Law 678: Introduction to Microeconomics
STANFORD LAW SCHOOL
Autumn Quarter 2012
Instructor: Alex Gould
ANSWERS TO ALL QUESTIONS FOR REVIEW AND PROBLEMS –
FRANK TEXT CHAPTERS 5,6,8,9,10,11,12
Chapter 5
Answers to Questions for Review
1. Because gasoline is relatively more expensive than other goods after the tax, consumers
substitute away from it and will spend only part of the tax rebate on gasoline. consequently
the consumption of gasoline does fall, but not as much as it would if the rebate were not
given.
2. A two-part pricing scheme exists when a seller charges a initiation fee or cover charge and
then a per unit charge as well. This is an attempt on the part of the seller to capture as much
consumer surplus as possible.
3. The demand of each individual will be different, but the industry demand for education will
surely be more inelastic than the demand facing any given school.
4. Heavy drinkers are generally lower income and consume a sizable portion of their budget in
alcohol. Therefore the income effect is stronger than is often thought.
5. The interest rate is the premium required to move future income to the present. Since future
goods are on the vertical axis and present goods are on the horizontal axis the budget line
becomes an exchange rate between future and present income.
6.
other goods ($/year)
b
q0
q1
a
gas (gal/year)
The most important reason is the increase in income. Assume that, 30 years ago, the budget
constraint was b and the optimal consumption was q0. Although the price of gas has
increased, so has income. The budget constraint (a) has become steeper, but it has also shifted
outward. Optimal consumption increases to q1, despite the increase in price.
7. According to the permanent income hypothesis, consumption in each year is a constant
proportion of the present value of lifetime income, or permanent income. Jennifer's lottery
winnings more than double her current income, but have a much smaller proportional effect
on her permanent income. So the proportional increase in her current consumption should be
smaller than the proportional increase in her current income.
Answers to Chapter 5 Problems
1.
Other goods ($/year)
Yr - Pe
Yr - 2Pe
Yp - Pe
Yp - 2Pe
1
Y*
Quality of Education
(Yr - Pe)/Pe
The rich family has income (Yr), the poor family has income (Yp), where Yr>Yp. The two
families have the same indifference maps. The rich family's budget constraint is the heavy
line, and the poor family’s budget constraint in the thinner one. The poor family maximizes
utility by purchasing only public education (i.e., 1 unit of quality), but the rich family buys
Y*>1 units of private education.
2.
Other goods ($/year)
M + 1000
M
a
b
1000
M/2
c
(M + 1000)/2 M
Gas(gallons/year)
Assume the consumer's original income was M. His original budget constraint is a; after the
gas price increase, it is b; and after the money from his uncle it is c. At the very end, he can
afford the original bundle he bought. But his indifference curve at the original optimum is
below his new budget constraint. By decreasing his gas consumption and increasing other
goods consumption, he can reach a higher indifference curve. (see dotted indifference curve)
3. The loss in consumer's surplus is 5, the area of the shaded trapezoid in the diagram:
4.
P= $4/movie, Q=8 movies/year, consumer surplus = $64. So maximum he will pay for
membership is $64.
5. Since her demand for caviar is inelastic at all prices, the increase in the price of caviar will
cause her total spending on it to go up. The money left over for hot dogs will decrease. Since
their price stays the same, consumption of hot dogs will decrease.
6. The two budget lines and last year's optimal bundle are shown in the diagram. A closer look
at the tangency point for last year's bundle shows that this year Jones can afford a bundle he
prefers to last year's.
Y
42
Last year's bundle
This year's bundle
34
30
Last year's budget
0
20
70
7. PV = 210 + 210/1.05 = 210 + 200 = 410 .
This year's budget
170
X
C2
Budget constraint when r = 0.20
462
430.5
Budget constraint when r = 0.05
210
210
385
410
C1
8. 1-for-1 substitutes means MRTP = 1 (slope of indifference curves = -1). In this case, Smith
will consume all of his resources in the next period.
9.
From Problem 7, Smith's intertemporal budget constraint is C2 = 430.5 - 1.05C1. Since Smith views
current and future consumption as one-to-one complements, he will consume equal amounts in both
periods C1 = C2. Setting C1 = C2 in his intertemporal budget constraint C2 = 430.5 - 1.05C1 yields C2 =
430.5 - 1.05C2, which solves for C1 = C2 = 210.
10. a) Facing an interest rate r = 0, Karen's intertemporal budget constraint is C2 = 150,000 - C1.
Her constraint has endpoints (C1 = 150,000, C2 = 0) and (C1 = 0, C2 = 150,000).
Future Consumption
($000) 150
C2 = 150000 – C1
75
0
75
Current Consumption ($000)
150
10. b) Facing an interest rate r = 0.1, Karen's new intertemporal budget constraint is
C2 = 157,500 - 1.1C1. Her new constraint has endpoints (C1 = 143,182, C2 = 0) and (C1 = 0,
C2 = 157,500).
Future Consumption
($000) 157.5
C2 = 157,500 – 1.1C1
75
0
11. a) $50,000/1.08 = $46,296;
75
Current Consumption ($000)
143.2
11. b) $50,000/1.1 = $45,455;
11. c) $50,000/1.12 = $44,643.
12. a) The highest attainable indifference curve passes through the bundle (100, 100).
12. b) Now the optimal bundle is to consume everything in the future. The bold line is the budget
line and the normal line is the indifference curve with an .8 MRTP.
C2
Optimal bundle
190
100
100
237.5
13. Kathy's intertemporal budget constraint is C2 = (1 + r)55,000 + 60,000 - (1 + r)C1. Her maximum
current consumption would occur by setting C2 = 0 and solving for C1 = 55,000 + 60,000/(1 + r). To
achieve C1 = 105,000, then 55,000 + 60,000/(1 + r) = 105,000 implies 60,000/(1 + r) = 50,000, which
solves for r = 0.2 (20% interest). Similarly, her maximum future consumption would occur by setting
C1 = 0 and solving for C2 = (1 + r)55,000 + 60,000. If C2 = 1200,500, then (1 + r)55,000 + 60,000 =
120,500, and so (1 + r)55,000 = 60,000, which solves for r = 0.1 (10% interest).
14. True
The enlarged picture would look like the one above. The original intertemporal budget
constraint is A (with slope -1.1), and the new constraint is B (with slope -1.2). The original
decision was point a. The new budget constraint also passes through a. But she can do much
better by choosing point b. The increase in interest rate causes her to save today and consume
more next period.
15. Because Joe's initial bundle (A in the diagram) was given to him, as opposed to having been
chosen by him, there is no presumption that it was optimal for the initial prices. Indeed, it
may be that the initial bundle turns out to be optimal for the new budget constraint, as shown,
in which case Joe is not better off as a result of the price change. So false.
Price
100
75
A
50
1
2
3 Quantity
16. The original budget constraint and the post-change budget constraint are shown as B1 and B2,
respectively. Harry curtails his mileage from M1 to M2. The heavy line is the extra revenue Tom and
Karen collect from the higher mileage charge, which is less than $10/wk.
Y
Y0 + 10
Y0
← Extra revenue from 40 cent fee < $10
Y2
C
A
Y1
B1 B2
M1 M2
Y0/.2
(Y0 + 10/.4)
B
miles/wk
17. a) Let R be the buyer's reservation price for the right to use the book for one year. Let U be
the price of a used book. Then the reservation price for a new book is R + U/(1+r) = R + $20
= $50 => R=30.
Reservation price for book with disappearing ink = R= 30
17. b) Profits with normal ink: (N/2)(R+20-m) = 25N -mN/2 = A
Profits with disappearing ink: N(R-m) = 30N - mN = B
B - A = N(5 - m/2) > 0 if and only if m < 10.
18. The opportunity cost of Herb's time is the $6/hr he can earn in the library. His optimal 2-part
tariff for tutoring is thus a $6/hr fee plus a fixed fee given by the 8 units of consumer surplus
each tutee would receive if there were no fixed fee. Thus his tutoring fee is $8 + $6/hr.
Confronted by this fee schedule, each graduate student will want to purchase 4 hr/wk of
tutoring. This gives Herb his desired 12 hr/wk, with total earnings of $96/wk. He should not
spend any time clerking in the library.
Price
10
6
⇐ area = 8
4
10
Quantity
19. If P0 is the tuition of other universities and Cornell provides a subsidy of kP0, CFCs will have
to pay only (1-k)P0 after the subsidy. The quantity (in 1000s) of CFCs attending other
universities in the absence of any subsidy is Q0 = 2-(P0/5). With the subsidy, this quantity
goes up to Q' = 2-((1-k)P0/5). The extra revenue Cornell will get (in $1000s) by being able to
sell the extra slots is
DTR = 15(Q'-Q0) = 15(kP0/5)= 3kP0.
Each subsidized CFC costs Cornell kP0. Since there are Q' students subsidized, the total
subsidy cost is equal to
S = kP0Q' = kP0 [2-((1-k)P0/5)] = 2kP0 -kP02/5 + k2P02/5 .
Cornell's goal is to chose the value of k that maximizes
D = DTR - S = kP0 + kP02/5 - k2P02/5 .
The first order condition is
dD/dk = P0 +P02/5 -2kP02/5 = 0,
which solves for k* = (5+P0)/2P0 .
Thus, if tuition at other universities (in $1000s) is P0 = 24, we have k* = .6.
Tuition in other universities
P (1000)
C
4
1
CS = $4.50
3
4
QC
20. For P0=12, we have k*= .71, which means that Cornell should pay .71% of the outside
tuition. If the tuition of other schools was low enough, (For example, k* = 4) then Cornell
should pay all the tuition and also give a cash bonus of $500 to each CFC who attends an
outside university.
21. His optimal strategy is to sell popcorn at marginal cost and then add the consumer surplus
from popcorn to the consumer's reservation price for the movie ticket. Thus, the price of
popcorn should be $1/qt, which yields a consumer surplus of $4.50 from popcorn. The ticket
price should be 30
$5 + $4.50 = $9.50.
P0
(1-k) P0
Additional Problems
2-P0/5
2-(1-k)P0/5
6
Q0 (1000)
1. Indicate for the following goods which is likely to have the more inelastic demand:
a.
b.
c.
Beck's beer or beer in general
insulin or Frisbees
gasoline over a 24-hour period or over a 6-month period
2. True or False: Suppose we measure the cross-price elasticity between automobiles and tires
using tires as X and autos as Y. If we change this to a situation where tires are Y and autos
are X, we will get the same answer. (Explain your answer.)
3. Joe and Rita are the only people in town that like peppermint stick ice cream. Joe's demand is
given by the equation P = 10 - 2Q, and Rita's demand is P = 10 - Q.
a. What is the total town demand?
b. Suppose Frank moves to town. His demand is given by the equation P = 10 - 3Q.
Now what is the total demand?
4. Suppose that the demand for crossing the Golden Gate Bridge is given by the equation
Q = 10,000 - 1000P.
a. If the toll (P) is $2, how much revenue is collected?
b. What is the price elasticity of demand at this point?
c. Could the bridge authorities increase their revenues by raising or lowering their price?
d. The Red and White Lines, a ferry service which competes with the Golden Gate Bridge,
began operating hovercrafts, which made commuting by ferry much more convenient.
How would this affect the elasticity of demand for the Golden Gate Bridge?
5. Indicate for the following whether the income elasticity of demand is likely to be positive,
negative, or zero.
a. hamburger (you earn $3,000 a year)
b. hamburger (you earn $20,000 a year)
c.
hamburger (you are a vegetarian)
d.
yachts
e.
champagne
6. The demand for candy bars is given by P = 5 - 0.01Q, where P is measured in dollars and Q
in candy bars.
a.
How much revenue is collected at $3?
b.
What is the elasticity of demand at $3?
c.
At what point is revenue maximized?
d.
If the supply curve is given by Q = 10P, what is the equilibrium price?
7. Is the cross-price elasticity positive or negative for the following items?
a.
tuna and peanut butter
b.
first-run movies and rental movies
c.
beer and pretzels
d.
personal computers and typewriters
8. You walk past a soft drink machine and your demand for a Coke is P = 2 – Q. You want one
bottle and the price of a bottle is $1.45. Do you buy the bottle? Why?
9. In the recession of 2007-09 interest rates nearly went to zero. Show using indifference curves
and budget lines what effect on savings a zero interest rate would have.
Chapter 6
Answers to Questions for Review
1. If anyone can fake the signal, it will cease to be a signal at all since it would be meaningless
information.
2. The full disclosure principle means that advertisers will be eager to separate their products
from products with lesser qualities.
3. Interviewees will have an incentive to tell information about which the employer may have
concern even if the employer is not allowed to ask for the information. Employers may
expect the worst, so the applicant will make sure that the employer knows that the worst is
not true.
4. The low-risk types subsidize the high-risk people in the group, because the insurance
company will charge a premium to cover the average claim.
5. The rate will be higher than it should be because those who are the best risks leave the pool
and self-insure. That raises the rates for those left, and the best risks left are again inclined to
self- insure. Thus the average premium keeps climbing.
6. It is logical that there are diminishing returns to wealth, and therefore risk aversion is normal.
7. Gambling and bungee jumping might help you start your list.
8. Focus on the idea that insurance companies will need to cover their risk and make profits.
9. The service contracts on small appliances and credit card insurance when the maximum loss
is only $50 are two of the obvious ones.
Answers to Chapter 6 Problems
1. If the general threshold for denying admission is 80, and if those who deny admission are
uniformly distributed between 80 and 100, then our best estimate of the messiness index of
someone who denies admission will be 90. The threshold will not be stable. Someone whose
messiness index is between 80 and 90 has good reason to let people in rather than be assumed
to have an index of 90. A threshold of 90 should be unstable for similar reasons, as indeed
will any disclosure threshold less than 100. In practice, the fact that some people do refuse to
let others see their messy apartments seems to indicate that actually seeing the mess firsthand
will be more damaging than having people conclude in the abstract that the apartment is
messy.
2. One salient fact about teenage males is that they have much higher automobile accident rates
than other groups. A company that charged the same rates to teenage males as it changes to
all other groups would therefore have to have higher premiums than those other companies
charge members of all other groups. There would then be no reason for these other group
members to remain with the company. In the end, the company with uniform rates for all
groups would have to charge a premium high enough to cover the expected losses of
members in the highest risk group.
3. If all consumers value nondefective cars at $6000 and used cars sell for only $1000, then no
nondefective cars will be offered for sale in the used market. The only used cars for sale will
be defective, so we know that the value consumers place on a defective car must be exactly
1000. Since consumers are risk neutral, the expected value of a new car, En, is simply the
sum of the expected values of nondefective and defective cars:
En = (1-d)(6000) + d(1000) = 4000, which solves for d = 0.4.
4. The expected value of a new motorcycle, En, is equal to En =9000 = (1-d) 1000 + d X,
where X is the price of a nondefective one and d is the proportion of defective motorcycles.
Therefore, 9000=0.8X + 0.2(1000), which solves for X=$11,000.
5. You know your car is not a lemon; but if you try to sell it, the market will assume it is, and
you will be unable to get full value for it. This makes it more worth your while to fix the car.
6. Because social workers receive very low salaries relative to the amount of education they
have, it is a reasonably safe inference that most of them chose that line of work for reasons
other than money. And if the primary motive for cheating at cards is monetary gain, it
follows that a social worker is not very likely to cheat. In the case of the used car
salesperson, by contrast, there is no similar presumption of nondefective motivation.
Moreover, there is at least some indication that the capacity to dissemble is linked to success
in selling.
7. The college degree is a signal to the employer about the “smartness” of an employee. Assume
that the smartness of an employee is distributed between 0 and S. The only costs to education
are monetary costs and the difficulty of passing courses, which is lower for smarter students.
Thus, for any two people with the same wealth, the smarter one is likely to have more
education. At the beginning of the century, let’s say that the average high-school graduate
had smartness level of Sh and the average college graduate had Sc, where Sc>Sh. Since the
monetary costs of education went down, more people are getting education, especially the
ones who were smart but could not afford it before. Also, smarter high school graduates will
now be getting college degrees. Assume the average smartness level of a high school
graduate now is Nh and of a college graduate is Nc. Then Nh<Sh and Nc<Sc. Of these four
quantities, Sc is the highest and Nh is the lowest, but we do not exactly know the relationship
between Sh and Nc. If Nc<Sh, then banks might raise their education criterion.
8.
The expected value of one toss of a six-sided die is
EV = (1/6)(1+2+3+4+5+6)=21/6=3.5 .
9.
The expected value of the gamble is given by
EV = (1/4)(20) + (1/4)(9) + (1/4)(-7) + (1/4)(-16) = +1.5 .
10. EU = (1/4)
+ (1/4)
+ (1/4)
Your utility without the gamble is
+ (1/4)
= 6/4 + 5/4 + 3/4 = 3.5.
= 4.0; so you will not accept the gamble.
11. a) 40% with probability 0.3
-100% with probability 0.2
10% with probability 0.5
E(interest rate)= 0.3(0.4) + 0.2(-1) + 0.5(0.1) = -0.03 = -3%
11. b) EU(govt. bond) = (1.08x10,000)2 = 116, 640,000
EU(junk bond) = 0.3(1.4x10,000)2 + 0.2(0)2 + 0.5(1.1x10,000)2 = 119,300,000
Since EU(junk bond) > EU (govt. bond), you will invest in the junk bond.
11. c) EU(govt. bond)
=
= 103.92
EU(junk bond) = 0.3
+ 0.2
+ 0.5
= 87.94 .
Since EU(junk bond) < EU (govt. bond), you will invest in the govt. bond.
12. EU(with ticket) = 0.25(110)2 + 0.75 (100)2
= 10,525.
The wealth level to give the same utility for sure is
w=
= 102.59.
Thus you would be willing to sell the ticket for 2.59.
13. EU (without insurance) = 0.99999
= 632.449 .
w = (632.449)2 = 399,992 .
The wealth level to give the same utility is
So you would be willing to pay $8 for this insurance.
14. With one trip, EU1 = (1/2)
+ (1/2)
=5
With two trips, there are four equally likely outcomes:
First Trip
0 break
500 break
0 break
500 break
1.
2.
3.
4.
Second Trip
0 break
0 break
500 break
500 break
Income
100
50
50
0
Probability
1/4
1/4
1/4
1/4
EU2 = (1/4)
+ (1/4)
+ (1/4)
+ (1/4)
= 2.5 + 1.77 + 1.77 = 6.04 So it is better
to take two trips than one, even though the expected number of eggs broken is the same either way.
Moral: Don't put all your eggs in one basket!
15. a) EV = (1/2)15 - (1/2)13 = 1.0
15. b) EU = (1/2)
+ (1/2)
15. c) EV = 0
EU = (1/2)
+ (1/2)
Without gamble U = 7 .
=4+3=7
= 4 + 5.83/2 = 6.91
15. d) Let x = the most you would pay to get out of the gamble. Then
49-x = 47.75
x = 1.25
16. a) EU = (
investment.
)/2 + (
)/2 = 10.5 <
16. b) With 2 equal partners, EU = [
so Smith will make the investment.
17. Expected utility without info = max[
= 6.91
= 10.536, so Smith will not make the
] /2 + (
, (.2
So without info, he will choose to become a lawyer.
) /2 = 10.55 >
+ .8
,
)] = max (9, 10) = 10.
Suppose info costs P;
Expected utility with info = 0.2
+ 0.8
Set EU with info = EU without info = 10 and solve for P:
P = 53.68. For any price less than this amount, he should pay Smith for his evaluation.
18. Assume that Smith has the policy that he will charge only if he tells the person he will
become a lawyer, and also assume that he never lies since he wants to make a reputation to
stay in this business. Thus, he charges $p with probability 0.2 and charges $0 with probability
0.8. The maximum amount John will be willing to pay for this deal will be given by,
EU(with info) = EU(without info)
0.2
+ 0.8
= 10 which solves for p = $704. So Smith would do much better if he
employs this policy!
19. a) For group 1, the reservation price of insurance is found by solving
= .5
+ .5
= 9, which yields x1 = 19.
For group 2, we get
= .9
+ .1
= 9.8, which yields x2 = 3.96.
19. b) If members of the two groups are indistinguishable, an insurance company will have to
charge the same premium to each. If its policyholders consisted of equal numbers of people
from each group, this premium would have to cover the expected loss, which is
[(.5)(36)+(.1)(36)]/2=10.8. Since this exceeds the reservation price of members of group 2,
nobody from that group would buy insurance. And with only group 1 members remaining in
the insured pool, the premium would have to rise to 18 in order to cover the expected loss for
members of that group.
19. c) If a company has the test described, and the test says a person is a member of group 2, then
the expected benefit payout from insuring that person is
x(.1)(36) + (1-x)(.5)(36) = 18 - 14.4x = E(L). Setting E(L) equal to the reservation price for group 2
we get 18 - 14.4x = 3.96, or x = .975. The test would have to be accurate 97.5% of the time in order
for a member of group 2 to find insurance an acceptable buy.
20. a) Let X1 denote the reservation price for members of group 1. X1 must satisfy the equation
= .5
+ .5
= 11, which solves for X1 = 23. The reservation price for
group 2 must satisfy
= .1
+ .9
= 11.8, which solves for X2=4.76.
20. b) The most an insurance company can charge and still include group 2 members is X2=4.76.
Let p be the proportion of group 1 members in the potential client pool. If the price is low
enough to attract group 2 members, it will necessarily also attract members of group 1. The
expected benefit payouts for members of the two groups, denoted B1 and B2, are given by
B1=.5(44)=22 and B2=.1(44)=4.4. The expected benefit payment per client, B, is thus a
weighted average of these expected payouts, where the weights are the respective population
shares in the client pool: B=p(22) + (1-p)(4.4)= 4.4 + 17.6p. Equating this expected benefit
payment to the reservation price X2, we have 4.4 + 17.6p = 4.76, which solves for p =
.36/17.6 = .02. Thus, if more than 2% of the potential client pool consists of members of
group 1, it will be impossible to include members of group 2.
21. Let m be Smith's initial wealth, and u be his utility function.
Picking A over B => uA = u(m+100) > EuB = .8u(m+150) + .2u(m)
Picking D over C => EuD = .4u(m+150) + .6u(m) > EuC = .5u(m+100) + .5u(m)
Rearranging terms of the last inequality, we have .5u(m+100) < .4u(m+150) + .1u(m). Dividing both
sides by .5 gives u(m+100) < .8u(m+150) + .2u(m), which is the reverse order of the inequality
implied by the choice of A over B, hence
the inconsistency.
Additional Problems
1. Suppose you have $100 to invest or store in a safe deposit box. Your only alternative to
storing is a stock which sells for $100. The stock is an initial public offering for a company
with a risky idea that is projected to double in value in a year if the idea works. The history of
such ventures is that 50% of the time they fail and you lose your money. The other half of the
time they double your money in a year.
a. What is the expected value of each option at the end of the year?
b. Which option would you take if your utility function for money is u(M) = M2 ?
c. Which option would you take if your utility function for money is u(M) = M1/2
2. Congratulations, you are a contestant on the famous game show "Let's Make a Deal" and you
have been selected you as a final contestant. You have a choice: you can take $64 in cash or
you can gamble. If you decide to gamble, there are three possible outcomes: door number
one, door number two, and door number three. Behind one of the doors is a prize valued at
$100, another door has a prize valued at $81, and one door has a prize worth $1.
a. What is the expected value of the gamble?
b. If you are risk neutral, which option would you choose?
c. Suppose your utility function is of the form u = M1/2; which option would you
choose?
d. Suppose your utility function is of the form u = M1/2; what is the smallest amount of
money that Monty could offer you (with certainty) so that you would just be
indifferent between the sure thing and the gamble?
3. Your father has had one accident and two speeding tickets during the last year. You are a
highly respected, honor student in your senior year of high school. You have a perfect driving
record, are active in Mothers Against Drunk Driving, and have taken all the driver training
requirements and more. Yet your car insurance rates are 25% higher than your father’s rates
and you have to pay the difference. You call the insurance company to complain. How could
the person from the company explain such an injustice in rates?
4. Give a case example where the positional externality concept is operative in international
affairs.
Chapter 8
Answers to Questions for Review
1.
You would be willing to pay more if case 1 were true.
2.
Gathering information is costly, and at some point the costs outweigh the benefits.
3.
The decision that leads to the best possible outcome may be too costly to find.
4.
No. If the marginal utility of wealth decreases with wealth, then weighing gains less heavily than
losses is consistent with utility maximization, and therefore rational.
5.
The policy of punishing students would be more effective because losses are felt more than gains of
the same size. This policy may not be a good one if you are interested in more than just attendance.
Answers to Chapter 8 Problems
1. a) Combine small loss with the larger gain, because V(450)>V(500)+V(-50).
1.
1.
1.
b) Segregate the small gain (the silver-lining effect): V(50)+V(-500)>V(-450).
c) Reckon the gains separately: V(500)+V(600)>V(1100).
d) Combine the losses: V(-1100)>V(-500)+V(-600).
2. (1) If the machine normally costs $4000, they could raise the price to $4500 and offer a "$500
cash rebate." If buyers code the rebate as a separate event, the Kahneman-Tversky value
function says it will more than compensate for the negative effect of the higher price (the
"silver-lining effect").
2. (2) Combine the all-terrain vehicle into a package with the new Sears Recreational Vehicle.
The resulting small percentage increase in the price of the RV will seem insignificant
[Psychophysics of perception (Weber-Fechner law); also principle of combining losses.].
3. Suppose a disease will claim 600 lives if we do nothing. Given a choice between program A,
which would save 200 lives with certainty, or program B, which would save 600 lives with
probability 1/3 and zero lives with probability 2/3, most people pick A. But given a choice
between program C, under which 400 people would die, or program D, under which there is a
1/3 chance no one will die and a 2/3 chance that all 600 will die, most people pick D. These
choices are inconsistent because the two pairs of alternatives are exactly the same. As a
second example, consider the following three apartments, which are identical expect for
monthly rent and distance from campus
a.
b.
$600/mo, 2 blocks from campus
$400/mo, 1.5 miles from campus
c.
$405/mo, 1.6 miles from campus
Because C is unambiguously worse than B, its availability should not influence the likelihood
that a person chooses B over A. And yet when people are given a choice between A, B, and
C, they are much more likely to choose B than if they are given a choice between only A and
B.
4. Increased subway patrols are likely to be assigned in years following unusually high crime
rates. Regression effects alone would lead us to expect crime rate reductions in the year
following an unusually bad year. So it is difficult to conclude that the reduced rates are the
result of increased patrols.
5. A "superb" meal at any restaurant is likely to be an unusually good one compared to the
meals usually served there. On his next visit, Claiborne is likely to encounter a "normal"
meal. This is the regression-to-the-mean effect.
6. Out of every 100 people Dalgliesh interviews, 60 are liars, 40 are truthful. Of the 60 liars,
Dalgliesh identifies 48 correctly. Of the 40 truth tellers, Dalgliesh mistakenly calls 8 liars.
So out of every 56 people he says are lying, 48 really are. The probability that Jones is lying
is thus 48/56 = 6/7. In this problem, taking base rates into account raises the accuracy of
Dalgliesh's prediction, because there was a better than even chance that a randomly chosen
person would be lying.
7. For every 100 taxis in a dark alley, 15 will be green, 85 blue. The witness will identify
0.8(15)=12 of the green taxis as green, the remaining 3 green taxis as blue; he will identify
0.8(85)=68 of the blue taxis as blue, the remaining 17 blue taxis as green. The probability
that the cab in question was green given that the witness said it was is thus equal to
12/(12+17)=0.413, and since this is less than half, the Green Taxi Company should not be
held liable.
8. You view the loss of the original deal as a loss of $400, the amount you would have saved.
The next deal is seen as a gain of $360. If you have a value function similar to the one
described in the text, V(-400) is much bigger than V(360), so you end up “feeling” you are
worse off. But this is irrational, since the regular ticket is $1067 and you should compare
your purchase of $708 to this amount and feel better off.
9. No. Since you would choose the initial offer on Hawaii to this one in any case, this new offer
is an “irrelevant” alternative. It should not even be considered, much less be allowed to affect
your decision about the two initial offers.
10. Mary should drive across town if and only if the amount she saves is greater than the cost of
the drive. In the 10%-off stereo sale she would save $100. She would save only $16 in the
40%-off sale on the blouse. And yet she makes the trip in the latter case but not in the
former. Her behavior is thus irrational.
11. Racquet C is dominated by racquet B, which has more control and the same amount of
power. The rational choice model says that adding C should not affect how people choose
between A and B. As an empirical matter, Tversky has shown that the availability of an
alternative like C tends to make people more likely to choose B over A.
12. Crusoe may know that he is sorely tempted to get some coconuts before he should if his plan
is to use them in the spring. Having the bears in the way acts as a commitment device to help
him live up to his plans.
Chapter 9
Answers to Questions for Review
1. a) an opera singer performing an aria;
1. b) Carl Lewis running the 100 meters;
1. c) an economics professor teaching intermediate micro
2. McDonald's hamburgers
3. The person hiring wants to know how much an additional worker will add to total production
which is the marginal product of the labor.
4. His IQ was below average for New York, but above average for California.
5. They are equivalent mathematically except for the fact that one can measure production
numerically but utility is a subjective value which can be discerned only ordinally.
6. Decreasing returns is a long-run phenomenon; diminishing returns is a short-run
phenomenon.
7. As shown in the diagram, MP is decreasing from L1 onward, whereas AP does not begin to
decline until L2. So false.
MP, AP
AP(L)
L
L1
L2
MP(L)
8. False. For the average product to increase, the new worker should contribute more than the
existing average. Thus his marginal product should be more than the average product before
his arrival.
9. Under constant returns the output will be 2, under decreasing returns to scale the output will
be less than 2 and under increasing returns to scale the output will be above 2.
Answers to Chapter 9 Problems
1. The graphs below answer question 1.
b.
a.
Q
Q=8+3L
144
2
Q=16L
Q
20
64
8
16
L
L
4
1
2
3
2. The production function in (1a) has a constant marginal product of labor for all levels of
labor input, and the production function in (1b) an increasing marginal product of labor for
all levels of labor input. So neither production function obeys the law of diminishing returns.
3.
The marginal product of labor equals its average product at the maximum value of AP. The MP of the
next worker hired will thus be less than his AP. The next worker should thus prefer to be paid his AP.
The employer would prefer to pay MP.
4. The missing numbers for the total product column are 0, 320, 480. The missing numbers for
the average product column are 180, 160, 140. The missing numbers for the marginal product
column are 180, 100, 60.
5.
The marginal product of the second hundred officers sent to Center City is only 35 arrests/hr, and this
amount is less than the 40 arrests/hr they could achieve in West Philadelphia. They should instead be
sent to West Philadelphia. The allocation is 100 officers to Center City and 400 to West Philadelphia.
6.
All 500 police officers should be sent to West Philadelphia.
7.
a)
Q
9
2
6
7
L
7.
b) Maximum production (Q=9) occurs at L=6. [Calculus trained students: To find the maximum, take
the first derivative and set it equal to zero and solve for L: dQ/dL = 3 - (1/2)L= 0, which yields L = 6,
Q = 9.]
7.
c) For 0<L<2, MPL is increasing. For 2<L<7, MPL is decreasing.
7.
d) MPL < 0 for L>6.
8. With an optimal allocation of time, the extra points earned from the last minute devoted to
each question will be the same. Someone who earned 2 extra points from the last minute
devoted to Problem 10, and 4 from the last minute devoted to Problem 8, ought to have spent
less time on Problem 10 and more on Problem 8. This is true irrespective of the total points
earned on each question.
9.
Q
Q=4L
12
L
3
AP, MP
4
AP=MP=4
L
10. This production function shows constant returns from A to C, increasing returns from C to E,
and decreasing returns from E to G.
K
G
14
12
10
8
6
4
2
F
Q=950
E
Q=900
D
Q=800
C
Q=500
B
Q= 300
A
Q=200
Q=100
1
2
3
4
5
6
7
L
11. The overall average of the population need not change if physics was on the high side
of average and economics on the low side of average. For example, if 3 economists each
have an IQ of 150 and 2 physicists have IQs of 155 and 160 respectively, then if the 155
physicist becomes an economist, both groups have higher IQ averages but the population
average has not changed.
Chapter 10
Answers to Questions for Review
1.
The law of diminishing returns implies that eventually the TVC curve will begin to rise at an
increasing rate
2.
As soon as diminishing returns set in, the MC curve will slope upward.
3.
Book publishing because the marginal labor cost of one book is a very small part of the cost of a book
while landscape work is labor intensive.
4. If MC is less than average costs (total or variable), then each additional unit produced should
pull down average cost. If MC is more than average costs (total or variable), then each
additional unit produced should increase average cost. If you have an average score in this
class of 90 and your next test (the marginal test) score is 85, your average is pulled down. If
the marginal test score is 95, the average for the class is pulled up.
5.
We have decreasing returns to scale.
6. If MC is greater for one production activity than for another , then total cost can be reduced
by shifting some production to the lower marginal cost operation. In this way that last unit is
produced at less cost and so total costs for the output fall.
Answers to Chapter 10 Problems
1.
Quantity
Total
Fixed Variable
ATC
AVC
AFC
of output
cost
cost
cost
___________________________________________________________
0
24
24
0
---______________________________________________________________
1
40
24
16
40
16
24
______________________________________________________________
2
74
24
50
37
25
12
______________________________________________________________
3
108
24
84
36
28
8
______________________________________________________________
4
160
24
136
40
34
6
______________________________________________________________
5
220
24
196
44
39.2
4.8
______________________________________________________________
6
282
24
258
47
43
4
______________________________________________________________
2. With K fixed at 2, we have Q=6L, which solves for L=Q/6. So we have:
VC= wL=wQ/6=Q/3;
FC=3K=6;
TC=6+(Q/3);
MC=1/3
AVC=1/3;
AFC=6/Q;
ATC=(6/Q)+(1/3);
MC
_____
16
_____
34
_____
34
_____
52
_____
60
_____
62
_____
$/t
TC
12
VC
6
FC
Q
18
$/Q
2.0
AFC
1/3
ATC
AVC=MC
18
Q
3. When MP=AP, marginal cost and average variable cost will be the same. To see this, note
first that MC= Δ VC/ Δ Q=w Δ L/ Δ Q=w/MP. Similarly, AVC=wL/Q=w/AP. So when
AP=MP, it follows that MC=AVC.
4. a) The firm minimizes costs when it distributes production across the two processes so that
marginal cost is the same in each. If Q1 denotes production in the first process and Q2 is
production in the second process, we have Q1 + Q2 = 8 and 0.4Q1 = 2 + 0.2Q2, which yields
Q1=6, Q2=2. The common value of marginal cost will be 2.4.
4. b) Note that for output levels less than 5, it is always cheapest to produce all units with
process 1.
MC1
$/Q
MC2
5
2
5
Qi
5. If K and L are perfect substitutes, only one of the inputs will be used for any given isocost
line. No matter what the isocost line's slope, we will always get a corner solution (except
where the slope is exactly -1).
K
Q1 Q2
Q3
L
6. If K and L are perfect complements, the two inputs will be used in fixed proportion, no matter
what the slope of the isocost line.
K
Q3
Q2
Q1
L
7.
The necessary condition for cost minimization is MPK/PK = MPL/PL. Here, MPK/PK = 2 and
MPL/PL = 4.5. Since this firm gets more output from the last dollar it spends on labor than from the
last dollar it spends on capital, it should buy less capital and more labor.
8. For this production function, as long as the input price ratio (PK/PL) remains 2:1, the optimal
input bundle will always have 2 units of capital for every 3 units of labor, i.e., K = 2L/3. For
a total cost of 70, we thus have PKK+PLL = 2(2L/3) + L = 70, which solves for L=30 and
K=20. (See diagram.)
Capital
35
Output Expansion Path (slope = 2/3
20
3.5
7
30
70
Labor
9. At the minimum-cost input bundle for producing Q*, we know that the extra output obtained
from the last dollar spent on labor is the same as the extra output obtained from the last dollar
spent on capital. Thus the two short-run marginal cost curves will take the same value at Q*.
10. The LAC curve is the outer envelope of the firm's two SAC curves, as shown by the locus
ABC in the diagram.
$/Q
SAC1
18
C
SAC2
LAC
6
A
B
Q
10
11. The LMC and SMC curves coincide at the output level for which LAC and SAC are equal. If
LMC ≠ SMC, it follows that SAC>LAC.
$/Q
SMC
LAC
SAC
LMC
Q
12. LRAC = LRTC/Q = Q2 - 20Q + 220.
LRMC = dLRTC/dQ = 3Q2 - 40Q + 220
LRMC
220
LRAC
120
260/3
Q
20/3
10
13. ATC = LTC/Q = Q + 10/Q
AVC = Q
AFC = 10/Q
MC = dLRTC/dQ = 2Q
MC
10
ATC
AVC
5
AFC
1
2
3
4
5
Q
Chapter 11
Answers to Questions for Review
1. Economic profit includes all costs, while accounting profit looks only at cash flow. The firm
should consider economic profit only.
2. Unless firms act as though their pricing decisions affect other firms, we should assume that
firms act as price takers.
3. The dry cleaning markets would be nearly perfect except that many people do not want to
drive far for their clothing pickups and dropoffs. In small towns there may only be one or two
cleaners so less competition will be present.
4. Price = TR/Q, so this firm's demand curve is given by P=a - 2Q. Since its price is a declining
function of output, it cannot be a perfectly competitive firm.
5. No, because managers often relate to their competition by trial and error actions moving in
the direction of what succeeds for them. This moves the firm to the quantity of output that is
consistent with perfect competition outcomes.
6. The firm should shut down if and only if its price is below AVC. MC can lie below AFC at
the same time price lies above AVC (see diagram). So false.
P
AVC
P*
AFC
MC
Q
Q*
7. The value of the last unit to consumers (the price) equals the opportunity cost of resources
necessary to produce that unit.
8. The effect of such a tax is to produce a parallel upward movement in each firm's long-run
average cost curve. The output level for which the minimum value of LAC occurs will thus
be the same as before, which means that firms in long-run equilibrium will each have the
same amount of output as before. So true.
9. A firm will have a long-run marginal cost function that is above average cost for all points
past the minimum point on the long-run average cost curve. If demand causes price to be
above the minimum average cost in the short-run, then firms could be operating where price
equals long-run marginal cost and they could be making economic profits. When entry occurs
in the long-run the price will fall and price will equal long-run marginal cost at the long-run
equilibrium output level. Thus the statement is false. See the diagram on the next page.
SMC
$/Q
LAC
SAC
P0
P*
LMC
Q*
Q 0
Q
10. Consumer surplus in a competitive industry is the area between the price line and the market
demand curve, not the individual firm's demand curve. Since the market demand curve is
downward sloping, there will in general be positive consumer surplus. Indeed, compared to
other market structures, perfect competition creates the maximum consumer surplus. So
false.
11. Pecuniary economies and diseconomies are industry wide concepts that are operative when
all firms act similarly to put pressure on input prices. Since many inputs effect all industries it
is less likely that any one industry will impact input prices substantially cause pecuniary
effects.
12. Yes, in the short run, firms that innovate first will reap economic profit until other firms catch
up and compete away the economic profit. Thus intensive innovation efforts are consistent
with the perfect competition model.
Answers to Chapter 11 Problems
1. Reading from the table and graph, price equals marginal cost at Q = 4. For a quantity of 4,
average total cost is ATC = 26. Thus π = (P – ATC)Q = (32- 26)4 = 24.
Price
64
48
32
ATC
MC
profit (6x4)
AVC
Price
26
16
0
2
4
6
Quantity
8
10
2. Setting price P = 10 equal to marginal cost of SMC = 2 + 4Q, solve for quantity 10 = 2 + 4Q
or 8 = 4Q or Q = 2. The fixed cost that leads to zero economic profit is calculated by solving
π = (P – AVC)Q – FC = 0 or (10 – 6)2 – FC = 0 for FC = 8.
3.
SR supply =
∑ MCi
MCi = 4 + Qi
Qi = MCi - 4
∑ Qi = Q = ∑ MCi - 4000
Q = 1000 MC - 4000
MC = P, so Q = 1000 P - 4000, which means that industry supply is given by
P = 4 + Q/1000.
SR equilibrium Q: 4 + Q/1000 = 10 - 2Q/1000
3Q/1000 = 6, Q = 2000, P = 6.
P
10
Consumer surplus
Producer surplus
S
6
4
D
2000
Q
Consumer surplus = area of upper triangle = 4000.
Producer surplus = area of lower triangle = 2000.
Total loss in surplus = 6000.
4. In the long run, both the demand and supply curves will be more elastic than in the short run,
making the loss in both consumer and producer surpluses smaller.
5. Since P = SMC > AVC, the firm should continue at its current level of output in the short
run. In the long run, it should select the plant size for which P = LMC = SMC. As indicated
in the diagram below, this means it should switch to a smaller plant size in the long run.
6.
Long-run equilibrium price for this industry will occur at the minimum value of LAC.
LAC= LTC/Q= Q2 - 10Q + 36
dLAC/dQ =2Q-10=0, which solves for Q=5.
At Q=5, LAC=25-50+36=11.
7. The LAC curve for firms in this industry is given by LTC/Q=Q+4. The minimum value of
LAC now occurs at an output level of 0, where LAC takes the value 4. As a practical matter,
the notion of an infinitesimally small firm has no meaning. Because of indivisibilities, a
firm's LAC curve will increase beyond some point as Q shrinks toward zero.
8. The taxi industry supply curve for Metropolis is a horizontal line at P=$0.20/mile. The
demand schedule intersects it at Q=80,000 miles/yr, which means 8 taxis. The equilibrium
fare will be $0.20/mile.
9. If the total number of taxis is reduced from 8 to 6, the equilibrium fare will rise to $0.40/mile.
Ignoring the opportunity cost of the medallion, each medallion owner will earn a profit of
$(0.40-0.20)10,000= $2000/yr. If the annual interest rate is 10%, a person would need
$20,000 in order to earn as much interest as a medallion holder earns each year in profit. So
medallions will sell in the market for $20,000 each. A person who buys a medallion at this
price will earn zero economic profit.
10. The short-run MC curve for firms in the industry is dSTC/dQ = 10 + 2wQ. The equilibrium
output is found by equating P and MC: 10 + 2wQ* = 28, which yields Q*=9/w. For firms
with normal managers, w = 2, so Q* = 9/2 = 4.5. Profit of normal firms =
= 28(4.5) - 2
2
(4.5) - 45 - M =40.5 - M. For the firm that hires Merlin, w = 1, so Q* = 9. Profit of firm with
Merlin as manager =
= 28(9) - 92 - 90 - Mm = 81 - Mm, where Mm is Merlin's salary.
The premium paid to Merlin in equilibrium will be exactly the amount required to equate his
firm's profits with those of other firms.
= 81 - Mm =
= 40.5 - M, so
Mm - M = 81 - 40.5 = 40.5.
11. a) With the new process your costs, excluding your payment for use of the patent, will be TC'
= 4 + Q + Q2. To find your profit maximizing output level, we equate your new marginal
cost, MC' = 1 + 2Q, to the industry price, which, as before, will be the minimum value of the
average cost curve associated with the prevailing technology: LAC = 8/Q + 2 + 2Q =>
dLAC/dQ = 2 - 8/Q2 = 0 => Q* = 2 => LAC = 10 = P*. If we use Q' to denote the patent
holding firm's profit-maximizing output level, we have MC'=10 = 1 + 2Q' => Q' = 4.5. The
patent holder's economic profit will thus be TR - TC = 45 – 4.5 – 20.25 = 16.25 So the most
you would be willing to pay for the patent is 16.25.
11. b) Because the patented process can reduce the costs of each of the 1001 firms by half, it is
worth considerably more than 16.25; thus the investor would not be willing to sell exclusive
rights to its use to one firm at that price. For example, he could sell the patent to two firms
for 16.24.
12. a) MC=
AP=MP, it follows that MC=AVC.
Similarly, AVC=wL/Q=w/AP. So when
12. b) Since the firm is perfectly competitive, its output price is equal to marginal cost, which
here is equal to AVC. So all of the firm's revenue is paid out to its workers, leaving none for
its cost of capital. Thus, if the firm stays open in the short run, its loss will be equal to its
fixed capital costs of $40/day, which is the same loss it would suffer if it were to shut down.
So the firm is indifferent between shutting down and remaining open in the short run.
13. TC = 0.2 Q2 - 5Q + 30.
MC = dTC/dQ = 0.4 Q - 5.
In equilibrium MC = P, which implies 0.4Q - 5 = 6, which solves for Q = 27.5.
Profit = revenue – cost = 27.5x6 - [0.2(27.5)2 -5(27.5) + 30] = 121.25. Since the firm earns
positive profit, it should stay open.
14. Demand is given by P = 5-0.002Q, and supply is given by P=0.2+0.004Q. In equilibrium,
sale and purchase prices are equal. Thus, we get 5-0.002Q=0.2+0.004Q, which solves for
Q=800 and P=3.4. With tax, assume the supply curve shifts upward by 1 unit, which makes
it: P=1.2+0.004Q.
When we solve 5-0.002Q=1.2+0.004Q, we get Q=1900/3 and P=56/15.
This is the price paid by the consumer. The supplier gets P=41/15.
The incidence of tax on the supplier is 2/3, and on the consumer it is 1/3.
The consumer surplus before tax is [(5-3.4)x800]/2 = 640.
The producer surplus before tax is [(3.4-0.2)x800]/2 = 1280.
The consumer surplus after tax is [(5-56/15)x1900/3]/2 = 401.11.
The producer surplus after tax is [(41/15-0.2)x1900/3]/2 = 802.22.
Lost consumer surplus is 238.88.
Lost producer surplus is 477.77.
15. 1) Since the supply curve faced by the individual firm is elastic, the advertisement (which
shifts the demand curve out) will increase quantity increase but leave price unchanged.
15. 2) The result will be a shift in the long-run supply curve. Price will increase and quantity
will decrease.
16. a) LAC = TC/Q = 4Q + 100 +100/Q.
The minimum point on LAC is found either by graphing the LAC curve or by taking the first
derivative and setting it to zero. dLAC/dQ = 4 - 100/Q2 = 0, which yields Q = 5.
In the long run P = LAC = 140
16. b) If demand is Q=1000-P, then at P=140, we get Q=860. So in long run equilibrium, there will be
860/5 = 172 firms.
16. c) Now LAC = (TC-36)/Q = 4Q + 100 + 64/Q. Again, the minimum point on LAC is found
either by graphing the LAC curve or by taking the first derivative and setting it to zero.
dLAC/dQ = 4 - 64/Q2 = 0, which yields Q = 4. In the long run P = LAC = 132.
17. At a world price of 30, domestic demand is 35 million bushels per year. Domestic producers
supply the 20 million bushels of this total, foreign producers the remaining 15 million (left
panel.) With a tariff of $20/bu, the import price becomes $50/bu. Because the domestic
market clears at $40/bu (center panel), this means that no beans will be imported. Since no
beans are imported, the tariff raises no revenue. Consumer surplus and producer surplus with
the tariff is the area of triangle ABC (center panel), which equals $1350/yr. Consumer
surplus and producer surplus before the tariff-- the shaded area in the right panel-- was
$1425/yr, which means that the tariff has reduced consumer and producer surplus by $75/yr.
18. (i) Costs will fall for all existing firms. At existing prices the firms will make positive
economic profits and increase output.
18. (ii) New firms will enter the industry because of profits.
18. (iii) The industry supply curve will shift out until profits are again driven down to zero. The
final result is that prices fall, quantity increases, and there are more firms than before. In
other words, consumers reap all the surplus from this innovation.
Chapter 12
Answers to Questions for Review
1. The five factors include, exclusive control over inputs, economies of scale, patents, a network
economy, and government licensing or franchising, Economies of scale derive from
technological conditions rather than institutional arrangements that can change anytime.
2. Yes if the transportation costs of cement from the next town make the competing cement
more expensive than the monopoly price of the local cement.
3. Since the demand curve slopes downward, marginal revenue will always be less than price;
because for each additional unit sold one must lower the price for all other goods sold.
4. On the inelastic portion of the curve, raising price will always increase revenue and (since
output will be lower) it also lowers costs. Therefore the firm should always move up the
demand curve to where it is not inelastic if profit maximization is a goal.
5. If MR intersects MC from below, then MC must be downward sloping; more output will
lower MC.
6. No effect. The same P and Q that maximize ∏ also maximize ∏ /2 .
7. Price would be 50% higher than marginal cost.
(P – MC) /P = 1 – MC/P = 1/3 or MC/P = 1 – 1/3 2/3 or P/MC = 3/2.
8. The price-quantity pair that maximizes profits will also maximize the profits minus a lump
sum tax. Such a tax is equivalent to any other fixed cost since it leaves the optimal pricequantity pair unaffected.
9. With a perfectly horizontal market demand curve, there will be no deadweight loss. So true.
10. Whoever owns the firm will want to increase profits by reducing x-efficiency.
11. The hurdle model gives the lower price only to those willing to jump the hurdle so the
markets are more easily segregated. Deadweight losses are reduced.
Answers to Chapter 12 Problems
1.
1) Increase output because MR > MC and P > AVC.
2) Reduce output because MR < MC (we know that MR < P and P = MC here).
3) Remain at current output. MR = MC, and P = TR/Q = 11 > AVC.
4) Figures can't be right (P < MR).
5) Figures can't be right (P = TR/Q = 3.99, which is clearly not equal to 35.00).
2.
MC = 2Q = MR = 100 - 2Q;
100 - 2Q = 2Q, so Q* = 25, P* = 75.
TR = 1875; TC = 641
Π = TR - TC = 1234
1. The profit maximizing level of output for a single-price monopolist occurs where MR = MC.
The linear demand curve P = 100 – Q has a marginal revenue of MR = 100 – 2Q. By equating
marginal revenue and marginal cost (100 – 2Q = 2Q) we get a quantity of 25. The price
charged for this quantity is read off the demand curve so P = 100 – Q = 100 – 25 = 75. The
monopolist’s price and quantity are unaffected by fixed costs. However, the monopolist earns
lower profits:
π = TR – TC = 75Q – (32 + Q2) = 1875 – 657 = 1218. The difference in profits equals the increase
in fixed costs.
2.
The profit-maximizing level of output for a single-price monopolist occurs where MR = MC. The
linear demand curve P = 100 – Q has associated marginal revenue of MR = 100 – 2Q. Setting marginal
revenue equal to marginal cost , MC = 8Q, we have 100 – 2Q = 8Q, which solves for Q = 10. The price
charged for this quantity is read off the demand curve:
P = 100 – Q = 100 – 10 = 90. The
monopolist’s price rises and quantity falls due to the increase in marginal costs. The monopolist earns
lower profit than before: π = TR – TC = 90Q – (16 + 4Q2) = 900 – 416 = 484.
Price
100
90
MC
ATC
D
42
MR
0
10
20
Quantity
30
40
50
3. MR should be equal in both markets. Since the price is fixed at 60 in the foreign market, MR
is also fixed at 60 in that market. This means that MR at home should also be 60. We have
MRhome = 100-2Q=60, which solves for Qhome = 20. Also MC should be equal to 60. MC =
2Q = 60 solves for Qtotal = 30. Therefore Qforeign = Qtotal-Qhome = 10. Price in the home
market = 100 - 20 = 80.
4.
The profit-maximizing level of output for a single-price monopolist occurs where MR = LMC, The
linear demand curve P = 100 – Q has associated marginal revenue of MR = 100 – 2Q. Setting marginal
revenue equal to marginal cost, LMC = 20, we have 100 – 2Q = 20, which solves for Q = 40. The price
charged for this quantity is read off the demand curve: P = 100 – Q = 100 – 40 = 60. A perfectly
competitive industry would produce the quantity such that P = LMC = 20 so that Q = 100 – 20 = 80.
The total surplus generated by perfect competition would be TS = (1/2)80(100 – 20) = 3200. By
comparison, the monopoly generates producer surplus PSm = 40(60 – 20) = 1600 and consumer surplus
CSm = (1/2)40(100 – 60) = 800 for a total surplus of TSm = 160 = 80 = 2400. The efficiency loss due to
monopoly is the amount by which total surplus under monopoly falls short of the total surplus under
perfect competition. (ΔTS = 2400 – 3200 = 800) The efficiency loss is the triangular area between the
demand curve and marginal cost (supply) with base equal to quantity by which ouput under perfect
competition exceeds output under monopoly.
Price
100
60
MC
MR
0
40
50
D
100
Quantity
5.
A perfectly discriminating monopolist sells the quantity where marginal cost intersects the demand
curve P = MC or 100 – 10Q = 20 or 10Q = 80 or Q* = 8. The monopolist’s economic profit is the area
under the demand curve down to average cost out to quantity.
PS = (1/2)(100 – 20)8 = 320. The
government could charge the firm any fixed fee up to 320.
Price
100
20
MC
D
0
8
10
Quantity
6.
MR = P(1 - 1/|η|) = MC, which implies that P = MC/(1 - 1/|η|)
Senior citizens: PS* = 1/(1-1/4) = 4/3
Adults: PA* = 1/(1-1/2) = 2.
7. Iraq: P=400-0.5Q => MR=400-Q, or Q=400-MR.
Iran: P=300-Q => MR=300-2Q, or Q=150 - MR/2.
When we add these horizontally, we get
Q=Q
+Q
=
400-MR for 0<Q<100, 550-(3/2)MR for Q>100.
Iraq Iran
MC=Q will intersect MR when Q>100.
In equilibrium, MR=MC=1100/3 - (2/3)Q = Q, which solves for Q=220 and MR=220.
Iraq: Q=400-MR=180 ; P=400-0.5Q=310.
Iran: Q=150-MR/2=40 and P=300-Q=260.
8. Since they have lower income, their demand is more price elastic than regular customers'. So
they are more willing to jump the hurdle to get a lower price. The hurdle is the coupon in this
case, and it is used to sort people according to their price elasticities of demand.
9.
|η| =2, so MR = P(1-1/|η|) = 10(1-1/2) = 5.
10. If demand is inelastic at the price ceiling, we know the monopolist could increase its profits
by raising its price. So false.
11. First look at how the Times prices its ads to outside advertisers, who have a downwardsloping demand curve for ad space. When the Times sets its price for outside ads, its rule is
to equate marginal revenue to marginal cost. Marginal cost is simply the cost of expanding
the paper to accommodate the extra ad. When the paper maximizes profit, the price it
charges outsiders for ads will thus be higher than the marginal cost of producing another ad.
When the Times advertises for its own features, its rule should be to continue placing more
ads until the marginal benefits (in terms of increased sales or higher prices) just equal the cost
of producing an extra ad. The opportunity cost to the Times of running another ad is thus the
marginal cost of producing the ad, which in general will be lower than the price it charges
outside advertisers.
12. See footnote in text associated with this problem. ∏ = PH QH + PL QL - 5(QH + QL) - 15
14. a) PH = 20 - 5QH,
PL = 20 - 5QH - 5QL
max [(20 - 5QH) QH + (20 - 5QH - 5QL) QL - 5QH - 5QL - 15] QH,QL
First-order conditions:
(1)
QH = 20 - 10QH - 5QL - 5 = 0
(2)
QL = 20 - 5QH - 10QL - 5 = 0,
which may be restated as
(1') 15 - 10QH = 5QL, so 3 - 2QH = QL
(2') 15 - 5QH - 10 (3 - 2QH) = 0, so -15 + 15QH = 0
Thus QH = 1; QL = 3 - 2QH = 1; PH = 15; PL = 10
14. b) = 15 + 10 - 5(2) - 15 = 0
14. c) MR = 20 - 10Q = MC = 5, so Q* = 1.5
P* = 20 - 5(1.5) = 12.5 = (12.5)(1.5) - 5(1.5) - 15 = -3.75
14. d) With a single price, Harry would be forced out of business in the long run, and consumers
would lose the surplus they enjoy under the two-price arrangement.
15. The publisher's net income from the project comes when it sets the price that corresponds to
the quantity for which marginal revenue and marginal cost are equal. The author's net
income from the project is maximized when the price is set at the level that maximizes total
revenue. The author's best price thus corresponds to the quantity for which marginal revenue
equals zero. As long as marginal production costs are positive, it follows that the publisher
will prefer a higher price than the author. So false.
16. The studio's maximum net income from the project comes when it sets the rental price that
corresponds to the quantity for which marginal revenue and marginal cost are equal. The
director's net income from the project is maximized when the price is set at the level that
maximizes total revenue. The director's best price thus corresponds to the quantity for which
marginal revenue equals zero. As long as marginal production costs are zero (which follows
from the assumption that all costs are fixed), it follows that the studio will also prefer the
price that equates marginal revenue to zero. So false.