CHAPTER 11
TEACHING TIPS
1. This chapter introduces several concepts that students will discover have interesting
applications in the real world and in their own experience. Discussing these applications,
perhaps using the text’s examples, will keep things lively.
2. The foundations for much of the analysis have been laid in previous chapters. It will
probably be helpful to emphasize those connections. In particular, the chapter uses
applications of utility theory and consumer choice (chapters 3 and 4), as well as game theory
and public goods (chapter 10).
3. Probabilities play a greater role in this chapter than perhaps any other, although the
level of complexity is kept low. Students who have poor preparation may need a little review.
4. The analysis of the “lemons problem” may create some confusion if it is not explained
carefully, as some students may be confused by “the demand curve that slopes up” in Figure
11.4. It may help to remind them that a good’s attributes are held constant when a demand
curve is drawn, but a different curve is needed to analyze the effect when attributes can
change.
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ANSWERS
R1. Suppose a woman named Neleh has the convex utility function shown in Figure
M11.1, showing increasing marginal utility for income. If her income is 40, she gets utility of
70 utils (point A). If her income is 50, she gets 110 utils (point B). If her income is 60, she
gets 200 utils (point C). If she were neutral with regard to risk, her utility from income of 50
would be halfway between her utility at 40 income and her utility at 60 income, which would
be 0.5(70) + 0.5(200) = 135. This utility/income combination is graphed as point M, and
represents the utility she would get from a situation that gave her a 50% chance of getting an
income of 40 and a 50% chance of an income of 60. But M is above B, which means that the
utility she would get from an income of 50 is actually less than her expected utility of a fair
gamble with the same expected total. In other words, she would prefer the 40-60 gamble to a
50 income “sure thing.” Compared to the 40-60 risky income, Neleh’s certainty equivalent
income is shown on the diagram at 54 (point N). She would be indifferent between a sure
income of 54 and a fair gamble giving her an equal chance of either 40 income or 60 income.
The payment Neleh would be willing to give up in order to take the risk is 4!
Figure M11.1 (Question 11.R1) Convex Utility and Risk Preference
R3. (a) Drug patents provide drug companies with incentives to take risks in researching
and testing new drugs. The added direct financial rewards of patent protection provide these
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incentives. However, the patents encourage drug and medical progress in other ways, since
research and test results will be made available to everyone interested, including other drug
companies, as part of the patent process. Also, the protection from competition granted by a
patent reduces the costs to drug companies of publishing their research results. The cost to
consumers will be that new drugs protected by patents will be priced higher than if the same
drugs were produced with greater competition.
(b) The main rationale for patents is that they encourage costly current activities
with uncertain future benefits. The benefits to society of patent protection are mostly longterm, since research will yield its results in the future. Most of the costs to producers are short
term, as are the higher prices (costs) to consumers. When new drugs are discovered in the
future, producers and consumers will both benefit. Also, when patents expire, most useful
drugs are produced generically by many companies and prices of previously-discovered drugs
will fall. (See Example 11.7)
R9. Adverse selection is the result of asymmetric information, and occurs when one
party in a trade knows more about the service or good being exchanged than the other.
Generally, buyers have less information about the good being purchased than sellers do. If the
buyers are aware of this, they will reduce the price they are willing to pay for a good as a
means of compensating for the risk involved.
R10. A seller’s reputation is one additional piece of information that buyers can use in
evaluating a good’s quality, even if product quality not otherwise observable. Thus, buying
from a reputable seller is less risky than buying from someone else. If consumers value high
quality products, then it will benefit producers to make them and establish a reputation for
doing so, even if it is not profitable in the short term. The initial cost to the firm is an
investment that will raise a seller’s future demand as long as reputation is maintained.
T1. (a) If houses which are otherwise the same (in age, size, number of bathrooms,
electrical fixtures, exposure to weather, etc.) are repaired more frequently by second owners
than by original owners, that might be evidence that the “lemon” houses are put on the resale
market, while the “peachy” or “cherry” houses are retained by the original owners. The second
owners of the lemons are then saddled with the repairs that the original owners avoided.
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(b) Other things being equal, the sooner a house is resold after purchase, the more
likely it is to be a “lemon.” If a new owner discovers too many problems that she does not
want to deal with, she may sell the house rather than put up with costly repairs. However,
since other factors may enter into the decision to sell a house (such as changes in the local job
market, the quality of schools, transportation, the location of shopping and entertainment
centers, etc.) these should also be considered before determining that a house is available
because it is a “lemon.” Still, a home buyer who encounters a “motivated seller” of a recentlybuilt house is probably wise to question the motivations of the seller.
T2. Advertising does not necessarily mean that a product is better. However, advertising
a brand as being higher quality is more profitable if the quality of the product is indeed higher.
This is especially true of goods that are purchased repeatedly. If the claims of high quality are
not borne out by consumer experience, the advertising will eventually be ignored (and the
investment wasted). A firm that does not produce high quality goods would be more
successful to advertise its low price or “good value for the money.”
T3. Assume that buyers base their overall willingness to pay for a car on the average
value to them of a randomly-selected car, and that they know that 20% are lemons (although
they do not know which particular cars are lemons). Buyers will be willing to pay
0.8 × ($8,000) + 0.2 × ($2,000) = $6,800 for a car. This price is above the reservation price for
good cars ($4,000) as well as the reservation price for lemons ($600), so both kinds of cars
will be traded (although all of the lemons will be sold).
T4. There is an adverse selection problem with such loans, since only those individuals
who know or suspect that they have poor credit will apply for them. Thus, the risk of offering
such loans is higher, and the interest rate must be higher to compensate the lender for the risk.
In this case, the adverse selection risk falls to the “seller” of the loan rather than the “buyer.”
T5. Risk-preferring faculty members are more likely to select the short-term option,
while those who are risk averse will tend to select tenure. In addition, those who may desire
flexibility, such as the option to take time off from their careers for family matters or move to
accompany a spouse, will tend to take the short-term option. There may also be an adverse
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selection situation that results from the choice, but since tenure is granted only after a
probationary period and short-term contracts are subject to review before renewal, the effects
are mitigated to some degree. Still, if a new faculty member is sure that she would not be good
enough to be granted tenure, she may be more likely to choose the short-term option.
T6. A patent gives a firm the exclusive right to produce (or license others to produce) a
particular type of product. However, it does not prohibit others from producing substitutes that
may be similar or even superior.
T11. It seems clear from Example 11.4 that patrons did value hygiene to some degree.
However, the costs of establishing a private ratings firm might have been higher than the
benefit to the hygienic restaurants and health-conscious patrons alike. Hygienic restaurants
may have already been able to develop reputations for cleanliness, in a less costly way,
without such a ratings system. Also, a voluntary private hygiene rating firm would have
entailed a cost for the clean restaurants that would not have been borne by less clean ones.,
since no non-hygienic restaurants will voluntarily pay to inform customers of their condition.
Even some hygienic restaurants might have found the costs of being rated were higher than the
benefits, and thus not subscribed to the service. Therefore, the information from such a system
would have been valuable but incomplete.
Having all restaurants post the results of the health inspections does not impose
greater costs on hygienic restaurants than on non-hygienic ones, as a private mechanism would
have done (in effect). Since health inspections were carried out before anyway, the added cost
of the posting program is probably quite small, but shared by all restaurants. It also provides
much more information to consumers (and is thus more valuable to them) than only having
some hygienic restaurants signaling their quality. If all restaurants are rated, it also increases
the incentive for poor restaurants to improve, since they cannot merely keep their status secret.
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TEST BANK
NUMERICAL EXERCISES
Table N1 (Question N1)
Income
Utility
Income
Utility
Income
Utility
$20,000
600
$45,000
945
$70,000
1270
$25,000
685
$50,000
990
$75,000
1365
$30,000
760
$55,000
1045
$80,000
1470
$35,000
830
$60,000
1110
$85,000
1590
$40,000
890
$65,000
1185
$90,000
1730
N1. The table above shows the utility that Morris Better derives from various levels of
income. Use it to answer the following.
(a) Suppose Morris is offered two jobs that only differ in salary. One job pays $35,000 a
year, but at the other there is a 1/3 chance of earning $30,000, a 1/3 chance of earning $35,000,
and a 1/3 chance of earning $40,000. Which job will he prefer?
(b) Instead suppose that one job pays $50,000 a year, but at the other there is a 1/3 chance
of earning $45,000, a 1/3 chance of earning $50,000, and a 1/3 chance of earning $55,000.
Which job will he prefer?
(c) Now suppose that one job pays $80,000 a year, but at the other there is a 50% chance
of earning $75,000, and a 50% chance of earning $85,000. Which job will he prefer?
(d) What is true about Morris’s preference for risk in each of your answers to (a), (b), and
(c)?
N2. Suppose Patti Whack earns $75,000 a year. In any given year, there is a .001 (0.1%)
probability that she will be in an accident that disables her for one year, preventing her from
earning any income. She can buy insurance for $100 that will pay her regular salary for one
year if she is disabled. Is the insurance a fair gamble? What is its Expected Net Gain? Under
what (if any) circumstances will she buy it?
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N3. Trina Tron sells used video camcorders on ePort, an online auction site. From past
experience, she knows that about 25% of the camcorders will need some kind of repair,
usually costing about $200. Buyers would be willing to pay $300 for a good used camcorder,
but only $100 for those that need repairs. Shipping charges are paid by the buyers, and they
have already factored them into their offer prices.
(a) Suppose Trina is willing to sell a good camcorder only if she is offered at least $275,
and will sell a bad camcorder if she is offered at least $75. However, she doesn’t know which
are bad or good, so she would be willing to sell each one for the average of these values. She
informs buyers that 25% might be bad. What is the highest bid Trina can expect to get when
she sells a camcorder and will she be willing to sell any?
(b) Trina tests the camcorders, and determines which ones are good. However, she does
not tell the buyers which are which. She is still willing to sell a good camcorder only if she is
offered at least $275, and will sell a bad camcorder if she is offered at least $75, which
camcorders will she sell?
(c) Trina’s practices get her bad seller ratings on ePort, so she decides to disclose which
camcorders are good and which are bad. How does this change things?
ANSWERS TO NUMERICAL EXERCISES
N1. (a) $35,000 a year has a higher utility (830) than the expected utility of the other option:
1
/3 (760) + 1/3 (830) +1/3 (890) = 826.67 .
(b) He will be indifferent, since $50,000 a year has the same utility (990) as the expected
utility of the other option: 1/3 (945) + 1/3 (990) +1/3 (1045) = 990.
(c) A 50% chance of earning $75,000, and a 50% chance of earning $85,000 has expected
utility of 0.5(1365) + 0.5(1590) = 1477.5. This is higher than the utility of a certain income of
$80,000 a year (1470). Thus, he will prefer the uncertain option.
(d) In (a), Morris is risk averse. In (b), he is risk neutral. In (c), he is risk-preferring. If
you examine the utility values, you will see that Morris has declining MU for income up to
$50,000, and has increasing MU for income at higher levels.
N2. The insurance is not a fair gamble, since a fair gamble requires that the net gain be zero. If
she is disabled, Patti is paid a net of $74,900 (her salary minus the premium), but if she is not
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disabled, she has a net of -$100 (the premium). Thus, the expected net gain is Exp(G) =
(0.001)($74,900) + (0.999)(–$100) = –$25.00.
She still might buy the insurance if she is sufficiently risk averse. If the expected utility with
the insurance is greater than the expected utility without the insurance, then she will buy the
insurance. If she insures, she is certain of net income of $74,900. If she does not, she has .001
probability of zero income and .999 probability of $75,000 income, so she insures if
U($74,900) > [0.001 × U(0)] + [0.999 × U($75,000)]
N3. (a) Buyers will be willing to pay the average value of the camcorders, or
0.25($100) + 0.75($300) = $250.
Trina would be willing to sell them if she gets bids of at least
0.25($75) + 0.75($275) = $225.
So, Trina will sell the camcorders, and the selling prices will fall between $225 and $250.
(b) Since buyers will only pay $250 for any given camcorder, Trina will only be willing
to sell the bad ones, since she will only sell the good ones if someone bids $275 or more. This
is the lemons problem, in which the bad camcorders crowd the good ones out of the market.
Notice, it only occurs if information is asymmetric, and Trina knows something that her buyers
do not. Eventually, Trina may discover that buyers share the information that all of the
camcorders she sells need repairs, and she will find the bids falling to $100 at most.
(c) Assuming that Trina’s reputation is not too badly tarnished, disclosing the condition of
each camcorder will eliminate the lemons problem. She can sell each bad camcorder for
between $75 and $100, and sell each working camcorder for between $275 and $300. If her
reputation is badly damaged, she might only be able to revive it by selling her good
camcorders for less than her reserve for a while, or offering some kind of guarantee.
OBJECTIVE QUESTIONS
B11.1
A person will always choose the option that gives her the highest expected wealth.
(T/F)
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B11.2
Pat is indifferent between the two options: (1) an hourly wage of $20 with certainly;
and (2) a wage that has a 25% of being $19, a 25% chance of being $20, and a 50%
chance of being $21. What is Pat’s risk premium?
a. $20.00
b. $.25
c. $0
d. $.50
B11.3
What is the expected value of a .9 probability of $100 and a .1 probability of $200?
a. $150
b. $112
c. $100
d. $110
e. $108
B11.4
If Chris is risk averse, which of the following is most likely to be Chris’s certainty
equivalent of a payment that has a .9 probability of $100 and a .1 probability of
$200?
a. $150
b. $112
c. $100
d. $110
e. $108
B11.5
If a person is risk averse, the certainty equivalent for an uncertain (risky) payment is
likely to be less than the expected value of the payment. (T/F)
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B11.6
The difference between the expected value of an uncertain (risky) payment and the
payment that would give a person the same utility if it were offered with certainty is
called the
a. risk premium
b. expected value
c. certainty equivalent
d. risk aversion
e. adverse selection
B11.7
Diminishing marginal utility of income implies that an individual
a. is risk preferring with regard to income.
b. is risk neutral with regard to income.
c. is risk averse with regard to income.
d. would accept a fair gamble if all of her income were otherwise riskless.
B11.8
A gamble is offered, in which the probability of winning is 75% and the probability
of losing is 25%. If the net payoff of winning is $100, how much is the cost of
losing, if the gamble is fair?
a. $75
b. $300
c. $125
d. $25
e. $100
B11.9
A risk adverse person with a large amount of risky or uncertain wealth will probably
accept some fair gamble or fair insurance contract. (T/F)
B11.10
A risk adverse person with a large amount of risky or uncertain wealth will probably
never accept any kind of unfair gamble or unfair insurance contract. (T/F)
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B11.11
Suppose you and a friend are in an electronics store, and you decide to buy a TV
there for $500. Your friend then mentions that he is 75% sure that the same model
was $40 cheaper at another store. How much is the value to you of checking the
price at the other store before making your purchase?
a. $40
b. $460
c. $20
d. $30
e. $0
B11.12
The “lemons” problem is one example of the effects of
a. informational cascades.
b. herd behavior.
c. adverse selection.
d. state-contingent outcomes.
e. unfair gambles.
B11.13
The “lemons” problem occurs when
a. goods differ in quality, but buyers cannot discern the differences before they buy.
b. goods differ in quality, but buyers can easily observe the differences before they
buy.
c. goods are identical, but sell for different prices.
d. goods differ in quality, and some sellers thus acquire a reputation for selling
higher quality goods than other sellers.
e. goods differ in characteristics, but buyers do not care about the differences.
B11.14
If consumers value high quality and are expected to make many future purchases,
establishing a reputation for producing a high quality product is likely to be
profitable regardless of whether the consumers are initially optimistic or pessimistic
about quality. (T/F)
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B11.15
When is a higher price most likely to be an indicator of a higher quality product?
a. It never will be.
b. When the costs to all consumers of obtaining information about product quality
are very high.
c. When the costs to at least some consumers of obtaining information about
product quality are low.
d. When new producers (without established reputations) introduce new products
about which little is known.
B11.16
Advertising will tend to be more profitable for firms selling low-quality goods than
for those selling high quality goods. (T/F)
B11.17
In an informational cascade,
a. individuals all receive the same information, and thus all do the same thing.
b. individuals don’t act on information they obtain themselves, but observe and
repeat the actions that others have taken.
c. individuals put greater weight on their own information than on the actions of
others, but still consider the actions that others have taken.
d. individuals ignore the actions of others, and unnecessarily duplicate the
information others have obtained.
B11.18
An informational cascade is most likely to form or persist in a group of people if
a. individuals in the group differ in their preferences or goals.
b. the information (signal) that prior decision-makers based their actions upon
becomes public knowledge.
c. a member of the group acquires private information that she knows is superior to
the information prior decision-makers possessed when they acted.
d. the actions of prior decision-makers is known, but the results of their actions are
not known.
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B11.19
In the absence of copyrights and patents,
a. there would be no monopolies, in the economic sense, since a copyright or
patent always creates a monopoly.
b. there would probably be just as many new creative works and inventions as
under a system with copyrights and patents.
c. new creative works and inventions would still be produced, but not as many as
would be produced if copyrights and patents existed.
d. no new creative works or inventions would be produced.
DISCUSSION QUESTIONS AND PROBLEMS
1. Why might a person buy insurance to protect her from the theft of a $1000
camera or item of jewelry and yet gamble a similar amount at a casino, where the odds are
against her winning?
2. What effect does seller reputation have on the lemon problem? What other ways
might be devised to reduce the problem?
3. For what specific goods would you expect advertising to be a signal of higher
product quality? Why?
4. There are some groups of consumers who actually enjoy learning about products
(“motor heads,” “nerds,” “gadget freaks,” etc.), even if it costs them something to do so. How
does that affect the analysis in the textbook of price as a signal of quality? What kinds of
goods would you then expect to have the greatest correlation between price and quality? Does
your experience match that expectation?
5. Name some kinds of decisions that might be subject to an informational cascade
(in addition to those listed in the textbook).
6. Can you name some decisions that would probably never exhibit an
informational cascade effect? Explain.
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7. Are informational cascades efficient or inefficient? Does anyone benefit from
them? Does anyone bear any costs because of them?
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CHAPTER 12
TEACHING TIPS
1. This Core chapter will require more than most in class time, as it covers a good
deal of material.
2. The Factor Employment Condition, mrpa = mfca, is most easily explained by
graphs. Algebraic development, beyond that already provided in the text, should be used for
strong classes only.
3. The demand for a factor, by the firm and the industry, is unfortunately rather
complex. Students will normally require a particularly careful explanation.
4. It is important, under the monopsony model of minimum wages, to explain why
the effective mfc has a horizontal range at the level of the minimum wage and then jumps to
rejoin the original mfc curve.
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ANSWERS
R1. The productivity consideration is the Marginal Product of the factor. The revenue
consideration is the Marginal Revenue associated with additional product.
R3. (a) If mrpa does not equal ha, the firm can always increase profits by altering the
quantity of factor A hired. If mrpa > ha, hiring another unit of factor A will entail a greater
addition to firm revenue (mrpa) than to firm costs (ha), so profits will increase. If mrpa < ha,
hiring one less unit of factor A will subtract more from firm costs than from firm revenues, and
again profits will increase.
(b) Whether a firm is a price-taker or a monopolist in the product market, this
condition must hold for profit maximization as long as the firm is a price-taker in the factor
market. (Monopoly power in the product market will be reflected in the shape of mrpa.)
(c) A subsidiary condition, that mrpa cuts ha from above, must also be met for
mrpa = ha to imply profit maximization.
R6. (a) Yes. The slope of the output isoquant shows the rate at which input B can be
substituted for input A while maintaining output. If one unit less of input A is employed,
the fall in output will be (approximately) mpa. The number of units of input B which must
be hired to maintain output will be (approximately) mpa/mpb. The approximation approaches
exactness for very small changes. So the absolute value of the slope at a point on the output
isoquant is mpa/mpb.
(b) The absolute value of the slope along an isocost line is the rate at which input B
can be traded for input A in the market — equal to ha/hb.
R7. (a) If only one factor is being varied then its mrp curve is the firm's demand curve
for that factor. However, with two complementary variable factors, we must consider the
interaction of the two. When the price of one factor A falls, the firm's first reaction will be to
move down mrpa and thus employ more of A. Since A is complementary to the second
factor B, this will raise mpb (hence mrpb shifts out). This causes the firm to employ more
B, which in turn raises mpa, shifting mrpa out. This process will bounce back and forth
until some limiting outcome is reached. The point is that after the fall in the price of A the
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firm finds itself on a new mrpa curve to the right of the old one. Since the demand curve for
A must pass through both mrpa curves, it must be flatter than both. The same reasoning
applies to the other factor.
(b) If the two factors are anti-complementary, a fall in the price of A will again
initially cause more of A to be employed. This reduces mpb and so shifts mrpb inward, thus
reducing the optimal employment of B. Since the factors are anti-complementary, this
increases mpa and so shifts mrpa out. As before, the final mrpa curve lies to the right of the
initial mrpa curve, so the demand curve will be flatter than either. Again, the same reasoning
applies to the other factor.
R9. (a) True. A drop in the hire-price of input A will lead to an increase in the
employment of input A and so normally to an increase in output. If the demand curve for the
product is inelastic, this will induce a relatively large fall in product price. So the industry will
respond to a fall in the hire-price with only a small increase in the employment of A (and a
small increase in output). The demand curve for input A will be steep and so tend to be
inelastic.
(b) True. The weaker the operation of the Law of Diminishing Returns, the more
gradual the decline in mpa, as more A is hired. When this decline is more gradual, firm
demand curves for factor A and the resulting market demand curve will be relatively flat and
so tend to be elastic.
(c) True. As the hire-price of input A falls, more A will be hired and so the
demand for complementary inputs will increase. The more elastic the supply curves of inputs
complementary to A, the greater the increase in employment of these inputs when the
demand for them increases. The large increase in the quantity of complementary inputs leads
to a large upward shift in mrpa and so to a relatively large increase in the quantity of factor A
employed. Consequently, each firm's demand curve (and so the market demand curve) for
input A will be flatter and so tend to be more elastic, the more elastic the supply of
complementary inputs.
T3. This problem hinges upon the degree of substitutability between factors. A plausible
answer is that, as all human beings share important similarities, different classes of labor are
likely to be better substitutes for each other than laborers are for machines. The greater the
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substitutability between two factors, the more an increase in the use of one will lower the
marginal product of the other. For example, employment of more soldiers by the Army will
make additional Marines less productive. Therefore, this argument suggests that different
classes of labor would be less complementary with each other than combinations of labor with
machines. (We do not have very strong confidence in this answer, however!)
T4. Unions might be expected to oppose immigration, since the resulting increase in
labor supply would depress the wages of union members.
*T6. (Amplification) Technological progress can take two forms: (1) labor saving,
where a given output can be produced by fewer workers (see Figure M12.1), (2) labor
amplifying, where a given number of workers can produce more output (see Figure M12.2). In
the labor-saving case, it is possible for the new tp to be flatter than tpL in the relevant region.
This would reduce mpL and thus tend to lower wage rates. In the labor-amplifying case, the
new tp is steeper than tpL.
Figure M12.1 (Question 12.T6) Labor-Saving Technological Progress
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Figure M12.2 (Question 12.T6) Labor-Amplifying Technological Progress
T7. If successful, a boycott lowers the product demand. This will then be reflected in a
lower VMP and MRP for labor, and thus a lower demand for workers’ labor.
T8. (a) The answer depends upon whether skilled and unskilled labor are
complementary or anti-complementary. If they are complementary, the reduced employment
of unskilled labor due to imposition of a minimum-wage law will reduce the demand for
skilled labor; if the skilled and unskilled are anti-complementary, the reverse will hold.
(b) Trade unions have historically favored minimum wage laws. Assuming, as is
true for the most part, that trade unions represent skilled workers, then presumably the skilled
workers regard the unskilled as anti-complementary to themselves. That is, they regard the
two categories as rather close substitutes, so that lesser employment of unskilled labor implies
more demand for skilled labor.
T9. If A and B are anticomplementary, the effect of a lower price for A will be similar to
the effect if they are complementary (the demand for A will get flatter). Thus, Figure 12.12 in
the textbook shows the effect on A’s demand of anticomplementary inputs as well as
complementary ones. The reason is that the lower initial price for A will increase employment
of A (sliding along the mrpa(b=b0) curve in the textbook’s Figure 12.12, to a quantity of A
such as â ). Since B is anticomplementary to A, the greater use of A will lower the Marginal
Product of B and lower the mrp for B. This will require that employment of B be reduced to
159
restore the Factor Balance Equation. The lower employment of B will increase the Marginal
Product of A, thus moving the mrpa curve up to one like mrpa(b=b1) curve in Figure 12.12
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TEST BANK
NUMERICAL EXERCISES
N1. Output X is produced with a single variable factor according to the production
function:
x = 100a2 – a3
(a) Find the expression for the Average Product apa. Find the maximum point of
apa.
(b) Find the expression for Marginal Product mpa. Find the maximum point of
mpa.
(c) At what value(s) of 'a' will apa and mpa intersect. Sketch the two curves.
N2. Suppose that the production function is given by the expression:
x = a0.5 + b0.5
(a) Provide general expressions for mpa, mpb, and MRSx (the Marginal Rate of
Substitution between the factors in the production of X). Sketch the isoquant map with 'a' on
the horizontal axis and 'b' on the vertical axis.
(b) If ha = 2 and hb = 1, what is MRSE (the Marginal Rate of Substitution in
Exchange)? What is the equation for the Scale Expansion Path (SEP)? Sketch it on the same
graph you drew in (a).
(c) Making use of the equation for the SEP, write down a relation between 'x' and
'a' that holds along this curve. Then write an equation relating C and 'a' along this curve.
Solving these equations simultaneously so as to eliminate 'a', express C as a function of 'x'.
Sketch this function.
N3. Consider a firm with a production function of the form:
f(a,b) = a0.5 b0.5
Suppose the use of both factors is increased by the same proportion, say by some scalar k. By
what proportion will output increase? Interpret.
161
N4. A monopolist hires a single variable factor, L, to produce output, Q, according to
the production function
Q = 4L0.25
The market demand function for this product is
Q = 40 – 2P.
If the services of factor L cost $2 per unit of L, no matter how much L is used, how much
L will be employed?
N5. An industry contains 100 perfectly competitive firms, each producing with a single
variable input. Each firm has the production function
qi = 2ai0.5.
The market demand function for the final product is
Q = 800 – 4P.
Assume unlimited amounts of A are available at a constant factor price of $50 per unit of A.
(a) How many units of A are employed by each firm when the industry is in shortrun equilibrium?
(b) Compute the price of the product and industry output in short-run equilibrium.
(c) Treating each firm as a price-taker at the price you calculated in (b), calculate the
demand for A, as a function of the wage w, for a single firm.
N6. Suppose a "typical" firm in the economy has a production function in the following
form, where X is output and m and f are quantities of male and female workers employed,
respectively, and k is a parameter reflecting the productivity of women in comparison with
men:
x = m0.5 + k(f) 0.5
(a) Assuming that, to begin with, k = 0.5, suppose the Scale Expansion Path (SEP)
equation were simply m = f. (The interpretation is that the wage ratio hf/hm is such that the
firm will want to employ equal numbers of the two sexes.) What would the wage ratio have to
be, numerically?
(b) As before, and suppose the wage for males is $2 per hour, and $1 per hour for
females. If the price of the final output is $8 per unit, solve for the optimal employment of
males and females.
162
(c) Suppose that, with k = 0.5 as before, a requirement of equal wage rates (hf =
hm) were imposed by law. What would the equation for the SEP become? Interpret in terms
of the firm's demand for male versus female employees.
(d) There is some reason to believe that current social changes are tending to
increase k. Suppose that k were to become equal to 1. What would then be the SEP at
equal wage rates?
ANSWERS TO NUMERICAL EXERCISES
N1.
(a) apa = tpa/a= 100a – a2. This is maximized where d(apa)/da =0
d(apa)/da = 100 – 2a = 0
a = 50
(b) mpa = d(tpa)/da = 200a – 3a2
mpa is maximized where d(mpa)/da = 0:
d(mpa)/da = 200 – 6a = 0
a = 200/6 = 33.33
(c) Set apa = mpa and solve for a: 100a – a2 = 200a – 3a2
This equation yields the solution values a = (0, 50). See Figure M12.3 for sketch.
Figure M12.3 (Question 12.N1) The apa and mpa Curves **>>
163
N2. (a) mpa = ∂x/∂a = 0.5a–0.5
mpb = ∂x/∂b = 0.5b–0.5
(0.5
" b % 0.5
mpa " a %
=$ ' =$ '
MRSx =
# a&
mpb # b &
See Figure M11.4 for a sketch. The isoquant shown is for x = 5.
!
(b) MRSE = ha/hb = 2/1 = 2
The SEP is expressed simply by the Factor Balance Equation:
(0.5
" b % 0.5
mpa " a %
=$ ' =$ ' = 2
MRSx=MRSE =
# a&
mpb # b &
(c)
x = a0.5 + b0.5
b = 4a (see Figure M12.4).
!
(substitute b = 4a).
x = a0.5 + 2a0.5
= 3 a0.5
a = x2/9
We know C = haa + hbb (Substitute b = 4a, ha = 2, hb = 1)
C = 2a + 4a
= 6a
Now substitute our earlier equation into this one:
" x2 % 2 2
C = 6$ ' = /3 x (See Figure M12.4 for sketch.)
#9&
N3. Just plug in the scalar as follows:
!
f(ka,kb) = (ka)0.5(kb)0.5 = k0.5a0.5k0.5b0.5
= ka0.5b0.5 = kf(a,b)
164
This production function is said to be "homogeneous of degree 1." The degree of homogeneity
is determined by the power to which the scalar k is raised after being cranked through the
function. In this case the scalar comes out unchanged as k1. This property of a function is
known as linear homogeneity, and the function is said to be linearly homogeneous. In
common English, linear homogeneity means that if you double all inputs you will double
output.
Figure M12.4 (Question 12.N2) The SEP and C Curves
N4. The Factor Employment Condition is ha = 2 = mrpL, where mrpL " MR(mpL).
First find MR and mpL:
165
!
MR = 20 – Q
mpL = dQ/dL = 2L–0.5
So mrpL = 2L–0.5 (20 – Q) = 2. Now we know from the production function that
Q = 4L0.5, so just substitute:
2L–0.5 (20 – 4L–0.5) = 2
40
40 " 8L0.5
= 2; 0.5 =10; L = 16
0.5
L
L
N5. (a) Since there are 100 firms, industry supply will be 100qi, so in equilibrium Q =
!
!
100qi = 800 – 4P. We know the firm will set ha = vmpa, and vmpai = P (mpai) = P(–Q/ –ai) =
P(a0.5). Therefore in equilibrium 50 = P(ai0.5). From the demand equation: 100qi = 800 – 4P,
we get P = 200 – 25qi. Therefore 50 = P × ai0.5 expands to 50 = (200 – 25qi) ai1/2. We now
have an equation in qi and ai, which we want to solve for ai. We know from the production
function that qi = 2ai0.5, so by substitution we get
50 = (200 – 50 ai0.5) ai0.5
The solution value turns out to be ai = 4.
(b) From (a), qi = 2 ai0.5 = 2 (40.5) = 4
Therefore industry output will be 100(4) = 400. In short-run equilibrium Q = 800 – 4P, so
400 = 800 – 4P. Solving, we get P = 100.
(c) From the Factor Employment Condition we get w = 100 ai0.5. Since the firm
employs a single variable factor, this relation specifies the firm's demand for A. All we have
to do is express ai in terms of w. The answer turns out to be ai =
N6.
!
(a) At the optimum:
1
hf
f "0.5
= 14 "0.5
hm 2 m
!
166
10000
w2
If, as specified by the form of the SEP, m = f, the right side of the equation is equal to 0.5.
Therefore the wage ratio must also be 0.5.
(b) The optimum condition is vmp " P(mp) = h for each factor.
vmpm = 8 (0.5m–0.5) = 2
vmpf = 8 (0.25f –0.5) =1
!
The solution values are m = f = 4.
(c) The equation of the SEP is expressed by the factor employment condition given
in (a). With equality of wages, this becomes:
f "0.5
=1
2m"0.5
If we express f in terms of m we get f = 4m as the equation of the SEP. The interpretation
is that the firm will demand 4 times as many males as females.
!
(d) If k = 1, then mpf = mpm, so the Factor Employment Condition reduces to m/f
= 1. The SEP becomes f = m.
OBJECTIVE QUESTIONS
B12.1
Along a production isoquant:
a. output is constant
b. input is constant
c. utility is constant
d. profits are maximized
e. None of the above.
B12.2
For a monopolist in the output market who is a competitor in the input market, the
profit-maximization condition is:
a. vmp = afc
b. vmp = mfc
c. MC = P
d. mfc = mrp.
167
B12.3
With a typical production function, the point of diminishing marginal returns is
reached before the point of diminishing average returns. (T/F)
B12.4
With a factor 'a' on the horizontal axis and 'b' on the vertical axis, a cheapening of
'a' would shift the SEP to the right. (T/F)
B12.5
As above. What is the vertical intercept of an isocost curve?
a. C/hb
b. ha/C
c. C
d. ha/hb.
B12.6
For normal factors, industry demand is always steeper than the horizontal sum of all
firms' demands. (T/F)
B12.7
The demand for a factor of production always slopes down. (T/F)
B12.8
A firm employs one factor (labor). The owner finds that when one worker is sick,
the value of production falls by $50. When a second worker is sick, production
falls by an additional $70. If the competitive wage is $60, what should the owner
do?
a. Keep the same number of workers
b. Fire two workers
c. Hire one more worker
d. Fire one worker.
B12.9
A competitive firm will never operate in the region of diminishing total returns.
(T/F)
B12.10
By similar reasoning, the firm will never operate in the region of diminishing
marginal returns. (T/F)
168
Figure B12.1 (Questions B12.11 and B12.12)
B12.11
Figure B12.1 shows a competitive firm producing one output (fish) using one input
(labor). What is the optimal employment of L, given a hire price of hLO?
a. Lo
b. L1
c. L2
d. L3.
B12.12
Returning to Figure B12.1, which of the following can definitely be inferred from
the diagram?
a. hL = mfcL
b. mfcL = vapL at the optimum
c. vmpL = mrpL
d. The firm is losing money.
B12.13
All profit-maximizing firms, whether monopolists, monopsonists, or competitors in
the input and/or output market, will set ha = mrpa, for some factor 'a'. (T/F)
B12.14
A monopsonist (sole buyer) will pay a wage less than mfc. (T/F)
169
B12.15
If the price of an input falls, a competitive firm will always use more of that input.
(T/F)
B12.16
Along the scale expansion path, which of the following necessarily holds?
a. mfc = mrp
b. The isoquants are tangent to the isocosts
c. MC = MR
d. None of the above.
Figure B12.2 (Questions B12.17 to B12.19)
B12.17
The initial optimum in Figure B12.2 is at point E. The flattening of the isocost
shows:
a. cheapening of 'a'
b. cheapening of 'b'
c. an increase in output
d. a fall in the use of 'a'.
170
B12.18
The substitution effect of the input price change is shown by the movement from:
a. F to G
b. E to F
c. E to G
d. S1 to D0.
B12.19
The scale effect is shown by the movement from:
a. E to F
b. F to G
c. E to G
d. None of the above.
B12.20
If the price of a regressive factor rises, what happens to output?
a. Rises
b. Falls
c. Unchanged
d. Can't be determined.
B12.21
The firm's demand curve for one of several factors is
its mrp
curve for that factor.
a. unrelated to
b. identical to
c. steeper than
d. flatter than
B12.23
If a monopsonist is forced to pay a minimum wage above the equilibrium wage, it
will employ fewer workers than before. (T/F)
171
DISCUSSION QUESTIONS AND PROBLEMS
1.
A firm which is competitive in all markets uses two variable inputs: K and L. The
price of L increases. Assuming that K and L are complements, explain (using vmp
diagrams) what happens to this firm's employment of K.
2.
A firm is competitive in all markets and uses two variable inputs, K and L. The
price of L rises, the price of output remains unchanged, and the firm, as a result of the price
change, uses less K than before. Is L an inferior factor to this firm? Explain.
3.
Production function: Q = 15L2 – 0.2L3
Labor Supply: hL = 144 + 23.4L
Market demand: P = $3 per unit of output
Find the optimal output, and the optimal employment of labor.
4.
Show how a minimum wage might increase the employment of labor under
monopsony. Show how it might not. Would the results be the same under competition?
5.
A firm has the production function:
Q = 4K + K0.5L0.5 + L
where Q, K, and L are the amounts of output, capital and labor respectively.
The hire price of capital is 4 and the hire price of labor is 1. Find the least cost combination of
K and L for producing an output of 100 units.
6.
A competitive firm produces output q with two variable factors, 'a' and 'b', with
hire prices ha and hb, respectively.
(a) Show the derivation of the firm's demand curve for factor 'a' assuming that 'a' and
'b' are complements.
(b) Show the derivation of the firm's demand curve for factor 'a' assuming that 'a' and
'b' are anti-complements.
(c) If vmpa = ha and vmpb = hb, then MC = P. True or false? Explain
172
CHAPTER 13
TEACHING TIPS
1. The leisure/income graph is an important application of preference theory generally and
indifference curves in particular. It may be necessary to briefly review some of the relevant
material in Chapters 3 and 4.
2. Students sometimes have difficulty grasping the idea that leisure is a "good," and this may
require some explanation.
3. The relation between Producer Surplus and economic rent is a subtle point, but rather
important. You may want to consider giving it a little more time in lecture.
173
ANSWERS
R1.
Land can be used for farming or as a backyard. A car can be used for business or
pleasure. A dog breeder may keep a puppy as a pet rather than selling it.
R2.
For concreteness, consider labor services. As wage rates increase, there are two
effects. A substitution effect operates to induce the resource supplier to work less — i.e., to
purchase less of the now higher-priced good, leisure. However, a higher wage also enriches
the resource owner, and this income effect operates to induce him to purchase more of all
normal goods — including leisure. So the income and substitution effects of a wage change
work in opposite directions. As long as the substitution effect dominates, the PEP will be
negatively sloped. This will be the case when the wage is low and few hours are worked.
Here, the income effect will be relatively small. At high wage rates where many hours are
worked, the income effect will be large and so may dominate the substitution effect and cause
a positively sloped PEP. Where the PEP is negatively sloped, the supply curve of labor is
positively sloped. Where the PEP is positively sloped, the supply curve of labor is negatively
sloped. So the supply curve of labor will be positively sloped at low wage rates, with the
possibility of a backward bend at high wage rates.
R6.
The boundary of an input monopolist's market opportunity set is concave to the
origin, while that of a competitive supplier is straight. The difference reflects the fact that the
input monopolist is such a big supplier in the market as to cause the hire price to fall
noticeably as the quantity of input offered increases. The competitive supplier of input
services, in contrast, does not noticeably affect the hire-price no matter what his level of
resource supply. The tangency optimum of the monopolist resource-owner will therefore lie
along a "budget curve" rather than a budget line.
R8.
Traditionally, factors of production have been classified as belonging to three
groups — land, labor, and capital. There is no functional basis for this classification: all three
are sources of productive services. The origin of the classification is historical-sociological. It
arose in 18th century England, where the incomes of the three major social classes derived
from ownership of characteristic types of resources. The aristocracy mainly owned land, the
174
rising bourgeoisie mainly owned industrial equipment ("capital"), and the working class
mainly owned labor power.
R11. The relevant equation is:
Rate of return =
Annual income yield
Purchase price of asset
If the rate of return on some asset A were greater than the rate of return on another asset B, the
purchase price of A would be bid up and the purchase price of B would be bid down. This
!
would lower A's Rate of Return and raise B's. There is no stable solution short of equality of
the rates of return.
T3.
(a) A progressive income tax would result in an after-tax budget line that bends
downwards, either smoothly as shown for convenience in Figure M13.1, or with discrete kinks
as in the case of the U.S. income tax with its various "brackets." The resource-owner's
optimum in comparison with a no-tax situation could shift to the right or left, depending on
whether the substitution effect or the income effect dominates (assuming leisure is a normal
good).
175
Figure M13.1 (Question 13.T3) The Effect of a Progressive Income Tax on the Optimum of
the Resource-Owner
(b) (See Figure M13.2) The time-and-a-half rule would put an upward kink in the
budget line, so that it becomes 50% steeper in the overtime region (say, beyond 8 hours of
work) than in the base-pay region. As for the resource-owner's optimum, Panels (a), (b) and
(c) illustrate three possible cases.
I)
The individual already works more than 8 hours at the base wage. In this case, the
optimum will move to the left if the substitution effect dominates, and to the right if the
income effect dominates.
ii)
The individual works exactly 8 hours at the base wage. In this case the optimum moves
to the left since, as is evident from the geometry of Panel (b), the individual can reach a higher
indifference curve only by moving to the left.
.
176
Figure M13.2 (Question 13.T.3) The Effect of Overtime Payments on the Resource Owner's
Optimum
177
iii) The individual works less than 8 hours at the base wage. In this case, if the indifference
curve passing through the original optimum is shaped like Wo, then the optimum will be
unchanged. But if the indifference curve is sufficiently flat to cut the upper leg of the kinked
budget line, the individual will now prefer to work more than 8 hours and earn overtime
NOTE: The assumption of an unchanged base wage may be unrealistic. A more likely
outcome is that time-and-a-half, by eliciting more labor supply, will result in a lower base
wage. As you might imagine, this introduces considerable complications.
T4.
(a) Panel (a) of Figure M13.3 illustrates a case where all resources are devoted to
reservation uses at the optimum point E on U1. Such a case is consistent with income being
a "bad" or a "neuter" but, as shown in the diagram, it is also consistent with income being a
good.
(b) Panel (b) illustrates the case where none of the resource is devoted to
reservation uses at the optimum point K on U1. Again, while such a case is consistent with
reservation uses being a "bad" or a "neuter," the diagram indicates that it is also consistent with
their being a good.
T7.
Any formula that sets a wage different from that dictated by supply and demand
would result in either shortages or surpluses of labor, and resources would not be directed to
their highest-valued use.
T8.
The supply curve of land to all uses (including reservation uses) can be regarded as
vertical, in the short run. But the supply of land to market uses will not be strictly vertical,
even in the short run, since owners will have alternative reservation uses for their land. Both
an income tax and a wealth tax on land would therefore affect market supply in the short run.
A wealth tax normally leads to increased market supply, since owners will suffer
impoverishment and will then cut down their reservation uses of land (apart from the unlikely
case that such uses are an inferior good). An income tax will, however, also have a strong
substitution effect in the opposite direction, and this will probably dominate so that less land
will be offered in the market for productive services. (For either type of tax there will also be
a long-run adverse effect on market supply; the reduced returns will tend to induce owners not
to maintain or develop land as a productive resource.)
178
Figure M13.3 (Question 13.T4) Corner Solution (Income and Reservation Uses Are Both
Goods)
179
T11. This question is somewhat defectively worded, and there is danger of losing sight of
the forest for the trees. The key point is that workers' incomes in the aggregate cannot rise
unless average wage rates times aggregate employment increases. Some of these "socialistic"
reforms tend to raise wage rates, at least for some workers, but have clearly adverse effects
upon aggregate employment. (Minimum wage laws, welfare relief, and trade unions all fall in
this category.) Apart from the directly impacted workers who may have their wage rates
increased, there are more or less complicated indirect repercussions upon others due to
complementarities — for example, if minimum wage laws reduce employment of the
unskilled, where will be a downward shift in demand for workers who are complements of the
unskilled. In the aggregate, since there is an adverse effect upon employment without any
general increase in productivity, these various reforms have all tended to reduce national
income and aggregate income of workers as well. (The effects of these two cannot diverge
greatly, as around two-thirds of national income has historically always gone as compensation
to labor.)
Only the 40-hour week (provision for time-and-a-half overtime pay) is on a somewhat
different footing. As this does tend to increase employment, it probably has raised measured
national income — but at the expense of desired leisure.
The general conclusion must be that these reforms do not explain the failure of the
"immiserization hypothesis." Rather, the main explanations are: (1) the accumulation of
factors complementary to labor (machines, buildings, roads, etc.) has raised marginal
productivity of workers, increasing the demand for labor so as to raise wage rates without
reducing employment, and (2) enormous advances in technology have improved the
productivity of all factors of production.
180
TEST BANK
NUMERICAL EXERCISES
N1.
A particular industry has the following demand curve for labor:
w = 40,000 – 100M
where w is the wage and M is the man-hours demanded per year. If the industry is
unionized and the union wishes to maximize the wage bill, what quantity of man-hours should
the union supply to the industry?
N2.
An individual has a utility function defined over leisure R and a composite market
good X:
U = x1/3 r2/3
This individual has nonwage income V of $3 per day, and can work as many hours as desired
for $2 per hour. There are 24 hours in the day () and the price of X is $1 per unit.
(a) How many hours per day will this individual choose to work?
(b) For arbitrary wage (w) and nonwage income (V) derive the labor supply
function for this person. Your function should have the form L = f(w,V).
(c) What is the reservation wage of this individual?
(d) For V = 0 draw the labor supply function of this individual. Use your answer
to (b) to construct this.
ANSWERS TO NUMERICAL EXERCISES
N1.
The union wants to maximize I =w(M) = 40,000M – 100M2. Just set the derivative
dI/dM equal to zero and solve:
40,000 – 200M = 0
M = 200
N2.
(a) The problem is to maximize U subject to the individual's budget constraint.
The equation of the budget constraint is easily gotten by noting that its slope is the negative of
the wage rate, and its vertical intercept is the wage times the number of hours in a day, plus
181
non-wage income (i.e., x = 24w + v – wr). In slope-intercept form, the equation is x = 51 –
2r. The equations that need to be satisfied for optimality are:
MRS=MUr/MUx = 2
x= 51 – 2r
MUr = 2/3 x1/3r–1/3; MUx = 1/3 x–2/3 r2/3
When these two are divided, the resulting mess reduces to 2x/r. Thus the two simultaneous
equations become:
2x
=2
r
!
x = 51 – 2r
The solution values are r = 17, x = 17.
(b) To derive the labor supply function it is easiest to first calculate the individual's
demand for leisure. Then labor supply will simply be 24 hours minus the amount of leisure
demanded. The demand function for leisure, as a function of w and v, is gotten by solving
the above simultaneous equations (with w and v variable) by eliminating X.
2x
=w
r
Substitute x = wr/2 into the budget constraint equation to get
!
wr
= 24w + v – wr
2
Which reduces to:
!
r = 16 +
2v
3w
Now, we know from before that L = 24 – r, so
!L = 24 – (16 +
!
2v
2v
)=8–
3w
3w
!
182
(c) To find the reservation wage, (i.e., where L = 0) just set v = 3 and
L = 0 and solve for w:
0=8–
2(3)
3w
Solving, w = 1/4.
!
(d) When v = 0, the labor supply equation becomes:
L = 8 – 0/3w = 8
This function is simple enough that we needn't draw it here. It is a vertical line at L = 8,
drawn in the (L,w) plane.
OBJECTIVE QUESTIONS
B13.1
If leisure is an inferior good, the labor supply curve will be positively-sloped (i.e., it
will have no backward-bending region). (T/F)
B13.2
Economic rent:
a. does not affect the stock of a good now in existence
b. does not affect the stock of a good now or in the future
c. is a rationing mechanism for the amount now in existence
d. is a surplus as far as the existence of the good is concerned
e. All of the above.
183
Figure B13.1 (Questions B13.3 to B13.5)
B13.3
Figure B13.1 shows the optimum of a resource owner. Assume that income (I) and
reservation uses of time (leisure, R) are both normal goods, and that there are no
sharp corners in the individual's indifference curves.
Suppose the individual is given additional non-wage income. At the new optimum, his MRS
between I and R will be:
a. greater than before
b. less than before
c. unchanged
d. can't tell.
B13.4
The new optimum will lie
the old.
a. to the right of
b. to the left of
c. directly above
d. can't tell.
184
B13.5
Now suppose the wage is increased, with non-wage income constant at Io. The
individual will work:
a. more
b. less
c. the same
d. can't tell.
B13.6
If we instead paid overtime beyond 8 hours worked, the individual would definitely
work more. (T/F)
B13.7
If we paid overtime beyond 4 hours worked, the amount of work would:
a. rise
b. fall
c. not change
d. can't tell.
B13.8
This individual's labor supply curve can't bend backwards. (Recall I and R are
both normal goods.) (T/F)
B13.9
Judging from the shape of this individual's budget line, he could be a monopolist.
(T/F)
B13.10 An individual who invests heavily in developing his labor skills will afterward earn a
higher wage, but he is also likely to work more hours. (T/F)
B13.11 Which of the following is the best explanation for the finding that some corporate
stocks persistently earn higher average rates of return than others?
a. The stocks are very risky.
b. The company's managers are very capable.
c. The company's stockholders have good alternative uses for their money.
d. These are stocks in "growth industries."
185
B13.12 An opera singer's next best job is driving a truck. Assuming he would willingly drive
the truck, the difference between his wages as a singer and his wages as a driver is an
economic rent. (T/F)
B13.13 Suppose taxes on labor income are increased. In a graph with income on the vertical
axis and leisure on the horizontal axis, the effect of the tax on each worker could be
pictured by
a. flattening the budget constraint
b. steepening the budget constraint
c. a parallel downward shift of the budget constraint
d. a parallel upward shift of the budget constraint.
B13.14 As above. A tax on labor income would definitely move the optimum to the right if
leisure were an inferior good. (T/F)
B13.15 Suppose a tax is imposed on all labor income in the U.S. If leisure is a normal good
to all workers, and the income effect resulting from the fall in after-tax wages is
stronger than the substitution effect, then:
a. Workers' before-tax incomes will certainly rise
b. Workers' before-tax incomes will certainly fall
c. Workers' after-tax incomes will certainly rise
d. Workers' after-tax incomes will certainly fall.
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DISCUSSION QUESTIONS AND PROBLEMS
1. "The price of pig
is something big
Because its corn, you'll understand
Is high-priced too;
Because it grew
Upon the high-priced farming land.
If you'd know why
The land is high
Consider this: its price is big
Because it pays
Thereon to raise
The costly corn, the high-priced pig."
H. Davenport
Resolve the paradox. Be sure to include a discussion of the relevance of economic rent.
2. Adam: "Let's reduce taxes on labor. That will increase work incentives and raise
GDP."
Alfred: "That won't work if the supply curve of labor is backward-bending. The
higher after-tax wages will reduce work effort, so GDP will be lower."
Adam: "Nonsense. If GDP is lower, everyone's wages must be lower, so with a
backward-bending labor supply curve you'd get more work effort."
Who is right? Explain.
3.
Carl works 40 hours per week at $5 per hour. His employer tells him that he can
either keep working the same hours at the same wage, or retire with a pension of $200 per
week. Carl chooses to keep working, even though at his optimum he regards work as a bad.
(a) Assuming 40 hours per week was his most preferred choice of hours, draw a
likely diagram of Carl's budget constraint, and indifference curves.
187
(b) Suppose Carl could collect his pension of $200 per week and had the option to
work for nothing. Would he work fewer hours than before?
4.
Are the following true or false? Explain in each case.
(a) Smith regards leisure as an inferior good. Therefore his labor supply curve
must be backward-bending.
(b) Jones' labor supply curve is backward-bending. Therefore leisure is a normal
good to Jones.
5.
Show how each of the taxes below would affect a worker's choice of income and
leisure.
(a) A 50% tax on non-wage income.
(b) A 50% tax on income from wages.
(c) A 50% tax on the amount of income that would be earned if he worked seven
hours per day.
6.
Since 1900, real wages as well as non-wage incomes have increased, while the
length of the workweek has decreased.
(a) Illustrate this change for a typical worker.
(b) Do the above observations imply that leisure is a normal good for most
people? Explain.
188
CHAPTER 14
TEACHING TIPS
1. This chapter is one of the most crucial of the book. In it, the topic of market
equilibrium is systematically treated for the first time, apart from the preliminary discussion in
Chapter 2.
2. As most of us remember from our own days as an intermediate student, the Edgeworth
box may be hard to get used to. Considerable patience should be exercised in explaining the
principles involved.
3. It is easy to confuse exchange with production. One of the more common errors is to
inadvertently say something that applies only where production can take place, when you are
actually talking about pure exchange. Much confusion can be avoided if you stress the fact
that exchange is simply a reshuffling of a fixed quantity of goods, while production always
involves a change in the physical quantities (social totals) of goods.
4. This section on transaction costs of the lump-sum variety is a difficult portion of the
chapter.
5. A very nice exercise for superior students is to explain why lump-sum transaction costs
lead to minimum transaction quantities (transaction supply and demand curves that begin some
distance away from the vertical axis).
6. The topic of money is particularly interesting because it constitutes a bridge to
macroeconomics.
189
ANSWERS
R1.
(a) Trade allows individuals to rearrange their endowed quantities of goods. Any
trade that takes place must leave both traders better off, and so results in an improved
allocation of goods relative to the endowment position. Trade also induces individuals to
specialize in the production of those goods to which their talents are particularly suited. This
rearrangement of productive activity increases the social totals of available goods.
(b) Consumptive improvement is shown as a move into the lens-shaped region of
mutual advantage. The Edgeworth box cannot illustrate productive improvement. It would,
however, expand as the quantities of goods rose.
R4.
An individual's "autarky price" for a good is that price at which he is just satisfied
with his produced quantity of the good. His net transaction demand for the good is therefore
zero. At higher prices, the individual becomes a net seller of the good; at lower prices, he is a
net buyer.
R5.
(a) At a competitive equilibrium in a world of pure exchange, for each individual
consuming both goods the MRSC must equal the ratio of market prices of the goods. For an
individual with an interior optimum, the rate at which he is willing to trade one good for
another must equal the rate at which such a trade can be made in the market.
(b) For each good, it must also be the case that the sum over individuals of the
desired quantities equals the social total available — the sum of individual endowments.
R8.
Only if every consumer is in a state of autarky at the same price, Px*, will St and Dt
intersect along the vertical axis. Otherwise, at any price some people will have positive
transaction demand and others will have positive transaction supply, so that St and Dt must
intersect in the interior.
R9.
Perfect markets require perfect communication, instantaneous equilibrium, and no
costs of transacting. Perfect competition requires price-taking behavior as well as perfect
markets.
190
R11. Raising the transaction costs of trading in narcotics, through increased lawenforcement activity, will increase the spread between the buyer's (gross) price and the seller's
(net) price of narcotics. This increased spread will lead to an increase in autarky (homegrown) solutions and a decrease in market transactions. Since such a shift to nonspecialization in production reduces the social totals, the production and consumption of
narcotics will fall.
R12. (a) Figure M14.1(a) illustrates the case of a proportional tax. The tax is so heavy
that the gap (G) is large enough to keep the gross-of-tax demand and supply (or, equivalently,
the net-of-tax) curves from intersecting at all.
(b) Panel (b) represents an aggregation, over all individuals, of individual net
supply and demand curves. For a sufficiently heavy lump-sum tax, even the summations over
all the individuals' transaction supply and demand curves will diverge enough so as not to
intersect at any positive value of X.
191
Figure M14.1(Question 14.R12) Markets Made Non-Viable by Taxation
192
R14. Transfer costs are inherent in the physical turnover of goods from one individual or
group to another. Exchange costs are incurred solely because market trading is used to
organize this transfer. The cost of transporting goods is a transfer cost. The costs of
negotiating and enforcing a contract are exchange costs.
T1.
Vintners, like anyone else, will wish to diversify their consumption. Since they are
specialized in the production of wine, they will want to trade their wine for other goods so as
to reach an interior consumptive optimum. In economic terms, Omar is suggesting that
Vintners should reach a corner solution — producing and consuming only wine.
T5.
Some markets have disappeared mainly because of reduction in demand. Leeches
are no longer sold to physicians, since bleeding has lost favor as a medical practice. Other
markets have disappeared because supply has become excessively costly. An example might
be the market for handmade shoes. One historically important market that has disappeared,
mainly because of higher transaction costs (in the form of legal penalties) is the international
slave trade.
T6.
Yes. A railroad lowers the cost of transporting goods between trading communities
and so shrinks the spread between the buyer's price and the seller's price. A tariff increases the
spread. As the spread decreases, trade is more likely and so the railroad does connect trading
communities. Conversely, the increase in the spread due to the tariff makes trade less likely
and so separates the trading communities.
T9.
Farm roadstands incur both lower transfer costs and lower exchange costs. The
goods do not have to be shipped (transportation costs), and middlemen are bypassed (exchange
costs).
T10.
(a) Money as a medium of exchange reduces the costs of verifying the
characteristics of traded goods (the character and authenticity of money are easily verified), as
well as the costs of handling and transporting goods to and from markets (a monetary
commodity is selected because, in part, it is cheap to handle and transport). Money also
eliminates a great deal of the costly multilateral bargaining that would be required for complex
193
transfers under barter; these same transfers can be organized with only bilateral contracting
given a monetary medium of exchange.
(b) Money as a store of value reduces the cost of holding trading inventories.
Individuals need hold only one trading inventory — money — instead of several.
T13.
In Figure 14.2 (in the textbook), John prefers points that are both below and to the
left of his endowment, while Ida prefers points that are both above and to the right of her
endowment. Thus, John would be willing to trade from E to R (R is both below and to the
left of E). Ida would not (it moves her in exactly the opposite direction from her preferred
points). Similarly, Ida would be willing to move from E to S (S is both above and to the right
of E), while John would not. Neither would be willing to move to V; V is both above and to
the left of E, which fits neither person’s criteria for increased utility.
T15.
This analysis uses the aggregate curves and definitions (Figure 14.6), but a similar
analysis applies to the individual curves (Figure 14.5). The price at which the transaction
demand and supply curves intersect (Pt*) is, by definition, the price for which the transaction
quantity demanded, XtD equals the transaction quantity supplied, XtS . But these quantities are
defined as XtD ≡ Xi – X and XtD ≡ X – Xi. Thus at the transaction equilibrium price, Xi – X
= X – Xi, or, X = Xi, which is exactly the condition that must hold at the price where the full
demand curve intersects the full supply curve.
!
!
!
!
T16.
!
(a) The Consumer Surplus is the gain to the buyers from being able to buy at the
prevailing price, even though they value the good more highly. It is thus the difference
between the marginal value or marginal willingness to pay for each unit and the price that must
be paid to acquire each unit, summed over the units purchased. The price is 6 tokens, so for the
first unit of the commodity, that difference is 16 – 6 = 10. For the second unit, it is 11 – 6 = 5.
Summing over the units purchased, the total is 10 + 5 = 15. If the “buyers” in the experiment
get to take home $15, then that amount is tangibly how much better off they are. Notice that it
would not make sense to purchase a third unit of the commodity, since the price, 6 tokens,
would exceed the marginal value, 3 tokens.
(b) The Producer Surplus is the gain to the sellers from being able to sell at the
prevailing price, even though the cost of acquiring the good is less than the price. It is thus the
194
difference between the price they are paid for each unit and the marginal cost of producing or
acquiring each unit, summed over the units sold. Each of the units acquired cost 6 tokens to
obtain. The price obtained by selling the first unit back to the experimenter is 16 tokens. So,
for the first unit of the commodity, the difference is 16 – 6 =10. For the second unit (price of
11, cost of 6), it is 11 – 6 = 5. Summing over the units purchased, the total producer surplus is
10 + 5 = 15. If the “sellers” in the experiment get to take home $15, then that amount
represents how much better off they are as sellers.
T17.
See Figure M14.2. Panels (a), (b) and (c) all show the same budget constraints. The
straight line (dashed line KL) shows her options if trade were costless. The kinked constraint
(solid segments K'E and EL') shows her constraint when transactions costs limit her options.
With transactions costs, Panel (a) depicts Ida preferring to sell some Y to get X,
moving from the hollow endowment E to the solid point F, and thus to a higher indifference
curve. Panel (b) shows her selling X to get Y by moving from E to the higher indifference
curve tangency at F. Panel (c) shows her retaining her endowed X and Y.
T18.
Figure M14.3 shows that, starting with the same endowment, E, the outcomes
depend on the shapes of the indifference curves, the price of X relative to Y, and the size of the
lump-sum cost. In all of the diagrams, the budget line for costless trade is shown as KL, while
the budget constraint with a lump sum transactions cost is the (parallel) MN.
In Panel (a), the individual becomes a buyer of X, moving from E to the preferred
point F (by selling Y to purchase X). This is due to the relatively low price of X, small
transactions costs, and indifference curves’ shapes. In Panel (b) the individual becomes a seller
of X, again moving to the preferred F from E. In Panel (b), the price of X is quite large, thus
discouraging X purchase by the individual and encouraging its sale (despite the somewhat
larger transactions costs than in (a)). Panel (c) shows a situation in which there might have
been trades that would produce a combination preferred to E without transactions costs (along
KL). However, transactions costs change the constraints so that there are no combinations
along MN that are preferred to E. Thus, the individual will keep the endowed combination of
X and Y.
195
Figure M14.2 (Question 14.T17) Individual Choices with Transactions Costs
196
Figure M14.3 (Question 14.T18) Individual Choices with Lump-Sum Transactions Costs
197
TEST BANK
NUMERICAL EXERCISES
N1.
An individual both produces and consumes bread. His full (consumption) demand
for bread is given by:
bd = 20 – 2P
Where P is the price of bread (B). His full (production) supply schedule is given by:
bs = 5 + P
(a) At what price will his net (transaction) supply and net (transaction) demand be
zero?
(b) Derive his transaction supply and demand curves for P ≤ 10.
(c) What happens above P = 10? Illustrate.
N2.
Isaac's MRSC between commodities X and Y is given by the expression MRSC
= –2y/x. Commodity Y is the numeraire, so that PY =1.
(a1) If Isaac's endowment position E is the combination (xo,yo) = (10,90), what
is the "sustaining price" Px0 at which Isaac will not want to trade away from position E?
(a2) Where (as in this case) the individual has an interior endowment, the budget
equation Pxx + Pyy = I must allow for the fact that the individual's endowed income I
depends upon the prices: specifically, I = Pxxo + Pyyo. Using the numerical data given above,
state the budget equation.
(a3) Use the budget equation and the tangency condition (involving the MRSC) to
develop Isaac's Price Expansion Path (PEP) equation and his (full) demand curve for
commodity X. Sketch these curves. [HINT: Use the appropriate axes for each!]
(a4) Remembering that Isaac has an interior endowment, now state his net or
transaction demand equation for X (denoting his net-demand quantity as xdt) for prices
below P and his net or transaction supply equation for X (denoting his net-supply quantity
as xst) for prices above Px0.
(b1) Suppose that instead of a fixed endowment, Isaac is endowed with a
transformation locus or Production-Possibility Curve (PPC) whose equation is given by
198
2x2 + y2 = 7500. What is the Marginal Rate of Transformation (MRST), the absolute slope
along the PPC?
(b2) Find Isaac's "Robinson Crusoe optimum," given his preferences as in (A)
above and this PPC. What is the "autarky price" Px0 for Isaac here?
ANSWERS TO NUMERICAL EXERCISES
N1.
(a) Net supply and demand are both zero when full supply and demand are equal at
any level. So set bd = bs and solve:
20 – 2P = 5 + P
3P = 15
P=5
(b) Net demand (b) is consumption demand minus the amount the individual
produces (full demand minus full supply). Similarly, net supply (b) is amount produced
minus the amount the individual consumes (full supply minus full demand). Mathematically:
bdt = bd – bs = 20 – 2P – (5 + P) = 15 – 3P
bst = bs – bd = 5 + P – (20 – 2P) = –15 + 3P
(c) See Figure M14.2. Above P = 10, the full supply bs is negative, which is
impossible. (Algebraic supply and demand functions must be used with caution for this
reason.)
199
Figure M14.2 (Question 14.N1) Net and Gross Supply and Demand Curves **>>
N2.
(a1) The sustaining price is that price for which MRSC = Px/Py (=Px since Py
=1). If we plug the given values of x and y into the expression for MRSC, we get MRSC =
2(90)/10 = 18. Therefore Px0= 18.
(a2) The equation of the budget constraint is:
Pxx + Pyy = Pxxo + Pyyo
Substituting the given values of x and y:
Pxx + y = 10Px + 90 (remember that Py = 1)
Px(x–10) + y = 90
(a3) We have the same old optimum conditions:
2y/x = Px
Px(x–10) + y = 90
To get the demand curve we eliminate y from the above two equations. To get the PEP we
eliminate Px.
200
PEP: (substitute Px = 2y/x into the second equation)
2y
(x–10) +y = 90
x
Simplifying:
!
xy = 30x + 20y/3
Demand Curve: (substitute y = Pxx/2 into the second equation)
Px(x–10) +
Px x
= 90
2
Simplifying:
%
2 " 90
x!
= $ + 10'
3 # Px
&
See Figure M14.3 for sketch.
!
(a4) Net demand = full demand – endowment
%
2 " 90
xdt = $ + 10' –10
3 # Px
&
= 60/Px –10/3
(See Figure M14.3 for sketch.)
Net supply = –net demand (for prices above Px0)
!
xst = 10/3 – 60/Px
(b1) The slope of the PPC is dy/dx. There are many ways to calculate this. The
easiest is to take the differential of 2x2 + y2 = 7500:
4xdx + 2ydy = 0
(b2) The condition that must hold at autarky is:
MRST = MRSC
"2x "2y
=
y
x
!
Substituting into
x=y
2x2 + y2 = 7500
201
2x2 + x2 = 7500
3x2 = 7500
x = y = 50 (the "Robinson Crusoe optimum")
"Px
= –2x/y = –2(50)/50 = –2
Py
Take the absolute value (remember Py = 1)
!
Px 0 = 2
202
Figure M14.3 (Question 14.N2) PEP and Demand Curves with Interior Endowment
203
OBJECTIVE QUESTIONS
Figure B14.1 (Questions B14.1 to B14.3)
B14.1 See Figure B14.1 For the steeper budget line, there is a surplus of y. (T/F).
B14.2 See Figure B14.1. What is the set of points preferred to E by both parties?
a. I and J
b. H only
c. The curve FG
d. the line EH
e. All points in the football-shaped region.
B14.3 See Figure B14.1. Where will both parties consume in competitive equilibrium?
a. E
b. F
c. G
d. H
e. I.
204
B14.4 If neither consumer in an Edgeworth box can be made better off without hurting the
other, which of the following must be true?
a. MRS is the same for each consumer.
b. Px/Py = MRS for each consumer.
c. One consumer has a monopoly of some good.
d. They are not on the contract curve.
B14.5 Starting from equilibrium in the Edgeworth box, a flattening of the budget line would
result in a surplus of X. (T/F) (Recall X is on the horizontal axis.)
B14.6 An individual in a two-good world of costless transactions is producing exactly what he
consumes. Which of the following must be true?
a. Self-sufficiency is a good to this person.
b. The point of production is identical to the endowment point.
c. The individual has no comparative advantage in producing either of the two
goods.
d. The slope of his production-possibilities curve is equal to –Px/Py.
205
Figure B14.2 (Question B14.7)
B14.7 Refer to Figure B14.2. The contract curve is:
a. the line segment ED
b. the curve between B and C
c. the curve labeled A
d. the curve EBF.
B14.8 The Fundamental Theorem of exchange states that:
a. people will trade until no further gains are possible
b. all voluntary trade benefits both traders
c. people always know what's best for them
d. each trader will try to gain at the other's expense.
206
Figure B14.3 (Questions B14.9 to B14.12)
See Figure B14.3. The following are matching problems. Each question gives the name of
something. You are to fill in the letter which best describes the given name. For
example, The endowment point F
B14.9 The contract curve
B14.10
The region of mutual advantage
207
B14.11
On Figure B14.3, the point of consumption by both parties in equilibrium will be
a. The area bounded by B,C,E, and F
b. C
c. D
d. The line segment between B and C
e. The curve labeled "A"
f. E
B14.12
On Figure B14.3, if J's endowment of X increases, which of the following will
happen?
a. The box expands vertically; the line segment (XI,E) gets longer.
b. The box expands vertically; (XI,E) is unchanged.
c. The box expands horizontally; (YI,E) gets longer.
d. The box expands horizontally; (YI,E) is unchanged.>
DISCUSSION QUESTIONS AND PROBLEMS
1.
The Fundamental Theorem of Exchange states that voluntary trade is mutually
beneficial.
(a) Demonstrate the theorem with an Edgeworth box.
(b) Identify at least one point in the box where there is no possibility of mutually
beneficial trades.
(c) Is a robbery ("Your money or your life") a mutually beneficial trade?
208
2. Figure B14.4 shows a two-person, two-good economy. The initial endowment is at E.
Figure B14.4 (Discussion Question 2)
(a) After all trades are completed, could the traders end up at B? Is it a
competitive equilibrium position given the initial endowment E?
(b) After all trades are completed, could the traders end up at C? Is it a
competitive equilibrium given the initial endowment E?
(c) After all trades are completed, could the traders end up at D? Could it be a
competitive equilibrium given the initial endowment E?
4.
Robinson and Friday live on an isolated island, consuming only bananas B, and
coconuts C. Robinson likes both bananas and coconuts, but Friday regards coconuts as a
neuter. Each individual starts with 5 bananas and 5 coconuts.
209
(a) Show the initial situation in an Edgeworth box, showing both the endowment
point and the region of mutual advantage.
(b) Show the set of all points that are possible outcomes of voluntary trade.
(c) Does Friday necessarily end up with all the bananas? Could he?
(d) Will Friday ever end up with any coconuts after trading?
5.
Ronald produces and consumes only movies M and jelly beans J. He is better at
producing movies than jelly beans, but he spends more time eating jelly beans than watching
movies.
(a) Draw Ronald's Production Possibilities Frontier, his budget constraint, and his
consumptive optimum.
(b) Excessive taxation drives Ronald to autarky. Show how this would happen in
your diagram. Why would Ronald want lower taxes?
6.
Why is money so often used as a medium of exchange, and barter used so seldom
210
CHAPTER 15
TEACHING TIPS
1. The topic of intertemporal choice is often puzzling to students because of the special
language used: interest, investment, time-preference, saving, etc. It is reassuring for students
to know that, apart from the special terminology, they do not have to learn a new subject
matter to deal with intertemporal problems. The standard price-theory techniques of
individual optimization and market equilibrium are completely valid and applicable in the
realm of intertemporal choice. Indeed, this is one area where practical businessmen and
government decisionmakers are aware of the relevance of economic analysis.
2. The concept of Present Value comes easily to most students. A real test of their
understanding is to see if they can handle changing interest rates.
3. The graphical interpretation of saving, borrowing, investment, and lending will not be
understood after just one pass. Making the connection with the discussion in Chapter 14 (full
versus transaction demand and supply, etc.) will do much to help understanding.
211
ANSWERS
R1.
For both intertemporal optimization and optimization at a moment in time, the
consumer chooses the most preferred point in his opportunity set. In each case, indifference
curves can be drawn to indicate preferences, and opportunity sets can be defined. For
moment-in-time optimization, the opportunity set is determined by the level of income and the
price-ratio — the rate at which X can be traded for Y in the market. Income determines the
size of the market opportunity set, and relative prices determine the slope of the budget line
(the shape of the opportunity set). These concepts have analogs in intertemporal optimization.
Wealth determines the size of the market opportunity set. The intertemporal price ratio or
interest rate — measuring the rate at which current consumption can be traded for future
consumption — determines the slope of the budget line (the shape of the market opportunity
set).
R3.
Wealth is the market value of an individual's intertemporal endowment. That is, it
is the Present Value of the individual's current and future income prospects.
R6.
(a) The Separation Theorem states that an individual's productive optimum is
independent of his preferences. So, given his productive possibilities, any individual, no
matter what his intertemporal utility function (his time-preference) may be, would choose the
same productive optimum — that which maximizes wealth.
(b) The importance of the Separation Theorem lies in the fact that it allows
individuals to delegate their productive optimizing decision to an agent who may know
nothing of his principal's time-preference. In fact, many individuals with differing utility
functions may combine their productive opportunities and delegate the productive optimizing
decision to the same agent, i.e., they may form a firm. As long as the agent maximizes the
wealth of the firm, each owner's wealth is also maximized.
(c) If the Separation Theorem did not hold, an individual's productive optimum
would depend upon his time-preference. Diverse individuals would not as readily combine
their productive opportunities. Since the productive optimum would depend on preferences,
only individuals with similar time-preferences would form firms. This would limit the way in
212
which individual productive opportunities could be combined, and so would tend to limit
production possibilities for the economy generally.
R8.
The equation r = P0/P1 – 1 defines the rate of interest r as the premium that
borrowers must pay when trading one-year future consumption claims for current consumption
claims. The equation r = z/V0 defines the rate of interest as the annual percentage yield of an
asset which provides a fixed yield (z) indefinitely. The first equation can be re-interpreted in
Present Value terms as follows. Consider first an asset yielding 1 unit of income at time-1 and
0 otherwise. Then its Present Value is V0 = 1/(1 + r). In terms of the equation above, P0 has
been set equal to unity (as numeraire), and P1 (the price today of a one-year future claim)
corresponds to V0. With these adjustments, this Present-Value equation is algebraically
identical with the original r = P0/P1 – 1. More generally, if the asset yields any amount of
income z1 at t = 1 (and zero otherwise), its Present Value becomes V0 = z1/(1 + r). Now
suppose instead that the asset yields the amount z at each and every date from t = 1 to
infinity. Then the result is V0 = z/r. Thus, we have seen, the interest rate r can be regarded
as the market premium on this year's versus next-year's claims (in exchanging only between
those two dates), or alternatively as the market ratio between the perpetual annual income
yielded by an asset and its value today.
R9.
The money rate of interest is the premium on current money relative to future
money. The real rate of interest is the premium on current actual consumption claims relative
to future actual consumption claims. If no price-level changes are anticipated, the money and
real rates of interest will be equal. If, however, price-level inflation is anticipated, the money
rate of interest will exceed the real rate by (approximately) the anticipated rate of price
inflation.
213
T1.
Cases (a) and (b) are illustrated in Panel (a) of Figure M15.1. In each case the
individual has low current income, but good future prospects, and so will likely be a borrower.
Cases (c) and (d) are illustrated in Panel (b). In each case the individual has high current
income relative to future prospects, and so will be a lender.
Figure M15.1 (Question 15.T1) Intertemporal Endowments
T5.
(a) Higher rates of time-preference will tend to result in higher real rates of interest.
Other things equal, higher real rates of interest will be reflected in higher money interest rates.
Factually, it appears that time-preferences have indeed been changing in Western countries.
214
The Protestant Ethic which stressed saving is declining, and less willingness to save implies
higher equilibrium real rates of interest.
(b) Higher rates of time-productivity will also tend to result in higher real rates of
interest, and consequently (other things equal) in higher money interest rates. There has been
tremendous technological advance in the past few decades, but it is not actually clear that rates
of time-productivity have increased.
(c) Time-endowments weighted toward the future will tend to result in high real
rates of interest, and consequently again in higher money rates. Increasingly optimistic
expectations as to the size of future incomes would thus partially account for rising interest
rates. But the factual evidence is unclear as to whether on balance expectations have become
more optimistic.
(d) Anticipations of high rates of inflation will lead to high money rates of interest.
The increasing rate of inflation experienced in the past decades has surely led to higher
anticipations of future inflation, and so to higher money rates of interest. (But high anticipated
inflation will not generally increase the real rate of interest.)
T7.
Mr. Micawber is proceeding on the premise that the individual will be strapped to
pay back the debt. He is forgetting that consumption and expenditures may be spread over
time. The fact that someone was able to incur the debt in the first place indicates that such an
expenditure pattern was within his intertemporal opportunity set. So by incurring the debt the
individual was maximizing his utility — not making himself miserable. The consequences to
which Mr. Micawber alludes would be the result of a mistake. They are not an unavoidable
result of borrowing.
T10. (a) In a pure exchange situation, the income tax’s effect on saving is ambiguous, but
it is most likely to reduce saving and investment. Intuitively, after taxes a person has both less
to save and less benefit to saving. Saving the same amount with taxes as without them would
require a person to reduce current consumption by the entire amount of the current tax.
Further, the reward for doing so is reduced because of the taxes on the interest earned in the
future.
Figure M15.2 shows the effect of taxes in a pure exchange model. The endowment
without taxes is E, and the maximum current consumption without taxes is c0 . At an interest
215
!
rate of 10%, the maximum future consumption possible without taxes is c1, and the budget
constraint is KE. The figure also shows the effect of an income tax of 1/3. Since both current
income and the interest are taxed, with taxes the endowment becomes ET, and the maximum
T
current consumption is co . The maximum future consumption possible with taxes is shown as
c1T (so the after-tax budget constraint becomes KTET). Given the indifference curves shown,
T
T
saving without
! taxes would be c0 - c0*. With taxes, the saving would be co -c0 *. In the
figure, taxes reduce current saving, but it is possible to construct indifference curves for which
this does not occur.
!
!
Figure M15.2 (Question 15.T10) Pure Exchange Effect of Taxes on Consumption and Saving
(b) In an exchange and production situation, the effect of an income tax on saving
and investment may be similar to those of pure exchange. However, because greater future
consumption can be acquired through investment of resources into future production, the effect
is potentially more complex. If we assume that all current income is taxed (regardless of
whether it is spent on consumption, lent at interest, or put into production) and that the future
production will be sold and yield taxed income. Then the individual would make investment
216
and production decisions based upon a reduced initial endowment, and its intersection with a
somewhat flatter market opportunities curve. The resulting market opportunities curve for
consumption in the two periods might resemble MM on textbook Figure 15.5, but a bit flatter.
Indeed, it may resemble Figure M15.2. Each individual has fewer resources in the present with
which to save and invest, and will have reduced rewards in the future for doing so. Even so,
the flatter slope of the market opportunities curve will probably mean that the proportion of
production output will be shifted slightly more towards investment.
However, saving that is devoted to future production might be taxed only once
(when the produced goods are sold). This means that saving some pre-tax resources (seed corn,
in the example in chapter 15) and investing them in future production is a means of escaping
some current taxes; since they aren’t sold in the current period, they are not taxed. Thus,
saving and investing in production is discouraged little (and may even be encouraged),
although selling current output and investing the proceeds at the market rate is still
discouraged by the tax.
217
TEST BANK
NUMERICAL EXERCISES
N1.
Suppose an annual crop of oranges can be grown forever using land according to the
production function H = 200A, where H = bushels of oranges/yr. and A = acres of land
cultivated. Oranges are sold in the city for $6/bushel, but cost $.05/bushel per mile to
transport. Let the annual interest rate be 10%.
(a) If land can only be used for cultivating oranges (outside the city), what will be
the equilibrium purchase price for land 20 miles outside the city?
(b) What will it be 60 miles outside the city?
(c) If land can also be rented out for grazing cattle at $200/yr. per acre, what is the
furthest distance from the city where oranges will be grown?
N2.
Mr. Z has no cash other than the $500 he has just received from his grandmother.
He is investigating his investment opportunities and discovers that he has two mutually
exclusive investment opportunities:
(a) One investment requires an initial expense of $650. This investment pays back
$200 after one year, an additional $540 at the end of two years, and $60 at the end of each and
every year thereafter.
(b) The second investment requires an initial expense of $400. This investment
pays back $630 at the end of two years.
Assume that banks permit unlimited borrowing or lending at the market rate of interest. The
market rates of interest are 25% on a one-year loan starting today and 20% on one-year loans
starting one or more years from today. What should Mr. Z do?
N3. An individual with no intertemporal productive opportunities lives exactly two
periods. His preferences between present consumption and future consumption are expressed
by the following utility function:
U = c02c1
218
He is initially endowed with 32 units of co and 50 of c1. The interest rate is 25%.
(a) Find his optimal consumption of co and c1.
(b) Calculate the amount of his savings, investment, and borrowing (or lending).
ANSWERS TO NUMERICAL EXAMPLES
N1.
(a) One acre produces 200 bushels, worth $1200 in the city. Twenty miles outside
the city each bushel will be worth $6–20($.05) = $5. An acre of this land therefore produces
200($5) = $1000 per year. The price of an acre will be the present value of a $1000 perpetuity
at 10%.
Price =
$1000
=- $10,000
.10
(b) 60 miles outside the city each bushel will be worth $6–60($.05) = $3, so an
acre can produce $600 per year. Therefore the price of an acre will be $600/.10 = $6000.
!
(c) Oranges will be grown out to the point where 200 bushels bring just $200 after
subtracting shipping costs. Therefore each bushel will be worth $1 after shipping costs. Using
X for miles outside of the city:
$6 – ($.05)X = $1
So X = 5/0.05 = 100 miles.
N2.
Find the Present Value (PV) of each project. Since the projects are mutually
exclusive, adopt the one with the higher PV.
PVa = –650 +
200
540
60 /.2
+
+
1.25 (1.25)(1.2) (1.25)(1.2)
= 70
PVb !
= –400 +
630
(1.25)(1.2)
= 20
Mr. Z should adopt project (a).
!
N3. (a) This is an optimization problem. First compute the relevant Marginal Utilities:
MU0 = ∂U/∂c0 = 2c0c1
MU1 =∂U/∂c1 = c02
219
The Marginal Rate of Substitution MRS= MU0/MU1 is thus 2c1/c0. From the fact that r = 25,
we can infer that P0/P1 = 1.25. Thus, treating c0 as numeraire, we get that
P0 = 1 and P1 = 0.8. The budget constraint then becomes
c0 + 0.8c1 = 32 + 0.8(50) = 72
Using this, we set up simultaneous equations to solved for c0 and c1:
c0 + 0.8c1 = 72
2c1/ c0 = 1.25
The solution values are c0 = 48, c1 = 30.
(b) Saving is equal to the endowed quantity of c0 minus the consumed quantity of
c0, or 32 – 48 = -16 (there is dis-saving). Investment is zero, since the individual has no
intertemporal productive opportunities. Borrowing is equal to the consumed quantity of c0
minus the produced quantity of c0. In pure exchange "the produced quantity" is simply the
quantity endowed. Borrowing is thus 48 – 32 = 16. Note that in pure exchange borrowing is
simply dis-saving (and lending would correspond to saving).
OBJECTIVE QUESTIONS
B15.1
An individual's MRS between present consumption (c0) and future consumption
(c1) is given by MRS = 2c1/c0. The price of c0 (call it P0) is 2. The price of future
consumption is 1. This means r = 100%. If the individual is endowed with 30 units
of c0 and no c1 (for PV = 60), how much will he lend? (HINT: This is an
optimization problem.)
a. 20
b. 15
c. 10
d. 5.
220
B15.2
Which of the following was not given as a reason for positive real interest rates?
a. Inflation
b. Preference for present over future consumption
c. High future endowment relative to present endowment
d. Improved productivity in the future.
Figure B15.1 (Questions B15.3 to B15.7)
B15.3
The individual in Figure B15.1 is a borrower. (T/F)
B15.4
See Figure B15.1. What is the amount of investment?
a. Coc – Cop
b. CoE – Cop
c. CoA – Cop
d. Coc – CoE.
B15.5
See Figure B15.1. What is the amount of saving?
a. Coc – CoA
b. Coc – Cop
c. Coc – CoE
d. CoE – CoA.
221
B15.6
See Figure B15.1. The existence of borrowing and lending opportunities changes the
opportunity set. By how much does present consumption increase as a result?
a. Can't tell
b. Coc – Cop
c. Coc – CoE
d. Coc – CoA.
B15.7
See Figure B15.1. Although saving does not equal investment for this individual,
saving must equal investment for the economy as a whole. (T/F)
B15.8
Which of the following is correct?
a. r = Po/P1
b. 1 + r = Po/P1
c. 1 + r = P1/Po
d. r = Po/P1 + 1.
B15.9
You have a choice of one of two investment projects. One has a higher present
value, the other a higher rate of return. You should pick the one with the higher
present value. (T/F)
B15.10 The less "impatient" people are for present consumption, the more valuable is future
consumption. Thus a dollar today will be worth more tomorrow, and the interest rate
will be higher. (T/F)
B15.11 Which of the following people is likely to be a borrower?
a. A young man with an elderly, wealthy, loving uncle in Australia
b. A 35-year-old baseball star
c. A sixty-year-old man who has just learned that his pension fund manager has
been indicted for embezzlement.
d. A silent film star.
222
B15.12 The interest rate is 25%, and the individual is endowed with 100 units of Co and no
C1. What is the equation of his budget line between C0 and C1?
a. C1 = (100-Co)/.8
b. C1 = .8(Co – 100)
c. .8Co + C1 = 100
d. .25 = Co + .8(100 – C1).
B15.13 The real annual interest rate is 15%. The present value of a 45 dollar-a-year
perpetuity is:
a. 100
b. 150
c. 675
d. 300.
B15.14 Robinson Crusoe's saving will exactly equal his investment. (T/F)
B15.15 The interest rate is 15%. Each of the following payment sequences represents
payments (a (–) sign represents an expense) received now, a year from now, and
two years from now. Which has the greatest present value? (HINT: No calculations
are necessary if you do this right.)
a. 0,0,100
b. –10,10,10
c. –100,100,100
d. –50,50,45.
B15.16 A person who invests and borrows cannot be saving. (T/F)
B15.17 The interest rate rises because of a sudden increase in people's preferences for current
consumption. Productive opportunities are unchanged. Investment will rise as a
result. (T/F)
223
B15.18 Which of the following would increase the real interest rate?
a. Inflation
b. Paying off the national debt
c. An increase in people's preferences for future consumption
d. Increased economic growth
e. None of the above.
DISCUSSION QUESTIONS AND PROBLEMS
1.
A farmer produces and consumes only corn. For every 10 bushels he sets aside for
seed, he gets 11 bushels next year. There are only two years. He now has 100 bushels, and his
utility function is:
U = CoC1
where Co is this year's consumption and C1 is next year's consumption.
(a) If there is no capital market, how much corn should he consume this year and
how much next year?
(b) If he can borrow and lend at 5%, how much should he consume this year and
how much next year?
2.
"I'd like to get my own computer, but their price is falling faster than my personal
discount rate. If this keeps up I'll never get one." Evaluate.
3.
"A person who is simultaneously investing and borrowing cannot be saving."
Evaluate.
4.
In each of the following cases, will the real rate of interest be relatively high or
relatively low? How about investments?
(a) A prophecy that the earth will end two years from now is widely believed.
(b) There are reliable reports that scientists are on the verge of producing robots
that can perform any job better and cheaper than humans.
224
(c) A sudden burst of hedonism causes everyone to live for the moment with no
thought for the future.
5.
John has entered a contest that promises the winner $50 this year and $50 the next
year. He figures that if he wins he will spend the first year's prize money immediately and
borrow some fraction of the second year's prize money, which he will also spend immediately.
On the day before the contest winner is announced, the interest rate rises.
(a) Assuming John wins the contest, will the increase in the interest rate necessarily make
him better off? (Draw a diagram.)
(b) If your answer to (b) is no, then under what circumstances (if any) will the rise in the
rate of interest make him better off?
225
CHAPTER 16
TEACHING TIPS
1. In the discussion of general equilibrium, and especially when explaining the various
conditions for efficiency, a diagram showing the social PPC and an inscribed Edgeworth box
is often helpful.
2. The section entitled "What Can Go Wrong? Almost Everything." is very useful for
deepening the student's understanding of the operation of the Invisible Hand. References to
the Coase theorem, with due regard for real-world applicability, are also helpful.
3. When discussing public goods, the concept of vertical summation of demand curves
needs careful attention. Students will be familiar with the technique from Chapter 4, but the
logic behind it is not obvious.
4. Students are often inclined to consider the Problem of Equality as a violation of the
laws of economics. Greater insight can be provided by pointing out that equality can be
thought of as a special kind of public good, which arises because of man's tendency to be
benevolent to those less fortunate than himself, and envious of those who are more fortunate.
226
ANSWERS
R1.
(a) The normally concave shape of the Social Opportunity Frontier in terms of
income indicates that a larger social total of income can be attained by social arrangements that
provide for at least some sharing between individuals. If individual j receives the entire
social total of income there is no incentive for the other individual k to contribute his
productive talents, whereas if k receives some of the social total of income he will be
motivated to assist in production.
(b) Since one person's (ordinal) utility cannot be quantitatively compared with
another's, all we can say about the shape of the Social Opportunity Frontier in utility terms is
that it is negatively sloped. Increasing the utility of one individual necessarily decreases the
utility of the other.
R2.
See Figure M16.1. An allocation is Pareto optimal if J's indifference curve is
tangent to K's indifference curve. Thus A, B, C, D and all other points on the contract curve
are Pareto optimal . An allocation is Pareto-preferred to another if at least one consumer is on
a higher indifference curve and neither is on a lower indifference curve. For example, points
A, F, and B are all Pareto-preferred to E, but F is not Pareto-optimal. Points C and D are
not Pareto-preferred to E, even though E is not Pareto-optimal while C and D are.
Figure M16.1(Question 16.R.2)
227
R4.
At every consumer's optimum, the slope of the indifference curve (MRS) at that
point is equal to the slope of the budget line (Px/Py). This does not prevent people's
indifference curves from having different shapes away from the optimum.
R5.
The Theorem of the Invisible Hand states that under ideal conditions (perfect
competition and perfect markets, no "direct" externalities, no public goods), optimizing
behavior on the part of individuals and firms, acting in their own self-interest, will lead to an
efficient social outcome.
R6.
(a) The conditions are
(I) Efficient Production MRSTA = MRSTB
(ii) Efficient Consumption MRSCA = MRSCB
(iii) Efficient balance between production and consumption
MRST = MRSC
(b) These conditions could in principle be achieved without using the market, for
example, by a dictator. However, the dictator would need to know all Marginal Rates of
Substitution in the economy — an unlikely achievement.
R7.
A price that is either too high or too low will reduce the volume of mutually
advantageous trading. The reason is that the amount exchanged is always the lesser of the
quantities demanded and supplied.
R9.
A public good is one that is not used up by consumption (e.g., radio signals). An
externality exists when the activity of some economic agent affects the interests of others
without compensation or redress. Where exclusion is impossible or at least not practiced, a
public good can be viewed as a special kind of beneficial "direct" externality. If one individual
provides the public good for himself, he simultaneously provides it for others.
228
R10. (a) Since the potential revenues of a private firm supplying a public good will
include only the demands of those consumers who are willing to pay, the inability to exclude
non-payers means that the firm's perceived demand curve is too low. So it will under-produce
the public good.
(b) Exactly the same argument holds for inability to exclude non-payers from
consuming a privately supplied private good.
R15. (a) The Coase Theorem states that as long as property rights are well defined and
the cost of transacting in these rights is negligible, the Invisible Hand will lead parties toward
an efficient outcome — regardless of the initial assignment of property rights. In particular,
"direct" externalities will tend to be internalized by bargaining.
(b) If rights are not well defined, trade in these rights will be difficult (costly) to
negotiate and to enforce. Consequently, little exchange of rights will occur; direct externalities
will tend to persist. The same conclusion would follow even if rights are well defined, so long
as the costs of transacting in these rights is high.
R16. (a) Appropriate activity is the acquisition of property rights without voluntary
exchange. Examples include homesteading, theft, and conquest.
(b) If appropriative activity is taking place, property rights cannot have been
perfectly well defined. Activities like theft and conquest (and the consequent diversion of
resources to defend against theft and conquest) are obviously inefficient. Activities like
homesteading are on a somewhat different footing, as they are certainly productive in and of
themselves. But in the absence of prior property rights, there is likely to be a wasteful
diversion of resources to "rushing" so as to pre-empt other claimants (as in the Oklahoma land
rush).
T3.
(a) Drivers of automobiles impose harmful externalities on one another. Each
driver imposes congestion costs on other drivers, and makes accidents more likely.
(b) It is certainly possible for mutual externalities to be beneficial to one party and
harmful to the other. A department store may be beneficial to nearby specialty shops if it
attracts enough additional customer traffic, and yet the specialty shops may be cutting into the
229
department store's trade. (This is somewhat analogous to the parasite-host relationship in
biology: The host helps the parasite, but the parasite hurts the host.)
T8.
The contract curve consists of all of the combinations for which it is not possible to
make one individual better off without making the other one worse off. If the contract curve
ran on the other side of the midpoint, it would cross through the region containing both
individuals’ “envious zones.” In the double-envious zone region, both individuals could be
made better off, because each of them would be made happier just by trading places with the
other. In other words, one person could be made better off and the other made better off as
well, which precludes having the contract curve there. So, the contract curve must not lie on
that side of the midpoint, but rather on the side that contains the mutual envy-free region.
230
T9.
Figure M16.2 shows an envy-neutral curve, (similar to textbook Figure 16.3). The
envy-neutral curve consists of all the pairs of points which are both diagonally opposite from
each other (relative to midpoint M) and lie on the same indifference curve. If you like, you can
think of each of the pairs as being on a straight line going through M, equidistant from M, and
on the same indifference curve. Points K and K' fit the first two criteria, but not the third, since
K' is preferred to K Point K gives less utility than point G (with indifference curve UG) while
point K' is preferred to G' (also on UG). Therefore, the two diagonally opposite points that are
the same distance from M as K and K. and are on the same indifference curve must be
somewhere like L and L'.
Figure M16.2 (Question 16.T9) Points on the Envy-Neutral Curve
231
TEST BANK
NUMERICAL EXERCISES
N1. You are a government official in charge of determining how many policemen
should patrol a neighborhood with three residents. Through careful questioning, you discover
that the residents would be willing to pay the following total amounts for various quantities of
police protection:
1 patrol
2 patrols
3 patrols
4 patrols
5 patrols
Resident 1
$100
$150
$175
$185
$190
Resident 2
$50
$60
$70
$80
$90
Resident 3
$100
$110
$110
$110
$110
If each patrol costs $35, how many patrols should be sent to the neighborhood?
N2.
Consider an economy made up of three identical individuals, each with a demand
function for good X of
xd = 10 – Px
(a) If X is a private good and the Marginal (social) Cost of producing each unit is
$5, what is the socially optimal level of output of X?
(b) If X is a pure public good, and the Marginal Cost of production is still $5,
what is the socially optimal level of output?
N3.
(A difficult problem). Robinson and Friday inhabit a desert island. There are two
goods: a "private good" G (grain) and a "public good" M (music). (When either plays, the
other also hears.) At the initial endowment situation, Robinson and Friday have, respectively,
gR and gF of grain but no music. Each can sacrifice grain to produce music on a 1:1 basis.
Thus, the production possibilities have simple linear forms: for Robinson, mR + gR = gR and
!
for Friday, mF + gF = gF . But since music is a "public good" Robinson and Friday each
!
consume the aggregate amount M = mR + mF.
!
!
232
(a1) The northeast boundary of Robinson's opportunity set (PPC) on M, gR axes
can be expressed as: M = mF + ( gR -gR) — verify this. Suppose Robinson's preferences are
such that his MRS in consumption (the absolute indifference curve slope on M,gR axes) can
be expressed as M/gR. If gR = 60 and supposing that mF = 10, what is Robinson's
!
consumptive optimum C? What is Robinson's production mR of the public good? Sketch
this solution.
!
(a2) Still assuming gR = 60, now consider mF as a variable (from Robinson's
point of view). Express algebraically the amount mR that Robinson will want to produce, as a
function of mF.
!
(b1) State the equation for the northeast boundary of Friday's opportunity set on
M,gF axes. If Friday's MRS in consumption is M/gF, and if gF = 40 while
mR = 20, what is Friday's consumptive optimum CF*? What will mF be for Friday? Sketch
this solution.
(b2) Still assuming
!
=
40
but
now
letting
mR be a variable for Friday, express
F
mF as a function of mR.
(c) Plot the functions in a(2) and b(2) on mR,mF axes. Solve algebraically to find
their intersection. Is this the equilibrium? Is it true that the wealthier individual (Robinson)
produces more than a proportionate share of the collective good? Explain.
ANSWERS TO NUMERICAL EXERCISES
N1. Using the criterion of aggregate willingness to pay for this public good, sum the values to
the residents of each additional patrol. The first patrol has a value of 250. The second has a
value of 320, an addition of 70. The third patrol has a value of 355, an addition of 35. Since
the social value of the third patrol is just equal to its cost, its employment is borderline in terms
of the preferences of these individuals. Just for completeness, you should also check that the
value of the two additional patrols is less than 35 each, which it is.
233
N2. (a) For a private good, sum horizontally to get the market demand:
Xd = 3(xd) = 30 – 3Px
Put Px on the left side:
Px = 10 – Xd/3
and set it equal to MC:
10 – Xd/3 = 5
The socially optimal output is the solution, X = 15. Each identical individual will consume x
= 5.
(b) For a public good, sum vertically to get the total demand price in terms of these
individuals' marginal willingness to pay:
Px = 3(10-xd) = 30 – 3xd
Set this equal to MC and solve:
30 – 3xd = 5
The optimal level of output is x = 25/3.
N3. (a1) The equation of Robinson's opportunity set is easily verified from the conditions
given in the problem:
M = mR + mF
mR + gR = gR
Solve the second equation for mR and substitute it into the first to verify that
M = mF + ( gR -gR). If mF = 10 and gR = 60, the equation for Robinson's PPC becomes:
!
M = 10 + 60 – gR
!
= 70 – gR
!
It is kinked at M = 10, since M is at least this amount if mF = 10 (see Figure B16.1). The
absolute slope of the PPC is 1, so when Robinson equates MRSC and MRST, he gets:
MRSC == 1 = MRST
Thus, M = gR. Plugging into the equation for M:
M = 10 + 60 – M
This yields the solution M = 35, from which it follows that gR = 35. (See Figure B16.1). If
Friday's production of music is mF = 10, Robinson must be producing 35 – 10 = 25 units of
music.
234
Figure B16.1(Question 16.N3) Robinson's Productive/Consumptive Optimum with One
(a2) From the equation of Robinson's PPC,
M = mF + (60 - M)
mR + mF = mF + 60 – mR – mF
2mR = 60 – mF
mR = 30 – 0.5mF
This expresses the amount of music Robinson will provide given a certain production of music
by Friday. It is also known as Robinson's Reaction Curve (to Friday's production of music) —
see Figure B16.2.
(b1) Friday's PPC has the form:
M = mR + ( gF – gF)
= 20 + 40 – gF
= 60 – gF
!
235
Figure B16.2 (Question 16.N3) Reaction Curves for Robinson and Friday **>>
His consumptive optimum is found by solving the equation of his PPC simultaneously with
his Substitution Equivalence Equation:
M = 60 – gF
The solution values are M = gF = 30. The sketch is similar to Figure B16.1 with appropriate
numerical changes.
(b2) From the equation of Friday's PPC:
M = mR + (40 – M)
mF + mR = mR + 40 - mF – mR
mF = 20 – mR
This is Friday's Reaction Curve to Robinson's production of music.
236
(c) Solve the two reaction functions simultaneously:
mR = 30 – 0.5mF
mF = 20 – mR
The solution values are mF = 20/3, mR = 80/3. This is the equilibrium, just as in a Cournot
duopoly situation. As you can see, Robinson does indeed produce more than his proportionate
share (in terms of his initial wealth) of the public good. Although the externality makes each
tend to slight production of the public good, the poorer individual (counting upon the other to
produce at least some of it) will slight it relatively more.
OBJECTIVE QUESTIONS
B16.1
Public goods are those which:
a. everyone consumes
b. have prices set at zero
c. cannot be produced efficiently by private firms
d. should be distributed equally to everyone
e. are not "used up" as they are consumed.
237
B16.2
You are a government official in charge of determining how many mosquito
abatement officers should patrol a neighborhood with three residents. The following
table shows the residents' willingness to pay for mosquito abatement:
1 treatment
2
3
4
5
tre
tre
tre
tre
at
at
at
at
m
m
m
m
en
en
en
en
ts
ts
ts
ts
Resident 1
$100
$150
$176
$185
$190
Resident 2
$50
$60
$70
$80
$90
Resident 3
$100
$110
$110
$110
$110
If each treatment costs 35, how many treatment should you apply?
a. 1
b. 2
c. 3
d. 4
e. 5.
B16.3
The appropriate way to specify the total demand for a public good is to:
a. sum individual demands horizontally
b. sum individual demands vertically
c. set a single price, and see how much each person demands
d. set a tax rate, and see how much the taxes will buy.
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B16.4
Which of the following is unlikely to be a public good?
a. Water
b. National defense
c. Pollution control
d. Mosquito abatement.
B16.5
In a world of costless transactions and perfectly specified property rights, who should
be liable (in the interests of economic efficiency) for injuries on the job?
a. Either employer or employee. It makes no difference.
b. The employer
c. The employee
d. All employees jointly.
B16.6
When a good's price is below the equilibrium level, more will be exchanged than at
the equilibrium price. (T/F)
B16.7
A competitive steel firm faces the following Marginal Cost function:
MCf = 50 + q
In addition to these private costs, the production of steel generates social costs given by:
MCg = 5 + 0.5 q
The competitive price of steel is $100 per unit. If the firm does not heed the social costs of
steel production, how much will it produce?
a. 20
b. 30
c. 40
d. 50.
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B16.8
If the steel firm is forced to pay for the externalities it generates, how much will it
produce?
a. 20
b. 30
c. 40
d. 50.
B16.9
An economy consists of three identical individuals, each with a demand function for
a good X of:
P = 10 – X
If X is a private good, and the Marginal Cost of each unit is $5, what is the socially optimal
production of X?
a. 15
b. 20
c. 25
d. 30.
B16.10 As above. If X is a public good, what is the socially optimal production of X?
a. 10/3
b. 15/3
c. 20/3
d. 25/3.
B16.11 As above. If X is a public good produced by a monopolist with MC = 6, how
much will be produced?
a. 4
b. 5
c. 6
d. 7.
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DISCUSSION QUESTIONS AND PROBLEMS
1. An isolated fishing village has two sources of food: an unowned lake, which produces
fish (F) according to the production function: F = 12L – L2 (where L represents the number
of fishermen in the lake at any given time), and an ocean, which produces fish according to the
production function F = 2L. There are twelve inhabitants of the village.
(a) Confirm that there will be 10 people fishing in the lake and 2 in the ocean. Calculate
the wage in terms of fish, and the total number of fish produced by the community.
(b) The inhabitants become aware of a significant externality problem in the lake. Their
solution is to let the lake come under private ownership, auctioning it off to the highest bidder.
(I)
Calculate the new wage in terms of fish, the number of fishermen that the new owner
will hire, and the community's total output.
(ii) What will the new owner be willing to bid for the lake?
2. A public good can be produced at $50 per unit. The demand curves of the two consumers
are shown in Figure B16.3. Picture the socially optimal output of the public good in this
diagram.
Figure B16.3
3. Give two examples of a "technological" externality and explain why it is an externality.
What efficiency condition is violated by the externality? Discuss ways in which the
externality might be eliminated by:
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(a) Taxation or subsidization.
(b) Unitization (single-ownership)
(c) Property reassignment.
4. "Thievery is a bad thing for victims, but a good thing for thieves, so a cold-blooded
economic analysis would be unable to say if thievery is good or bad." Evaluate.
5. An apple orchard provides free nectar for a beekeeper, while the beekeeper provides free
pollination for the apple farmer. Each benefits greatly by the presence of the other.
(a) Could this situation be inefficient? If so, is it necessarily inefficient?
(b) Is it true that inefficiency can be avoided only if the orchard and the bees are owned
by the same person?
6. Highway congestion is an example of a technological externality. A given driver imposes
congestion costs on others, but does not heed the costs himself.
(a) Draw a typical driver's private Marginal Cost curve MCP, and the social Marginal
Cost curve MCS. Is one curve necessarily higher than the other?
(b) In the same diagram you used for (a), locate the efficient level of driving, and show
the deadweight loss that results from over-use of the highway.
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CHAPTER 17
TEACHING TIPS
This chapter makes for both easy reading and interesting classroom discussion. Coverage of
this exciting new extension of economic analysis will go far towards deepening the students'
interests in economics.
ANSWERS
R3.
(a) A delegate may make decisions not in the interests of his constituents because
he is unaware of those interests or because he lacks incentive to act in the interest of his
constituents. The second is probably much the more important problem. Between elections a
delegate is relatively free from control by his constituents. Since elections tend to be
infrequent, a delegate may act against the interest of his constituents for some time before he
has to face them. And of course, by clever campaigning he may win reelection despite his
misdeeds in office.
(b) Stockholders have somewhat more protection than citizens. First of all,
politicians may be in a position to make decisions affecting almost all of citizens' wealth, and
even their lives; managers can only make decisions affecting that portion of an individual's
wealth which he has contributed to the corporation. Second, a dissenting stockholder may sell
his shares. A citizen does not have the opportunity to sell his "ownership" share in
government (except by going into exile).
R4.
(a) Bureaucrats face less competition, once employed, than elected officials (there
may be some rent-seeking in obtaining their positions). They may feel less inclined to put “the
will of the people” into effect. Still, they would be concerned with promotions and job
security, and would thus be careful to please their superiors, who are usually other bureaucrats.
Appointed officials may feel some political pressure to adhere to the policies of those who
appointed them.
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(b) Bureaucrats also face somewhat less competition than firm managers, and are
probably under less scrutiny. The methods for achieving promotion are also somewhat
different. Many bureaucrats are isolated from both their “shareholders” (taxpayers) and their
“customers” (citizenry), and therefore less influenced by them.
R6.
(a) The conditions are: (i) Voters always prefer proposals that are nearer over those
farther from their ideal positions. (ii) There is a continuum of options offered to voters.
(b) Single-issue majority elections with a large number of voters are the most likely
to meet these conditions.
R7.
(a) See Figure 17.5 in the text. By comparing Panels (a) and (b), we can see that
mutual antipathy, which means both parties regard the others' income as a bad, gives the
indifference curves a positive slope (Panel (a)). The region of mutual advantage MSS' is thus
smaller than in Panel (b), where the indifference curves are negatively sloped. Naturally, it is
harder for two parties to reach an agreement when neither wants the other to gain from the
agreement.
(b) See Figure 17.4 in the text. For a given location of the point M, the more the
social opportunity frontier bows in toward the origin, the more likely it is that point M will lie
outside the frontier as in Panel (a). When this happens, it means that each party expects to do
better by fighting than by compromising. The result of rivalry is that each party must make
large sacrifices to satisfy the other, so neither will give in.
(c) See Figure 17.3 in the text. The greater the confidence of either party, the
farther is point M from the origin, so it is more likely that M will be only slightly below the
social opportunity frontier or even outside it (as in Panel (b)). The region of mutual advantage
(MSS' in Panel (a)) will be small or nonexistent, making compromise difficult or impossible.
R8.
See Figure 17.5 Panel (a), in the text. Supposing that the Blues and Grays agree on
an efficient compromise, they would locate somewhere along the segment SS'. But if the
compromise is unenforceable, one party may gain by violating the agreement. For example, if
the Grays cheat, society would move to some point above S. The Blues, recognizing this
possibility, would be unwilling to negotiate a compromise.
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R10. Four games are illustrated in Table 17.1 in the text. Games are more likely to lead
to cooperative solutions when both parties stand to gain more from cooperation than from
conflict.
R11. With single-peaked preferences and only one dimension of choice, an option near
the middle will always win a majority over one farther from the middle; thus there can be no
cycling. With more than one dimension of choice, we have the situation shown in Figure 17.2
in the text. The petals represent options that can command a 2:1 majority over option X.
Since such a diagram can be drawn for any point X, cycling will always occur if there is a
continuum of options, and may or may not occur for a finite number of options.
T4.
(a) Under a system of majority rule (e.g., democracy) the decision of the majority
will become law. Thus the majority can exploit the minority.
(b) Even in a majority rule system, a minority that constitutes a compact interest
group can often bring its desires more effectively to bear upon the voters' delegates
(legislators, elected officials, bureaucrats, etc.) who actually make the decisions. So a diffuse
majority may have less political weight than an organized minority.
T7.
The arguments in favor of open corruption are somewhat like the arguments for
permitting purchase of votes under the majority system. In each case there is a tendency
toward Pareto-efficiency, as the side with more to gain can afford to pay more. But, in either
case, the solution is not necessarily Pareto-preferred to the original situation. In fact, the side
that can afford to pay less is almost certain to be victimized (even totally expropriated) under
either of these systems. This latter feature is of course a very serious objection. Another
difficulty is that, under a system of open corruption, there seems to be no way of compelling
the corrupt officials to live up to their agreements, or otherwise to limit their exploitation of
the public.
T9.
Figure M17.1 shows some examples. In Panel (a), the Grays are optimistic while the
Blues are pessimistic. In Panel (b), the Grays have rivalrous opportunities, while the Blues
prosper if the Grays do. Panel (b) is analogous to the relationship between a host (the Grays)
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and a parasite (the Blues). The Grays suffer if the Blues prosper, but the Blues can only
prosper if the Grays do. They will live in peace only if the outcome is in the dark overlapping
area. Panel (c) shows the situation in which the Grays do not like the Blues, as indicated by the
indifference curve UG. On the other hand, the Blues like the Grays, as indicated by their
indifference curve UB.
Figure M17.1 (Question 17.T9) Non-symmetrical Situations
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T11. Whether the rivalry is great or small, being the first mover always limits the choices
left to the second mover. The degree of rivalry determines whether that limitation is good or
bad for the first mover. If the second mover’s interests are opposed to those of the first mover,
then the second mover is left with no choice but to do what is in the first mover’s worst
interest. What is best for the second mover, knowing what the first mover has done, will be the
worst thing for the first mover. Thus, when rivalry is great, the second mover has the
advantage. If the rivalry is small, the first mover limits the choices of the second mover as
well. However, what is best for the second mover, given the movement of the first mover, is
what is also best for the first mover. The first mover takes the lead, and the second mover’s
best choice is to follow the lead of the first.
T12. Because of cycling, picking the choices people have (or the order in which those
choices are presented) can determine the outcome of the choices they make. Thus, arranging
“contests” between candidates, bills, or issues can determine the outcome more than merely
voting on them.
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TEST BANK
DISCUSSION QUESTIONS
1. Explain how a democracy may be subject to intransitivity in its choices. Use an
example with three voters, A, B, and C, and three projects, a, b, and c.
2. Corporate stockholders vote for managers just as citizens in a democracy vote for
public officials. Given this, is there any difference between the incentive structure faced by a
corporate manager and that faced by a public official? Is there a difference between the
incentives of the "voters" in a corporation and the voters in a democracy?
3. Political "strongmen" run their countries as if the country were their property. Suppose
the various states of the U.S. were all run in this way. How would this differ from our current
system if citizens were freely mobile between states? What if each ruler could prevent his
citizens from leaving?
4. Explain the free-rider problem and how it comes about. In what sense can government
remedy the free-rider problem?
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ANSWERS TO OBJECTIVE QUESTIONS
Chapter 1
B1.1. F; B1.2. d; B1.3. c; B1.4. c; B1.5. d; B1.6. d; B1.7. a; B1.8. F
Chapter 2
B2.1. F; B2.2. a; B2.3. a; B2.4. F; B2.5. F; B2.6. b; B2.7. c; B2.8. a; B2.9. F;
B2.10. a; B2.11. b; B2.12. d; B2.13. a; B2.14. F; B2.15. F; B2.16. T; B2.17. T;
B2.18. T; B2.19. T; B2.20. c; B2.21. F
Chapter 3
B3.1. c; B3.2. b; B3.3. T; B3.4. c; B3.5. b; B3.6. T; B3.7. c; B3.8. a; B3.9. T
Chapter 4
B4.1. F; B4.2. T; B4.3. F; B4.4. c; B4.5. F; B4.6. F; B4.7. d; B4.8. d; B4.9. c;
B4.10. F; B4.11. F; B4.12. a; B4.13. b; B4.14. T; B4.15. c; B4.16. c; B4.17. T;
B4.18. a; B4.19. a; B4.20. a
Chapter 5
B5.1. F; B5.2. F; B5.3. a; B5.4. T; B5.5. F; B5.6. T; B5.7. d; B5.8. d; B5.9. b;
B5.10. c; B5.11. b; B5.12. a; B5.13. b; B5.14. a; B5.15. c; B5.16. T
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Chapter 6
B6.1. F; B6.2. T; B6.3. c; B6.4. T; B6.5. c; B6.6. b; B6.7. c;
B6.8. F; B6.9. d; B6.10. b; B6.11. F; B6.12. c; B6.13. b; B6.14. T; B6.15. T;
B6.16. T; B6.17. T; B6.18. F; B6.19. T; B6.20. T
Chapter 7
B7.1. F; B7.2. b; B7.3. b; B7.4. a; B7.5. F; B7.6. c; B7.7. c; B7.8. a; B7.9. c;
B7.10. b; B7.11. T; B7.12. d; B7.13. F; B7.14. T; B7.15. T
Chapter 8
B8.1. b; B8.2. T; B8.3. d; B8.4. b; B8.5. b; B8.6. a; B8.7. d; B8.8. F; B8.9. F;
B8.10. a; B8.11. c; B8.12. d; B8.13. d; B8.14. b
Chapter 9
B9.1. T; B9.2. T; B9.3. F; B9.4. T; B9.5. c; B9.6. F; B9.7. b
Chapter 10
B10.1. d; B10.2. a; B10.3. T; B10.4. T; B10.5. c; B10.6. c; B10.7. b; B10.8. b;
B10.9. c; B10.10. a
Chapter 11
B11.1. F; B11.2. b; B11.3. d; B11.4. e; B11.5. T; B11.6. a;
B11.7. c; B11.8. b; B11.9. T; B11.10. F; B11.11. d; B11.12. c;
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B11.13. a; B11.14. T; B11.15. c; B11.16. F; B11.17. b; B11.18. d;
B11.19. c
Chapter 12
B12.1. a; B12.2. d; B12.3. T; B12.4. T; B12.5. a; B12.6. T; B12.7. T; B12.8. d;
B12.9. T; B12.10. F; B12.11. c; B12.12. a; B12.13. F;
B12.14. T; B12.15. T; B12.16. b; B12.17. a; B12.18. b; B12.19. b; B12.20. a;
B12.21. d; B12.22. c; B12.23. F
Chapter 13
B13.1. T; B13.2. e; B13.3. c; B13.4. a; B13.5. d; B13.6. T; B13.7. d; B13.8. F;
B13.9. F; B13.10. T; B13.11. a; B13.12. T; B13.13. a;
B13.14. T; B13.15. a
Chapter 14
B14.1. F; B14.2. e; B14.3. d; B14.4. a; B14.5. F; B14.6. d; B14.7. c; B14.8. b;
B14.9. e; B14.10. a; B14.11. c; B14.12. d
Chapter 15
B15.1. c; B15.2. a; B15.3. T; B15.4. b; B15.5. c; B15.6. d; B15.7. T; B15.8. b;
B15.9. T; B15.10. F; B15.11. a; B15.12. a; B15.13. d;
B15.14. T; B15.15. a; B15.16. F; B15.17. F; B15.18. d
Chapter 16
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B16.1. e; B16.2. c; B16.3. b; B16.4. a; B16.5. a; B16.6. F; B16.7. d; B16.8. b;
B16.9. a; B16.10. d; B16.11. a
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