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Chapter 15
Factor Markets
Chapter Outline
15.1 Factor Markets
A Firm’s Short-Run Factor Demand Curves
A Competitive Firm’s Short Run Factor Demand Curve
Effect of a Change in the Wage
Solved Problem 15.1
A Noncompetitive Firm’s Short-Run Factor Demand Curve
A Firm’s Long-Run Factor Demand Curves
A Competitive Firm’s Long-Run Factor Demand Curve
Comparing Short-Run and Long-Run Labor Demand Curves
Competitive Factor Markets
A Factor Market Demand Curve
Competitive Factor Market Equilibrium
Application: Black Death Raises Wages
Solved Problem 15.2
15.2 Capital Markets and Investing
Interest Rates
Discount Rate
Stream of Payments
Application: Saving for Retirement
Investing
Net Present Value Approach
Solved Problem 15.3
Internal Rate of Return Approach
Solved Problem 15.4
Durability
Application: Durability of Telephone Poles
Time-Varying Discounting
Time Consistency
Behavioral Economics
Falling Discount Rates and the Environment
Application: Falling Discount Rates and Self–Control
Capital Markets, Interest Rates, and Investments
Solved Problem 15.5
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15.3 Exhaustible Resources
When to Sell an Exhaustible Resource
Price of a Scarce Exhaustible Resource
Price in a Two-Period Example
Rents
Rising Prices
Application: Redwood Trees
Why Price Might Not Rise
Abundance
Technical Progress
Changing Market Power
Teaching Tips
Chapter 15 can be covered any time after Chapter 11. Section 15.1 on competitive factor markets can be
covered any time after Chapter 8. You might consider this option if your primary goal is to give maximum
exposure to the competitive model.
Students typically don’t have much trouble with competitive factor markets. It makes intuitive sense that
as long as a worker adds more value in output than their wage, they should be hired. The only point that
may require clarification is the difference between the marginal worker and the infra–marginal workers.
Students may need to be reminded of diminishing returns that cause MPL to fall and that only the last
worker’s marginal revenue product is equal to the wage.
Factor markets in monopolized industries follows fairly easily from the competitive model and can be
covered in a single class session. The most straightforward presentation is to simply compare factor
demands when the output market is competitive versus when the output market is a monopoly.
If most students have already taken a course in finance, then you can probably skip most of Section 15.4
and concentrate on the internal rate of return material as it relates to the investment in human and physical
capital. If not, you will need to begin with the time value of money. This is a topic that most students have
thought surprisingly little about. You might point this out to the class by asking them about their own behavior
(college students, as a group, tend to be somewhat myopic). If your department does not have a finance
requirement, students are likely to receive little formal exposure to this topic.
You might begin the discussion by trying to get the class to state the important difference between
durable and nondurable goods. Stock and flow variables are distinguished by whether they provide a
one-time service (or utility) or a stream of services over a period of time. Once the class is comfortable
with the concept of a capital good, you can ask them how the decision to purchase such a good should be
made. You might frame the discussion by asking if the U.S. government should expense all government
expenditures in the current period when calculating the budget deficit. If your school has any substantial
capital projects under way, you can frame the question with respect to the school’s budget process. The
trail of the discussion logically leads to the decision to not invest in any capital goods project unless it pays
for itself in a single year. As this is clearly not the case, you can introduce the real and nominal interest
rate, inflation rate, and present value as tools to calculate the wisdom of human or physical capital goods
investment. You may want to distinguish between the discount rate and the depreciation rate, which is
strictly an accounting rule. Although depreciation rates have tax consequences that affect the cost of
capital, they are not related to the longevity of capital in any systematic way.
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Section 15.2 describes the process of making rational choices over time. Current events are a great way to
get the class interested in this topic. It may be the agreement of a top executive to a compensation package
in which little is paid in cash and the balance comes in the form of stock options, or the decision of Americans
to retire early or continue working past age 65. The popular press is a continual source of anecdotes about
individuals and firms struggling with the decision to take an action sooner or later. Likewise, in Section
15.3, the tension between business interests and environmental groups over natural resource use gets lots
of media attention. Frequently, the source of the tension is the implicit discount rate that each side is using
to calculate the value of the resource in question.
Additional Applications
A Temporary Fix for Restrictive Labor Law in Europe1
For decades, European firms have struggled with very strict labor laws and union agreements that made
laying off unneeded workers nearly impossible. The inability to trim the labor force when necessary made
many firms reluctant to add new workers. Recent changes in labor laws, combined with an increased
willingness to accept flexible arrangements by local unions, have made for big changes in the labor markets
in France, Sweden, and Spain. As part of the change in hiring policies, firms are making much greater use
of temporary employees—who can be laid off without severance—than ever before. This gives the firms
the flexibility to add new workers when needed, without having to make long–term commitments. In
Sweden, several large industrial employers, including Ericsson, Saab, and ABB, have a pool of “shared”
workers, a solution that pleases the firms as well as many of the workers. Niclas Arkstal, a technician who has
assembled air conditioners and telephones for separate companies, likes the new system: “It’s so
flexible . . . I don’t worry about boredom anymore.”
The countries where there have been changes in work rules have experienced better job growth than
countries that have been slow to embrace flexibility. Since 1994, job growth is up 6.2 percent in Spain, 6.9
percent in The Netherlands, and 4 percent in Britain. In contrast, Germany experienced a 3.3 percent
decrease in employment between 1994 and 1997. With the large increases in temporary employment, temp
agencies are among the fastest growing firms in Europe. Italy was the last to legalize temporary
employment agencies. Manpower Inc., a U.S.-based firm with offices throughout the recently deregulated
countries in Europe, plans to open 35 offices there this year.
In many cases, the use of temps has restored firms to profitability. Moulinex, a French household appliances
maker, after five straight years of losses, reduced its 11,300 employee work force by 2,700 and reduced work
hours from 39 to 33 per week for the remaining workers. They also employ as many as 1,000 temps at any
given time to keep up with production. As a result, the company earned a profit of $5.5 million in 1997
and expects to be profitable again in 1998. Chairman Pierre Blayou noted, “In France, we are afraid of hiring
full time workers. Once you feel that you have readjusted the company, you are cautious. You think, ‘If I
lose an order, I have to start the whole process over again.’ We don’t want to do this every six months.”
1. Are there certain types of employees that a firm would not want to lay off and try to rehire frequently?
What factors would cause a firm to keep such a worker for extended periods of slack demand?
2. If temporary employees are in competition with full-time union employees, what do you predict will
happen to wage rates in the full time sector?
1 Helene Cooper and Thomas Kamm, “Loosening Up: Much of Europe Eases Its Rigid Labor Laws, and Temps Proliferate,” Wall
Street Journal. June 4, 1998:A1, A6.
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Money-Back Interest2
The Mellon Bank wrote to potential MasterCard customers that they were offering “the first and only
credit card that can refund up to 100 percent of your interest. . . . You just have to ask for it.” With their
Cornerstone MasterCard, you can get a “full” rebate on your interest payments if you wait 20 years and
a partial rebate after two years. Offsetting this advantage, the card charged an interest rate that was 6 or
more percentage points above the lowest rate available. Moreover, you lost the entire rebate if you didn’t
use the card for any 12-month period within the next 20 years.
Does this offer sound good to you? It did to 700,000 people who got the card. Apparently these customers
did not understand that repayment in 20 years is not worth a lot today. After adjusting for inflation, the
present value of such payments is small. Moreover, cardholders face uncertainty. Mellon may not exist in
20 years. Even if it does, the bank reserves the right to change the terms, charge higher interest, or cancel
the plan altogether, leaving the customer no option but to cash out with a partial rebate.
Suppose you had a $2,500 balance on your account in 1995. The Cornerstone card’s rate was 20.9 percent,
so you’d pay $522.50 in interest. A competing Wachovia card that had a 12.9 percent rate would have
resulted in $322.50 in interest. Suppose you kept the Cornerstone card for two years and asked for the
rebate. At the end of the second year, you would receive a 25 percent rebate of your interest payments, or
$130.63. Even ignoring adjusting for inflation and discounting, you’re better off with the less expensive
card, which saved you $200 in the first year. If you got a full rebate in 20 years, the $522.50 you would
receive isn’t worth much today. Ignoring inflation, and assuming annual compounding, the present value
of that future payment would only be $46.15 assuming a 12.9 percent rate (the lower of the two card
rates). At the higher rate of 20.9 percent, the present value of the payment would only be $11.74. It’s a
good thing you are less gullible than at least 700,000 people.
1. Why might a “no annual fee” credit card like to insist that its customers leave some portion of each
monthly statement unpaid for at least one month?
2. Is there some set of interest rates for the Mellon and Wachovia cards at which the consumer would be
indifferent between receiving the rebate and paying interest with a traditional card? How would you
calculate it?
Discussion Questions
1. Sports stars are paid many times more than school teachers. Is that desirable from a social standpoint?
2. Comparable worth proponents call for wages to be set by the social value of the job rather than the
value of the work to the employer. How would such an approach affect our economy? What are the
social advantages and disadvantages of this approach?
3. U.S. law allows labor unions to organize entire industries. How would a union’s market power
change if it had to organize each firm individually?
4. How many monopsonies can you identify? In which markets do they operate?
5. Suppose there is only one firm in a town that hires workers. Under what conditions is the firm a
monopsonist?
6. Some past civilizations, thinking that interest should not be charged, passed usury laws forbidding it.
What are the private and social benefits or costs of allowing interest to be charged?
2 Saul Hansell, “Plastic That Pays You Back May Not Be Your Best Payoff,” New York Times, March 19, 1995:12.
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7. Imagine you run a cigarette company and are interested in maximizing profits. You know that the
more cigarettes you sell this year, the greater the number will be of customers who die. If your
advertising affects the number of cigarettes your customers smoke per day, should you encourage
them to smoke more or less? Does your answer depend on the interest rate? What else will it depend
upon?
8. Can we analyze land in the same way we analyze other types of capital?
9. Is it profitable for a monopolist to engage in planned obsolescence, where it makes products that last
for a very short time even though it could produce products that would last much longer for minimal
additional cost?
10. We analyzed how prices are determined with an exhaustible resource. How do you think the answer
would change if the resource were renewable, like water?
11. If a monopoly owned all the world’s oil, it would raise prices so the oil in the ground would be used
up less rapidly. Does it follow that the world would be better off if the oil supply was monopolized?
12. If you own an oil well in the North Sea or America, are you more likely to sell your oil this year or in
two years if you think that OPEC will fall apart sometime next year?
13. Does a monopoly make decisions about investing in capital differently than a competitive firm? If so,
how?
Additional Questions and Problems
1. In a competitive market, firms sell output at a price of $20. Marginal productivity per hour of the
workers is described by the equation MPL = 40 − L. What is the firm’s demand curve for labor? If
the firm can hire labor from a competitive labor market at a wage of $5 per hour, how many workers
should the firm hire?
2. If a firm produces using fixed proportions production, what is the effect on labor demand of an
increase in the rental price of capital? How does your answer differ if the inputs are perfect
substitutes instead?
3. If the demand for labor is perfectly inelastic and the supply is perfectly elastic, what is the incidence
of a tax of $1 per hour on wage? Show the solution using a graph.
4. Demand for labor in a given market is LD = 100 − 2w and supply is LS = 2w. Compare the competitive
and monopsony equilibrium levels of employment and wage.
5. Suppose a firm produces according to the production function Q = 2L0.6K0.2, and faces wage rate $10,
a rental cost of capital $5, and sells output at a price of $20. Compute the profit-maximizing factor
demands. (Hint: See Equation 15.7 in the text and discussion that follows it.)
6. Show using a graph that if a monopolist in an input market faces a monopsonist in the same input
market, the equilibrium level of input use is indeterminate.
7. Major league baseball has occasionally been troubled by extended strikes that have eroded fan
interest in the game. Can you interpret the difficulties the players and owners have had in negotiating
collective bargaining agreements in the context of the models in this chapter? Explain.
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8. Use a graph to show the effect of free agency on the wages paid by a team in the NHL. Assume that
prior to free agency players could only play for the team that drafted them.
9. In a competitive market, a firm produces a good with price p. Suppose the marginal product of the
labor it hires is MPL. What is the marginal revenue product of its labor?
10. Suppose the interest rate is 7 percent. Which is worth more, $10,000 today or $18,000 seven years
from now? Which would you prefer if your discount rate was zero? What if it was infinite?
11. Compare the value of $1,000 invested at 5 percent after three years when interest is compounded
annually versus semi annually (twice a year).
12. Given that all individuals face the same interest rates at any given time, why do we observe
differences in savings versus consumption between individuals with the same income level?
13. Using Equation 15.6, discuss the incentives of students if government loans are available for college
at a nominal interest rate that is less than the inflation rate.
14. A firm is considering buying a machine for $500. It expects to earn $200 profits from its use for each
of the next four years, after which the machine can be sold for scrap in year five for $50. At an interest
rate of 10 percent, use the net present value rule to decide if they should make the investment or not.
15. Answer Question 14 using the internal rate of return (irr) approach, assuming that the machine costs
$1,000 but lasts forever.
16. One of the difficulties in choosing an appropriate level of advertising is judging the longevity or
persistence of its effects. Suppose you could run an ad that cost $9,000 that would increase sales by
$3,500 for the next three years. Should you purchase the ad or not if the current interest rate is 5
percent? What if the price increased to $10,000?
17. If all government expenditures are expensed (paid for in the current period) rather than amortized
(paid for over the life of the commodity), what is the wisdom of a balanced budget amendment?
How would it alter the physical and human capital investment decisions made by the government?
18. Why might a college athlete invest heavily in training to become a professional basketball player
given that the chances of succeeding are less than 2 percent? Does this mean that investing in human
capital in the form of practicing jump shots is necessarily a bad investment?
19. When the Federal Reserve Board acts to cut interest rates, they hope to stimulate the economy.
However, some individuals are made worse off by these changes. Who benefits and who suffers
when interest rates fall?
20. If an investment would generate a steady profit flow of $10 million a year forever and its market
price is $100 million, what is the internal rate of return?
21. Suppose you buy a big-screen TV with $1,000 down and $500 per year for the next two years. If the
interest rate is fixed at 5 percent, what is the present value of the TV?
Answers to Additional Questions and Problems
1. Calculate the marginal revenue product of labor, and set it equal to the wage to determine labor demand.
dL = MRPL = p3 MPL = 20(40 – L) = 800 – 20L