomes a marine biologist, she will spend ,000 on education in the first period and earn ,000 in the second period. If she becomes a concert pianist, she will spend ,000 on education in the first period and then earn ,000 in the second period. (a) suppose debbie can lend and borrow money at a 5 percent annual rate. 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, and. If the rate of interest is 15 percent, however, the present value calculations become and.