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Answers to Selected
Problems
I know the answer! The answer lies within the heart of all mankind! The
answer is twelve? I think I’m in the wrong building. —Charles Schultz
Chapter 2
1. The statement “Talk is cheap because supply exceeds
demand” makes sense if we interpret it to mean that
the quantity of talk supplied exceeds the quantity
demanded at a price of zero. Imagine a downwardsloping demand curve that hits the horizontal, quantity axis to the left of where the upward-sloping
supply curve hits the axis. (The correct aphorism is
“Talk is cheap until you hire a lawyer.”)
5. Shifts of both the U.S. supply and U.S. demand
curves affected the U.S. equilibrium. U.S. beef consumers’ fear of mad cow disease caused their
demand curve in the figure to shift slightly to the left
from D1 to D2. In the short run, total U.S. production was essentially unchanged. Because of the ban
on exports, beef that would have been sold in Japan
and elsewhere was sold in the United States, causing
p, Price per pound
For Chapter 2, Problem 5
S1
S2
e1
p1
p 2 = 0.85p1
e2
D1
D2
Q 1 Q 2 = 1.43Q 1
Q, Tons of beef per year
the U.S. supply curve to shift to the right from S1 to
S2. As a result, the U.S. equilibrium changed from e1
(where S1 intersects D1) to e2 (where S2 intersects
D2). The U.S. price fell 15% from p1 to p2 = 0.85p1,
while the quantity rose 43% from Q1 to Q2 =
1.43Q1. Comment: Depending on exactly how the
U.S. supply and demand curves had shifted, it would
have been possible for the U.S. price and quantity to
have both fallen. For example, if D2 had shifted far
enough left, it could have intersected S2 to the left of
Q1, and the equilibrium quantity would have fallen.
11. In the figure, the no-quota total supply curve, S in
panel c, is the horizontal sum of the U.S. domestic
supply curve, Sd, and the no-quota
foreign supply
_
curve, Sf. At prices less than p , foreign suppliers
_
want to supply quantities less than the quota, Q. As
_
a result, the foreign supply curve under the quota, S f,
is the same as the no-quota
foreign supply
curve, Sf,
_
_
for prices less than p . At prices above p , foreign sup_
pliers want to supply more but are limited to_ Q.
Thus, the foreign
supply curve _with a quota, S f is
_
vertical at Q for prices
_ above p . The total supply
curve_ with the quota, S , is _the horizontal sum of Sd
and S f. At any price above p , the total supply equals
the quota plus the domestic supply. For example at
p*,_the domestic supply is Q*d and the
_ foreign supply
_ _
is Qf , so the total supply is Q*
+ Qf ._ Above p , S is
d
the domestic supply curve shifted
_ Q units
_ to the
right. As a result, the portion of S above p has_ the
same slope as Sd. At prices less than or equal to p the
same quantity
is supplied with and without
_
_ the
quota, so S is the same as S. At prices above p , less
_
is supplied with the quota than without one, so S is
steeper than S, indicating that a given increase in
price raises the quantity supplied by less with a
quota than without one.
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Answers to Selected Problems
(b) Foreign Supply
p, Price
per ton
p, Price
per ton
For Chapter 2, Problem 11
(a) U.S. Domestic Supply
–
p, Price
per ton
Sd
(c) Total Supply
Sf
Sf
p*
p*
p*
p–
p–
p–
–
Qd
–
Qd*
Qf
Qd , Tons per year
–
S
S
–
–
Q, Tons per year
Qf , Tons per year
imposed, the equilibrium is e3, where _Dh intersects
the total supply curve with the quota, S . The quota
raises the price of steel in the United States from p2
to p3 and reduces the quantity from Q2 to Q3.
12. The graph reproduces the no-quota total American
supply curve of steel,
S, and the total supply curve
_
under the quota, S , which we derived
_ in the answer
to Question 11. At a price below p , the two supply
curves are identical because the quota is not binding:
It is greater than
_ quantity foreign firms want to
_ the
supply. Above p , S lies to the left of S. Suppose that
the American demand is relatively low at any given
price so that the demand curve, Dl_, intersects both
the supply curves at a price below p . The equilibria
both before and after the quota is imposed are
_ at e1,
where the equilibrium price, p1, is less than p . Thus,
if the demand curve lies near enough to the origin
that the quota is not binding, the quota has no effect
on the equilibrium. With a relatively high demand
curve, Dh, the quota affects the equilibrium. The noquota equilibrium is e2, where Dh intersects the noquota total supply curve, S. After the quota is
21. We showed that, in a competitive market, the effect
of a specific tax is the same whether it is placed on
suppliers or demanders. Thus, if the market for milk
is competitive, consumers will pay the same price in
equilibrium regardless of whether the government
taxes consumers or stores.
22. The law would create a price ceiling (at 110% of the
pre-emergency price). Because the supply curve shifts
substantially to the left during the emergency, the
price control will create a shortage: A smaller quantity will be supplied at the ceiling price than will be
demanded.
p, Price of steel per ton
For Chapter 2, Problem 12
–
S (quota)
S (no quota)
e3
p3
p2
p–
p1
e2
e1
D h (high)
D l (low)
Q1
–
Qd + Qf Qd* + Qf Qd* + Qf*
Qf*
Q3 Q2
Q, Tons of steel per year
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Answers to Selected Problems
20pb + 3pc + 2Y. As a result, ∂Q/∂Y = 2. A $100
increase in income causes the quantity demanded to
increase by 0.2 million kg per year.
24. To solve this problem, we first rewrite the inverse
demand functions as demand functions and then add
them together. The total demand function is Q =
Q1 + Q2 = (120 − p) + (60 − 1_2 p) = 180 − 1.5p.
28. Equating the right-hand sides of the tomato supply
and demand functions and using algebra, we find
that ln p = 3.2 + 0.2 ln pt. We then set pt = 110,
solve for ln p, and exponentiate ln p to obtain the
equilibrium price, p ≈ $61.62/ton. Substituting p
into the supply curve and exponentiating, we determine the equilibrium quantity, Q ≈ 11.78 million
short tons/year.
30. The elasticity of demand is (ΔQ/Δp)(p/Q) = (−9.5
thousand metric tons per year per cent) ×
(45¢/1,275 thousand metric tons per year) ≈ −0.34.
That is, for every 1% fall in the price, a third of a
percent more coconut oil is demanded. The crossprice elasticity of demand for coconut oil with
respect to the price of palm oil is (ΔQ/Δpp)(pp/Q) =
16.2 × (31/1,275) ≈ 0.39.
39. Differentiating quantity, Q(p(τ)), with respect to τ,
we learn that the change in quantity as the tax
changes is (dQ/dp)(dp/dτ). Multiplying and dividing
this expression by p/Q, we find that the change in
quantity as the tax changes is ε(Q/p)(dp/dτ). Thus,
the closer ε is to zero, the less the quantity falls, all
else the same.
Because R = p(τ)Q(p(τ)), an increase in the tax rate
changes revenues by
dR
dp
dQ dp
=
Q+ p
,
dτ
dτ
dp dτ
where ε is the elasticity of demand of labor. The sign
of dW/dw is the same as that of 1 + ε. Thus, total
labor payment decreases as the minimum wage forces
up the wage if labor demand is elastic, ε < −1, and
increases if labor demand is inelastic, ε > −1.
Chapter 3
3. If the neutral product is on the vertical axis, the
indifference curves are parallel vertical lines.
5. Sofia’s indifference curves are right angles (as in
panel b of Figure 3.5). Her utility function is U =
min(H, W), where min means the minimum of the
two arguments, H is the number of units of hot dogs,
and W is the number of units of whipped cream.
8. See MyEconLab, Chapter 3, Solved Problem.
9. In the figure, the consumer can afford to buy up to
12 thousand gallons of water a week if not constrained. The opportunity set, area A and B, is
bounded by the axes and the budget line. A vertical
line at 10 thousand on the water axis indicates the
quota. The new opportunity set, area A, is bounded
by the axes, the budget line, and the quota line.
Because of the rationing, the consumer loses part of
the original opportunity set: the triangle B to the
right of the 10-thousand-gallons quota line. The consumer has fewer opportunities because of rationing.
For Chapter 3, Problem 9
Other goods per week
23. The demand curve for pork is Q = 171 − 20p +
N-3
Quota
Budget line
using the chain rule. Using algebra, we can rewrite
this expression as
dR
d p ⎛⎜
d Q ⎞⎟ d p ⎛⎜
d Q p ⎞⎟ d p
⎟⎟ =
⎟⎟ =
=
Q⎜⎜1 +
Q(1 + ε).
⎜⎜Q + p
dτ
dτ ⎝
d p ⎟⎠ d τ ⎝
d p Q ⎟⎠ d τ
Thus, the effect of a change in τ on R depends on the
elasticity of demand, ε. Revenue rises with the tax,
given an inelastic demand (0 > ε > −1), and falls
with an elastic demand, ε < −1.
40. We can determine how the total wage payment,
W = wL(w), varies with respect to w by differentiating. We then use algebra to express this result in
terms of an elasticity:
⎛
dW
dL
d L w ⎞⎟
⎟ = L (1 + ε),
= L+w
= L⎜⎜1 +
⎜⎝
dw
dw
d w L ⎟⎟⎠
A
0
B
10
12
Water, Thousand gallons per month
15. Suppose that Dale purchases two goods at prices p1
and p2. If her original income is Y, the intercept of
the budget line on the Good 1 axis (where the consumer buys only Good 1) is Y/p1. Similarly, the intercept is Y/p2 on the Good 2 axis. A 50% income tax
lowers income to half its original level, Y/2. As a
result, the budget line shifts inward toward the
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origin. The intercepts on the Good 1 and Good 2
axes are Y/(2p1) and Y/(2p2), respectively. The
opportunity set shrinks by the area between the original budget line and the new line.
21. Andy’s marginal utility of apples divided by the price
of apples is 3/2 = 1.5. The marginal utility for
kumquats is 5/4 = 1.2. That is, a dollar spent on
apples gives him more extra utils than a dollar spent
on kumquats. Thus, Andy maximizes his utility by
spending all his money on apples and buying 40/2 =
20 pounds of apples.
22. Given a quasilinear marginal utility function,
U(q1, q2) = u(q1) + q2, the marginal utility of the
first good is U1 = ∂U(q1, q2)/∂q1 = du(q1)/dq1 > 0,
which is independent of q2 because u(q1) is not a
function of q2. The marginal utility of the second
good is U2 = ∂U(q1, q2)/∂q2 = 1, which is independent of q1 and q2. Using Equation 3.3, we find that
the marginal rate of substitution is MRS = −U1/U2 =
−[du(q1)/dq1]/1 = −[du(q1)/dq1] < 0, so the indifference curves are downward sloping. The MRS is independent of q2 because du(q1)/dq1 is independent of q2.
Thus, at any given q1, the MRS, which is the slope of
the indifference curve, must be the same for all the
indifference curves. Using the same reasoning as in the
text, these indifference curves must be parallel.
23. David’s marginal utility of Z is 2 and his marginal
utility of B is ∂U/∂B = ∂(B + 2Z)/∂B = 1. If we plot
B on the vertical axis and Z on the horizontal axis,
the slope of David’s indifference curve is −UZ/UB =
−2. The marginal utility from one extra unit of Z is
twice that from one extra unit of B. Thus, if the price
of Z is less than twice that of B, David buys only Z
(the optimal bundle is on the Z axis at Y/pZ, where
Y is his income and pZ is the price of Z). If the price
of Z is more than twice that of B, David buys only
B. If the price of Z is exactly twice as much as that
of B, he is indifferent between buying any bundle
along his budget line.
25. Nadia determines her optimal bundle by equating
the ratios of each good’s marginal utility to its price.
a. At the original prices, this condition is UR/10 =
2RC = 2R2 = UC /5. Thus, by dividing both sides
of the middle equality by 2R, we know that her
optimal bundle has the property that R = C. Her
budget constraint is 90 = 10R + 5C. Substituting
C for R, we find that 15C = 90, or C = 6 = R.
b. At the new price, the optimum condition requires
that UR /10 = 2RC = R2 = UC /10, or 2C = R. By
substituting this condition into her budget constraint, 90 = 10R + 10C, and solving, we learn
that C = 3 and R = 6. Thus, as the price of chick-
ens doubles, she cuts her consumption of chicken
in half but does not change how many slabs of
ribs she eats.
33. Given the original utility function, U, the consumer’s
marginal rate of substitution is −U1/U2. If V(q1, q2)
= F(U(q1, q2)), the new marginal rate of substitution
is −V1/V2 = −[(dF/dU)U1]/[(dF/dU)U2] = −U1/U2,
which is the same as originally.
38. If we apply the transformation function F(x) = xρ to
the original utility function, we obtain the new utility function V(q1, q2) = F(U(q1, q2)) = [(qρ1 + qρ2)1/ρ]ρ
= qρ1 + qρ2, which has the same preference properties
as does the original function.
39. Using Equation 3.3, we find that the marginal rate of
substitution is −U1/U2 =−ρq1ρ−1/(ρq2ρ−1) = −(q1/q2)ρ−1.
Chapter 4
6. An opera performance must be a normal good for
Don because he views the only other good he buys as
an inferior good. To show this result in a graph,
draw a figure similar to Figure 4.4, but relabel the
vertical “Housing” axis as “Opera performances.”
Don’s equilibrium will be in the upper-left quadrant
at a point like a in Figure 4.4.
7. The CPI accurately reflects the true cost of living
because Alix does not substitute between the goods
as the relative prices change.
9. On a graph show Lf, the budget line at the factory
store, and Lo, the budget constraint at the outlet
store. At the factory store, the consumer maximum
occurs at ef on indifference curve If. Suppose that we
increase the income of a consumer who shops at the
outlet store to Y* so that the resulting budget line L*
is tangent to the indifference curve If. The consumer
would buy Bundle e*. That is, the pure substitution
effect (the movement from ef to e*) causes the consumer to buy relatively more firsts. The total effect
(the movement from ef to eo) reflects both the substitution effect (firsts are now relatively less expensive)
and the income effect (the consumer is worse off
after paying for shipping). The income effect is small
if (as seems reasonable) the budget share of plates is
small. An ad valorem tax has qualitatively the same
effect as a specific tax because both taxes raise the
relative price of firsts to seconds.
25. The figure shows that the price-consumption curve is
horizontal. The demand for CDs depends only on
income and the own price, q1 = 0.6Y/p1.
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Answers to Selected Problems
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For Chapter 4, Problem 25
q2, Movie DVDs, Units per year
(a) Indifference Curves and Budget Constraints
e1
6
e3
e2
Price-consumption curve
I3
I1
L2
L1
0
4
12
I2
30
L3
q1, Music CDs, Units per year
p1, $ per units
(b) CD Demand Curve
E1
45
E2
15
E3
6
0
CD demand curve
4
12
27. Guerdon’s utility function is U(q1, q2) = min(_21q1, q2).
To maximize his utility, he always picks a bundle at
the corner of his right-angle indifference curves.
That is, he chooses only combinations of the two
goods such that _21q1 = q2. Using that expression to
substitute for q2 in his budget constraint, we find
that
Y = p1q1 + p2q2 = p1q1 + p2q1/2 = (p1 + 0.5p2)q1.
Thus, his demand curve for bananas is q1 =
Y/(p1 + 0.5p2). The graph of this demand curve is
downward sloping and convex to the origin (similar
to the Cobb-Douglas demand curve in panel a of
Figure 4.1).
30
q1, Music CDs, Units per year
29. Barbara’s demand for CDs is q1 = 0.6Y/p1.
Consequently, her Engel curve is a straight line with
a slope of dq1/dY = 0.6/p1.
32. From Philip’s budget constraint, Y = p1q1 + q2, we
know that q2 = Y − p1q1. Substituting that expression into his utility function, we have U = q1 + Y
− p1q1. Philip chooses q1 so as to maximize this
unconstrained objective. His first-order condition is
1/(2 q1 ) − p1 = 0, so his demand function for the
first good is q1 = 1/(4[p1]2). Substituting this demand
function into our earlier expression for q2 from the
budget constraint, we learn that his demand function
for the second good is q2 = Y − 1/(4p1). Because his
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Answers to Selected Problems
demand function for q1 is independent of Y, a
change in p1 has no income effect, so the total effect
equals the substitution effect. This last result holds
for any quasilinear utility function.
Chapter 5
15. Parents who do not receive subsidies prefer that poor
parents receive lump-sum payments rather than a
subsidized hourly rate for child care. If the supply
curve for day care services is upward sloping, by
shifting the demand curve farther to the right, the
price subsidy raises the price of day care for these
other parents.
16. The government could give a smaller lump-sum subsidy that shifts the LLS curve down so that it is parallel to the original curve but tangent to indifference
curve I2. This tangency point is to the left of e2, so
the parents would use fewer hours of child care than
with the original lump-sum payment.
26. The proposed tax system exempt an individual’s first
$10,000 of income. Suppose that a flat 10% rate is
charged on the remaining income. Someone who
earns $20,000 has an average tax rate of 5%,
whereas someone who earns $40,000 has an average
tax rate of 7.5%, so this tax system is progressive.
28. As the marginal tax rate on income increases, people
substitute away from work due to the pure substitution effect. However, the income effect can be either
positive or negative, so the net effect of a tax increase
is ambiguous. Also, because wage rates differ across
countries, the initial level of income differs, again
adding to the theoretical ambiguity. If we know that
people work less as the marginal tax rate increases,
we can infer that the substitution effect and the
income effect go in the same direction or that the
substitution effect is larger. However, Prescott’s
(2004) evidence alone about hours worked and
marginal tax rates does not allow us to draw such an
inference because U.S. and European workers may
have different tastes and face different wages.
29. The figure shows Julia’s original consumer equilibrium: Originally, Julia’s budget constraint was a
straight line, L1 with a slope of −w, which was tangent to her indifference curve I1 at e1, so she worked
12 hours a day and consumed Y1 = 12w goods. The
maximum-hours restriction creates a kink in Julia’s
new budget constraint, L2. This constraint is the same
as L1 up to 8 hours of work, and is horizontal at Y =
8w for more hours of work. The highest indifference
curve that touches this constraint is I2. Because of the
restriction on the hours she can work, Julia chooses to
work 8 hours a day and to consume Y2 = 8w goods,
at e2. (She will not choose to work fewer than 8 hours.
For her to do so, her indifference curve I2 would have
to be tangent to the downward-sloping section of the
new budget constraint. However, such an indifference
curve would have to cross the original indifference
curve, I1, which is impossible—see Chapter 3.) Thus,
forcing Julia to restrict her hours lowers her utility: I2
must be below I1.
Y, Goods per day
For Chapter 5, Problem 29
Time constraint
L1
e1
Y1 = 12w
L2
Y2 = 8w
e2
I2
24
H 1 = 12
H2 = 8
I1
H, Work hours per day
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Comment: When I was in college, I was offered a
summer job in California. My employer said,
“You’re lucky you’re a male.” He claimed that, to
protect women (and children) from overwork, an
archaic law required him to pay women, but not
men, double overtime after eight hours of work. As
a result, he offered overtime work only to his male
employees. Such clearly discriminatory rules and
behavior are now prohibited. Today, however, both
females and males must be paid higher overtime
wages—typically 1.5 times as much as the usual
wage. As a consequence, many employers do not let
employees work overtime.
30. Hong and Wolak (2008) estimate that Area A is
$215 million and area B is $118 (= 333 − 215) million (as you should have shown in your figure in
answer to Question 1).
a. Given that the demand function is Q = Xp−1.6,
the revenue function is R(p) = pQ = Xp−0.6.
Thus, the change in revenue, −$215 million,
equals R(39) − R(37) = X(39)−0.6 − X(37)−0.6 ≈
−0.00356X. Solving −0.00356X = −215, we
find that X ≈ 60,353.
b. We follow the process in Solved Problem 5.1
ΔCS = −∫
39
37
60, 353p−1.6d p1 =
60, 353 −0.6
p
0 .6
39
37
≈ 100, 588(39−0.6 − 37−0.6 )
≈ 100, 588 × (−0.00356) ≈ −358.
This total consumer surplus loss is larger than the
one estimated by Hong and Wolak (2008) because
they used a different demand function. Given this
total consumer surplus loss, area B is $146 (=358 −
215) million.
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in equal proportions: one disc and one hour of
machine services.
10. The isoquant for q = 10 is a straight line that hits the
B axis at 10 and the G axis at 20. The marginal
product of B is 1 everywhere along the isoquant. The
marginal rate of technical substitution is 2 if B is on
the horizontal axis.
19. Not enough information is given to answer this question. If we assume that Japanese and American firms
have identical production functions and produce
using the same ratio of factors during good times,
Japanese firms will have a lower average product of
labor during recessions because they are less likely to
lay off workers. However, it is not clear how
Japanese and American firms expand output during
good times (do they hire the same number of extra
workers?). As a result, we cannot predict which
country has the higher average product of labor.
22. The production function is q = L0.75K0.25 (a) As a
result, the_ average product of labor,_ holding_ capital
fixed at K, is APL = q/L = L−0.25K0.25 = (K/L)0.25.
(b)_ The marginal product of labor is MPL = dq/dL =
_3
0.25. (c) If we double both inputs, output dou4(K/L)
bles to (2L)0.75(2K)0.25 = 2L0.75K0.25 = 2q, where q
is the original output level. Thus, this production
function has constant returns to scale.
24. Using Equation 6.8, we know that the marginal rate
of technical substitution is MRTS = MPL/MPK = 2_3.
27. The marginal product of labor of Firm 1 is only 90%
of the marginal product of labor of Firm 2 for a particular level of inputs. Using calculus, we find that
the MPL of Firm 1 is ∂q1/∂L = 0.9∂f(L, K)/∂L =
0.9∂q2/∂L.
29. This production function is a Cobb-Douglas produc-
Chapter 6
1. One worker produces one unit of output, two workers produce two units of output, and n workers produce n units of output. Thus, the total product of
labor equals the number of workers: q = L. The total
product of labor curve is a straight line with a slope
of 1. Because we are told that each extra worker produces one more unit of output, we know that the
marginal product of labor, dq/dL, is 1. By dividing
both sides of the production function, q = L, by L,
we find that the average product of labor, q/L, is 1.
6. The isoquant looks like the “right angle” ones in
panel b of Figure 6.3 because the firm cannot substitute between discs and machines but must use them
tion function. Even though it has three inputs instead
of two, the same logic applies. Thus, we can calculate the returns to scale as the sum of the exponents:
γ = 0.27 + 0.16 + 0.61 = 1.04. That is, it has
(nearly) constant returns to scale. The marginal
product of material is ∂q/∂M = 0.61L0.27K0.16M−0.39
= 0.61q/M.
Chapter 7
1. If the plane cannot be resold, its purchase price is a
sunk cost, which is unaffected by the number of
times the plane is flown. Consequently, the average
cost per flight falls with the number of flights, but
the total cost of owning and operating the plane rises
because of extra consumption of gasoline and main-
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tenance. Thus the more frequently someone has a
reason to fly, the more likely that flying one’s own
plane costs less per flight than a ticket on a commercial airline. However, by making extra (“unnecessary”) trips, Mr. Agassi raises his total cost of
owning and operating the airplane.
= MP2, where the last minute spent on Question 1
would increase your score by as much as spending it
on Question 2 would. Therefore, you’ve allocated
your time on the exam wisely if you are indifferent
as to which question to work on during the last
minute of the exam.
3. The total cost of building a 1-cubic-foot crate is $6.
10. Because the franchise tax is a lump-sum payment
It costs four times as much to build an 8-cubic-foot
crate, $24. In general, as the height of a cube
increases, the total cost of building it rises with the
square of the height, but the volume increases with
the cube of the height. Thus, the cost per unit of volume falls.
that does not vary with output, the more the firm
produces, the less tax it pays per unit. The tax per
unit is ᏸ/q. (The lump-sum is a fixed cost, so the tax
per unit is calculated the same way as we do to
obtain the average fixed cost.) If the firm sells only 1
unit, its cost is ᏸ; however, if it sells 100 units, its tax
payment per unit is only ᏸ/100.
The firm’s after-tax average cost, ACa, is the sum
of its before-tax average cost, ACb, and its average
tax payment per unit, ᏸ/q. Because the average tax
payment per unit falls with output, the gap between
the after-tax average cost curve and the before-tax
average cost curve also falls with output, as shown
on the graph.
Because the franchise tax does not vary with output, it does not affect the marginal cost curve. The
marginal cost curve crosses both average cost curves
from below at their minimum points. Because the
after-tax average cost curve lies above the before-tax
average cost curve, the quantity, qa, at which the
after-tax average cost curve reaches its minimum, is
larger than the quantity qb at which the before-tax
average cost curve achieves a minimum.
4. You produce your output, exam points, using as
inputs the time spent on Question 1, t1, and the time
spent on Question 2, t2. If you have diminishing
marginal returns to extra time on each problem,
your isoquants have the usual shapes: They curve
away from the origin. You face a constraint that you
may spend no more than 60 minutes on the two
questions: 60 = t1 + t2. The slope of the 60-minute
isocost curve is −1: For every extra minute you
spend on Question 1, you have one less minute to
spend on Question 2. To maximize your test score,
given that you can spend no more than 60 minutes
on the exam, you want to pick the highest isoquant
that is tangent to your 60-minute isocost curve. At
the tangency, the slope of your isocost curve, −1,
equals the slope of your isoquant,−MP1/MP2. That
is, your score on the exam is maximized when MP1
Costs per unit, $
For Chapter 7, Problem 10
MC
ACa = ACb + ᏸ/q
ᏸ /q
ACb
qb
qa
q, Units per day
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13. From the information given and assuming that there
are no economies of scale in shipping baseballs, it
appears that balls are produced using a constant
returns to scale, fixed-proportion production function. The corresponding cost function is C(q) =
(w + s + m)q, where w is the wage for the time period
it takes to stitch one ball, s is the cost of shipping one
ball, and m is the price of all material to produce one
ball. Because the cost of all inputs other than labor
and transportation are the same everywhere, the cost
difference between Georgia and Costa Rica depends
on w + s in both locations. As firms choose to produce in Costa Rica, the extra shipping cost must be
less than the labor savings in Costa Rica.
15. According to Equation 7.11, if the firm were minimizing its cost, the extra output it gets from the last
dollar spent on labor, MPL/w = 50/200 = 0.25,
should equal the extra output it derives from the last
dollar spent on capital, MPK/r = 200/1,000 = 0.2.
Thus, the firm is not minimizing its costs. It would
do better if it used relatively less capital and more
labor, from which it gets more extra output from the
last dollar spent.
20. If −w/r is the same as the slope of the line segment
connecting the wafer-handling stepper and the stepper technologies, then the isocost will lie on that line
segment, and the firm will be indifferent between
using either of the two technologies (or any combination of the two). In all the isocost lines in the figure, the cost of capital is the same, and the wage
varies. The wage such that the firm is indifferent lies
between the relatively high wage on the C2 isocost
line and the lower wage on the C3 isocost line.
24. Let w be the cost of a unit of L and r be the cost of
a unit of K. Because the two inputs are perfect substitutes in the production process, the firm uses only
the less expensive of the two inputs. Therefore, the
long-run cost function is C(q) = wq if w ≤ r; otherwise, it is C(q) = rq.
30. The average cost of producing one unit is α (regard-
less of the value of β). If β = 0, the average cost does
not change with volume. If learning by doing
increases with volume, β < 0, so the average cost
falls with volume. Here, the average cost falls exponentially (a smooth curve that asymptotically
approaches the quantity axis).
35. The firm chooses its optimal labor-capital ratio using
Equation 7.11: MPL/w = MPK/r. That is, 1/2q/(wL)
= 1/2q/(rK), or L/K = r/w. In the United States where
w = r = 10, the optimal L/K = 1, or L = K. The firm
produces where q = 100 = L0.5K0.5 = K0.5K0.5 = K.
Thus, q = K = L = 100. The cost is C = wL + rK =
N-9
10 × 100 + 10 × 100 = 2,000. At its Asian plant,
the optimal input ratio is L*/K* = 1.1r/(w/1.1) =
11/(10/1.1) = 1.21. That is, L* = 1.21K*. Thus, q =
(1.21K*)0.5(K*)0.5 = 1.1K*. So K* = 100/1.1 and
L* = 110. The cost is C* = [(10/1.1) × 110] +
[11 × (100/1.1)] = 2,000. That is, the firm will use
a different factor ratio in Asia, but the cost will be
the same. If the firm could not substitute toward the
less-expensive input, its cost in Asia would be C** =
[(10/1.1) × 100] + [11 × 100] = 2,009.09.
Chapter 8
2. How much the firm produces and whether it shuts
down in the short run depend only on the firm’s variable costs. (The firm picks its output level so that its
marginal cost—which depends only on variable
costs—equals the market price, and it shuts down
only if market price is less than its minimum average
variable cost.) Learning that the amount spent on the
plant was greater than previously believed should
not change the output level that the manager
chooses. The change in the bookkeeper’s valuation
of the historical amount spent on the plant may
affect the firm’s short-run business profit but does
not affect the firm’s true economic profit. The economic profit is based on opportunity costs—the
amount for which the firm could rent the plant to
someone else—and not on historical payments.
3. Suppose that a U-shaped marginal cost curve cuts a
competitive firm’s demand curve (price line) from
above at q1 and from below at q2. By increasing output to q2 + 1, the firm earns extra profit because the
last unit sells for price p, which is greater than the
marginal cost of that last unit. Indeed, the price
exceeds the marginal cost of all units between q1 and
q2, so it is more profitable to produce q2 than q1.
Thus, the firm should either produce q2 or shut
down (if it is making a loss at q2). We can derive this
result using calculus. The second-order condition
for a competitive firm requires that marginal cost
cut the demand line from below at q*, the profitmaximizing quantity:
dMC(q*)/dq > 0.
9. Some farmers did not pick apples so as to avoid
incurring the variable cost of harvesting apples.
These farmers left open the question of whether they
would harvest in the future if the price rose above
the shutdown level. Other, more pessimistic farmers
did not expect the price to rise anytime soon, so they
bulldozed their trees, leaving the market for good.
(Most farmers planted alternative apples such as
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Granny Smith and Gala, which are more popular
with the public and sell at a price above the minimum average variable cost.)
25. The shutdown notice reduces the firm’s flexibility,
which matters in an uncertain market. If conditions
suddenly change, the firm may have to operate at a
loss for six months before it can shut down. This
potential extra expense of shutting down may discourage some firms from entering the market
initially.
33. The competitive firm’s marginal cost function is
found by differentiating its cost function with respect
to quantity: MC(q) = dC(q)/dq = b + 2cq + 3dq2.
The firm’s necessary profit-maximizing condition is
p = MC = b + 2cq + 3dq2. The firm solves this
equation for q for a specific price to determine its
profit-maximizing output.
35. Because the clinics are operating at minimum average cost, a lump-sum tax that causes the minimum
average cost to rise by 10% would cause the market
price of abortions to rise by 10%. Based on the estimated price elasticity of between −0.70 and −0.99,
the number of abortions would fall to between 7%
and 10%. A lump-sum tax shifts upward the average
cost curve but does not affect the marginal cost
curve. Consequently, the market supply curve, which
is horizontal and the minimum of the average cost
curve, shifts up in parallel.
36. To derive the expression for the elasticity of the
residual or excess supply curve in Equation 8.17, we
differentiate the residual supply curve, Equation
8.16, Sr(p) = S(p) − Do(p), with respect to p to
obtain
d Sr
d S d Do
=
−
.
dp
dp
dp
Let Qr = Sr(p), Q = S(p), and Qo = D(p). We multiply both sides of the differentiated expression by p/Qr,
and for convenience, we also multiply the second term
by Q/Q = 1 and the last term by Qo/Qo = 1:
d Sr p
d S p Q d Do p Qo
=
−
.
d p Qr
d p Qr Q
d p Qr Qo
We can rewrite this expression as Equation 8.17 by
noting that ηr = (dSt/dp)(p/Qr) is the residual supply
elasticity, η = (dS/dp)(p/Q) is the market supply elasticity, εo = (dDo/dp)(p/Qo) is the demand elasticity of
the other countries, and θ = Qr/Q is the residual
country’s share of the world’s output (hence 1 − θ =
Qo/Q is the share of the rest of the world). If there are
n countries with equal outputs, then 1/θ = n, so this
equation can be rewritten as η r = nη − (n − 1) εo.
37. See the text for details:
a. The incidence of the federal specific tax is shared
equally between consumers and firms, whereas
firms bear virtually none of the incidence of the
state tax (they pass the tax on to consumers).
b. From Chapter 2, we know that the incidence of a
tax that falls on consumers in a competitive market is approximately η/(η − ε). Although the
national elasticity of supply may be a relatively
small number, the residual supply elasticity facing
a particular state is very large. Using the analysis
about residual supply curves, we can infer that
the supply curve to a particular state is likely to
be nearly horizontal—nearly perfectly elastic. For
example, if the price in Maine rises even slightly
relative to the price in Vermont, suppliers in
Vermont will be willing to shift up to their entire
supply to Maine. Thus, we expect the incidence
on consumers to be nearly one from a state tax
but less from a federal tax, consistent with the
empirical evidence.
c. If all 50 states were identical, we could write the
residual elasticity of supply, Equation 8.17, as ηr
= 50η − 49εo. Given this equation, the residual
supply elasticity to one state is at least 50 times
larger than the national elasticity of supply, ηr ≥
50η, because εo < 0, so the −49εo term is positive
and increases the residual supply elasticity.
38. Each competitive firm wants to choose its output q
to maximize its after-tax profit: π = pq − C(q) − ᏸ.
Its necessary condition to maximize profit is that
price equals marginal cost: p − dC(q)/dq = 0.
Industry supply is determined by entry, which occurs
until profits are driven to zero (we ignore the problem of fractional firms and treat the number of firms,
n, as a continuous variable): pq − [C(q) + ᏸ] = 0. In
equilibrium, each firm produces the same output, q,
so market output is Q = nq, and the market inverse
demand function is p = p(Q) = p(nq). By substituting the market inverse demand function into the necessary and sufficient condition, we determine the
market equilibrium (n*, q*) by the two conditions:
p(n*q*) − dC(q*)/dq = 0,
p(n*q*)q* − [C(q*) + ᏸ] = 0.
For notational simplicity, we henceforth leave off
the asterisks. To determine how the equilibrium is
affected by an increase in the lump-sum tax, we evaluate the comparative statics at ᏸ = 0. We totally differentiate our two equilibrium equations with
respect to the two endogenous variables, n and q,
and the exogenous variable, ᏸ:
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dq(n[dp(nq)/dQ] − d2C(q)/dq2) +
⎛ d2C ⎞⎟
⎜⎜ −
q ⎟⎟
d p ⎜⎜⎜ d q2 ⎟⎟⎟
=
⎟ > 0.
⎜
d Q ⎜⎜ D ⎟⎟⎟
⎜⎜
⎟⎟
⎝
⎠
dn(q[dp(nq)/dQ]) + dᏸ (0) = 0,
dq(n[qdp(nq)/dQ] + p(nq) − dC/dq)+
dn(q2[dp(nq)/dQ]) − dᏸ = 0.
We can write these equations in matrix form (noting
that p − dC/dq = 0 from the necessary condition) as
⎤
⎡
2
⎢ n dp − d C q dp ⎥
⎥
⎢
2
d Q ⎥ ⎡⎢ d q ⎤⎥ ⎡⎢ 0 ⎤⎥
⎢ dQ dq
d ᏸ.
⎥⎢
⎢
⎥=
dp
d p ⎥ ⎢⎣ d n ⎥⎦ ⎢⎣ 1 ⎥⎦
⎢
nq
q2
⎥
⎢
dQ
dQ ⎥
⎢
⎦
⎣
There are several ways to solve these equations.
One is to use Cramer’s rule. Define
n
D=
dp
d2C
− 2
dQ dq
nq
dp
dQ
q
dp
dQ
q2
dp
dQ
⎛ dp
d p ⎛⎜ d p ⎞⎟
d2C ⎞⎟ 2 d p
⎟q
⎟⎟
−q
= ⎜⎜⎜n
−
⎜nq
⎜⎝ d Q d q2 ⎟⎟⎠ d Q
d Q ⎜⎝ d Q ⎟⎠
=−
where the inequality follows from each firm’s sufficient condition. Using Cramer’s rule:
q
dp
dQ
1 q2
dp
dQ
dq
=
dᏸ
D
n
dp
d2C
− 2
dQ dq
nq
dn
=
dᏸ
dp
dQ
dp
dQ
> 0, and
D
−q
=
0
1
D
dp
d2C
−
n
d Q d q2
=
< 0.
D
The change in price is
d p(nq)
dᏸ
=
Chapter 9
4. If the tax is based on economic profit, the tax has no
long-run effect because the firms make zero economic profit. If the tax is based on business profit
and business profit is greater than economic profit,
the profit tax raises firms’ after-tax costs and results
in fewer firms in the market. The exact effect of the
tax depends on why business profit is less than economic profit. For example, if the government ignores
opportunity labor cost but includes all capital cost in
computing profit, firms will substitute toward labor
and away from capital.
7. Solved Problem 8.5 shows the long-run effect of a
lump-sum tax in a competitive market. Consumer
surplus falls by more than tax revenue increases, and
producer surplus remains zero, so welfare falls.
29. The specific subsidy shifts the supply curve, S in the
d2C 2 d p
q
> 0,
q2 d Q
dq
0
N-11
dp ⎡ dn
dq ⎤
⎢q
⎥
+n
⎢
dQ ⎣ dᏸ
d ᏸ ⎥⎦
⎡⎛ dp
⎤
d2C ⎞
⎢ ⎜⎜n
− 2 ⎟⎟⎟q nq d p ⎥⎥
⎢
⎜
⎟
⎜
dp ⎢⎝ dQ dq ⎠
dQ ⎥
=
−
d Q ⎢⎢
D
D ⎥⎥
⎥
⎢
⎥⎦
⎢⎣
figure, down by s = 11¢, to the curve labeled S −
11¢. Consequently, the equilibrium shifts from e1 to
e2, so the quantity sold increases (from 1.25 to 1.34
billion rose stems per year), the price that consumers
pay falls (from 30¢ to 28¢ per stem), and the amount
that suppliers receive, including the subsidy, rises
(from 30¢ to 39¢), so that the differential between
what the consumers pay and what the producers
receive is 11¢. Consumers and producers of roses are
delighted to be subsidized by other members of society. Because the price to customers drops, consumer
surplus rises from A + B to A + B + D + E. Because
firms receive more per stem after the subsidy, producer surplus rises from D + G to B + C + D + G
(the area under the price they receive and above the
original supply curve). Because the government pays
a subsidy of 11¢ per stem for each stem sold, the
government’s expenditures go from zero to the rectangle B + C + D + E + F. Thus, the new welfare is
the sum of the new consumer surplus and producer
surplus minus the government’s expenses. Welfare
falls from A + B + D + G to A + B + D + G − F.
The deadweight loss, this drop in welfare Δ W =
−F, results from producing too much: The marginal
cost to producers of the last stem, 39¢, exceeds
the marginal benefit to consumers, 28¢.
30. At a price of 30, the quantity demanded is 30, so the
consumer surplus is 1_2(30 × 30) = 450, because the
demand curve is linear.
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p, ¢ per stem
For Chapter 9, Problem 29
S
39¢ A
⎧
⎪
s = 11¢ ⎨
⎪ 30¢
⎩ 28¢
S − 11¢
C
B
e1
F
e2
D
E
G
Demand
s = 11¢
1.25
1.34
Q, Billions of rose stems per year
34. a. The initial equilibrium is determined by equating
the quantity demanded to the quantity supplied:
100 − 10p = 10p. That is, the equilibrium is p =
5 and Q = 50. At the support price, the quantity
supplied is Qs = 60. The market clearing price
was p = 4. The deficiency payment was D =
(p − p)Qs = (6 − 4)60 = 120.
b. Consumer surplus rises from CS1 = 1_2(10 − 5)50
= 125 to CS2 = 1_2(10 − 4)60 = 180. Producer surplus rises from PS1 = 1_2(5 − 0)50 = 125 to PS2 =
1
_
2 × (6 − 0)60 = 180. Welfare falls from CS1 + PS1
= 125 + 125 = 250 to CS2 + PS2 − D = 180 +
180 − 120 = 240. Thus, the deadweight loss is 10.
37. Without the tariff, the U.S. supply curve of oil is horizontal at a price of $14.70 (S1 in Figure 9.9), and the
equilibrium is determined by the intersection of this
horizontal supply curve with the demand curve. With
a new, small tariff of τ, the U.S. supply curve is horizontal at $14.70 + τ, and the new equilibrium quantity is determined by substituting p = 14.70 + τ into
the demand function: Q = 35.41(14.70 + τ)p−0.37.
Evaluated at τ = 0, the equilibrium quantity remains
at 13.1. The deadweight loss is the area to the right
of the domestic supply curve and to the left of the
demand curve between $14.70 and $14.70 + τ (area
C + D + E in Figure 9.9) minus the tariff revenues
(area D):
14.70+ τ
DWL =
∫
14.70
14.70+ τ
=
∫
14.70
⎡ D( p) − S ( p)⎤ d p − τ ⎡ D( p + τ) − S ( p + τ)⎤
⎣⎢
⎦⎥
⎣⎢
⎦⎥
⎡3 .54 p−0.67 − 3 .35p0.33 ⎤ d p
⎣⎢
⎦⎥
−0.67
0.33 ⎤
⎡
−τ ⎢3 .54( p + τ)
− 3 .35( p + τ) ⎥ .
⎣
⎦
To see how a change in τ affects welfare, we differentiate DWL with respect to τ:
⎧14.70+ τ
d DWL
d ⎪
⎪
=
⎨ ∫ ⎡⎢⎣ D( p) − S ( p)⎤⎥⎦ d p
dτ
dτ ⎪
⎪
⎪
⎩ 14.70
⎫
⎪
⎪
− τ ⎡⎣⎢ D(14 .70 + τ) − S (14 .70 + τ)⎤⎦⎥ ⎬
⎪
⎪
⎪
⎭
= ⎡⎣⎢ D(14 .70 + τ) − S (14 .70 + τ)⎤⎦⎥ − [ D(14 .70 + τ)
⎡ d D(14 .70 + τ) d S (14 .70 + τ) ⎤
⎥
−S (14 .70 + τ )] − τ ⎢⎢
−
⎥
dτ
dτ
⎢⎣
⎥⎦
⎡ d D(14 .70 + τ) d S (14 .70 + τ) ⎤
⎥.
= −τ ⎢⎢
−
⎥
dτ
dτ
⎢⎣
⎥⎦
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pose that, before they got married, Chris and Pat
each spent 10 hours a day in sleep and leisure activities, 5 hours working in the marketplace, and 9
hours working at home. Because Chris earns $10 an
hour and Pat earns $20 an hour, they collectively
earned $150 a day and worked 18 hours a day at
home. After they marry, they can benefit from specialization. If Chris works entirely at home and Pat
works 10 hours in the marketplace and the rest at
home, they collectively earn $200 a day (a one-third
increase) and still have 18 hours of work at home. If
they do not need to spend as much time working at
home because of economies of scale, one or both
could work more hours in the marketplace, and they
will have even greater disposable income.
If we evaluate this expression at τ = 0, we find that
dDWL/dτ = 0. In short, applying a small tariff to the
free-trade equilibrium has a negligible effect on
quantity and deadweight loss. Only if the tariff is
larger—as in Figure 9.9—do we see a measurable
effect.
Chapter 10
1. A subsidy is a negative tax. Thus, we can use the
same analysis that we used in Solved Problem 10.1
to answer this question by reversing the signs of the
effects.
17. If you draw the convex production possibility fron-
11. As Chapter 4 shows, the slope of the budget con-
tier on Figure 10.5, you will see that it lies strictly
inside the concave production possibility frontier.
Thus, more output can be obtained if Jane and
Denise use the concave frontier. That is, each should
specialize in producing the good for which she has a
comparative advantage.
straint facing an individual equals the negative of
that person’s wage. Panel a of the figure illustrates
that Pat’s budget constraint is steeper than Chris’s
because Pat’s wage is larger than Chris’s. Panel b
shows their combined budget constraint after they
marry. Before they marry, each spends some time in
the marketplace earning money and other time at
home cooking, cleaning, and consuming leisure.
After they marry, one of them can specialize in earning money and the other at working at home. If they
are both equally skilled at household work (or if
Chris is better), then Pat has a comparative advantage (see Figure 10.5) in working in the marketplace,
and Chris has a comparative advantage in working
at home. Of course, if both enjoy consuming leisure,
they may not fully specialize. As an example, sup-
Chapter 11
5. Yes. See “Electric Power Utilities.” in MyEconLab’s
textbook resources for Chapter 11, which illustrates
that the demand curve could cut the average cost
curve only in its downward-sloping section.
Consequently, the average cost is strictly downward
sloping in the relevant region.
For Chapter 10, Problem 11
(b) Married
Time constraint
Y, Goods per day
Y, Goods per day
(a) Unmarried
Time constraint
LCombined
LP
LC
24
0
H, Work hours per day
N-13
48
24
0
H, Work hours per day
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22. For a general linear inverse demand function, p(Q) =
a − bQ, dQ/dp = −1/b, so the elasticity is
ε = −p/(bQ). The demand curve hits the horizontal
(quantity) axis at a/b. At half that quantity (the midpoint of the demand curve), the quantity is a/(2b),
and the price is a/2. Thus, the elasticity of demand is
ε = −p/(bQ) = −(a/2)/[ab/(2b)] = −1 at the midpoint of any linear demand curve. As the chapter
shows, a monopoly will not operate in the inelastic
section of its demand curve, so a monopoly will not
operate in the right half of its linear demand curve.
32. See MyEconLab, Chapter 11, “Humana Hospitals,”
for more examples. For saline solution, p/MC ≈ 55.4
and the Lerner Index is (p − MC)/p ≈ 0.98. From
Equation 11.9, we know that (p − MC)/p ≈ 0.98 =
−1/ε, so ε ≈ 1.02.
37. A profit tax (of less than 100%) has no effect on a
firm’s profit-maximizing behavior. Suppose the government’s share of the profit is β. Then the firm
wants to maximize its after-tax profit, which is
(1 − γ)π. However, whatever choice of Q (or p) maximizes π will also maximize (1 − γ)π. Figure 19.3
gives a graphical example where γ = 1/3.
Consequently, the tribe’s behavior is unaffected by a
change in the share that the government receives. We
can also answer this problem using calculus. The
before-tax profit is πB = R(Q) − C(Q), and the aftertax profit is πA = (1 − γ)[R(Q) − C(Q)]. For both,
the first-order condition is marginal revenue equals
marginal cost: dR(Q)/dQ = dC(Q)/dQ.
41. Given the demand curve is p = 10 − Q, its marginal
revenue curve is MR = 10 − 2Q. Thus, the output
that maximizes the monopoly’s profit is determined
by MR = 10 − 2Q = 2 = MC, or Q* = 4. At that
output level, its price is p* = 6 and its profit is π* =
16. If the monopoly chooses to sell 8 units in the first
period (it has no incentive to sell more), its price is
$2 and it makes no profit. Given that the firm sells 8
units in the first period, its demand curve in the second period is p = 10 − Q/β, so its marginal revenue
function is MR = 10 − 2Q/β. The output that leads
to its maximum profit is determined by MR = 10 −
2Q/β = 2 = MC, or its output is 4β. Thus, its price
is $6 and its profit is 16β. It pays for the firm to set
a low price in the first period if the lost profit, 16, is
less than the extra profit in the second period, which
is 16(β − 1). Thus, it pays to set a low price in the
first period if 16 < 16(β − 1), or 2 < β.
Chapter 12
2. This policy allows the firm to maximize its profit by
price discriminating if people who put a lower value
on their time (so are willing to drive to the store and
move their purchases themselves) have a higher elasticity of demand than people who want to order by
phone and have the goods delivered.
3. The colleges may be providing scholarships as a form
of charity, or they may be price discriminating
by lowering the final price for less wealthy families
(who presumably have higher elasticities of
demand).
28. Equating the right-hand sides of the demand and
supply functions, 100 − w = w − 20, and solving,
we find that w = 60. Substituting that into either the
demand or supply function, we find that H* = 100
− 60 = 60 − 20 = 40. To find w*, we need to equate
areas A and C in the figure in Solved Problem 12.1.
We could integrate, but with a linear demand function, it is easier to calculate the area of triangles. The
area of A is 1_2(100 − w*)2 while the area of B is
1
_
2
2(w* − 60) . Equating these areas and solving, we
find that w* = 80. Substituting
that into the demand
_
function, we obtain H = 20.
32. See MyEconLab, Chapter 12, “Aibo,” for more
details. The two marginal revenue curves are MRJ =
3,500 − QJ and MRA = 4,500 − 2QA. Equating the
marginal revenues with the marginal cost of $500,
we find that QJ = 3,000 and QA = 2,000.
Substituting these quantities into the inverse demand
curves, we learn that pJ = $2,000 and pA = $2,500.
Rearranging Equation 11.9, we know that the elasticities of demand are εJ = p/(MC − p) = 2,000 ÷
(500 − 2,000) = −4_3 and εA = 2,500/(500 − 2,500)
= −_45. Thus, using Equation 12.3, we find that
pJ
pA
=
1 + 1/(− 45 ) 1 + 1/ ε
2, 000
A
.
= 0 .8 =
=
1 + 1/ ε J
2, 500
1 + 1/(− 43 )
The profit in Japan is (pJ − m)QJ = ($2,000 − $500)
× 3,000 = $4.5 million, and the U.S. profit is $4 million. The deadweight loss is greater in Japan, $2.25
million (= 1_2 × $1,500 × 3,000), than in the United
States, $2 million (= 1_2 × $2,000 × 2,000).
33. By differentiating, we find that the American
marginal revenue function is MRA = 100 − 2QA,
and the Japanese one is MRJ = 80 − 4QJ. To determine how many units to sell in the United States, the
monopoly sets its American marginal revenue equal
to its marginal cost, MRA = 100 − 2QA = 20, and
solves for the optimal quantity, QA = 40 units.
Similarly, because MRJ = 80 − 4QJ = 20, the optimal quantity is QJ = 15 units in Japan. Substituting
QA = 40 into the American demand function, we
find that pA = 100 − 40 = $60. Similarly, substituting QJ = 15 units into the Japanese demand func-
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Answers to Selected Problems
tion, we learn that pJ = 80 − (2 × 15) = $50. Thus,
the price-discriminating monopoly charges 20%
more in the United States than in Japan. We can also
show this result using elasticities. From Equation
2.22, we know that the elasticity of demand is εA =
−pA/QA in the United States and εJ = − 1/2PJ /QJ in
Japan. In the equilibrium, εA = −60/40 = −3/2 and
εJ = −50/(2 × 15) = −5/3. As Equation 12.3 shows,
the ratio of the prices depends on the relative elasticities of demand: pA/pJ = 60/50 = (1 + 1/εJ) ÷
(1 + 1/εA) = (1 − 3/5)/(1 − 2/3) = 6/5.
35. From the problem, we know that the profit-
maximizing Chinese price is p = 3 and that the quantity is Q = 0.1 (million). The marginal cost is m = 1.
Using Equation 11.11, (pC − m)/pC = (3 − 1)/3 =
−1/εC , so εC = −3/2. If the Chinese inverse demand
curve is p = a − bQ, then the corresponding
marginal revenue curve is MR = a − 2bQ. Warner
maximizes its profit where MR = a − 2bQ = m = 1,
so its optimal Q = (a − 1)/(2b). Substituting this
expression into the inverse demand curve, we find
that its optimal p = (a + 1)/2 = 3, or a = 5.
Substituting that result into the output equation, we
have Q = (5 − 1)/(2b) = 0.1 (million). Thus, b = 20,
the inverse demand function is p = 5 − 20Q, and the
marginal revenue function is MR = 5 − 40Q. Using
this information, you can draw a figure similar to
Figure 12.4.
Chapter 13
2. The payoff matrix in this prisoners’ dilemma game is
Duncan
Squeal
Squeal
Stay Silent
–2
–2
Larry
Stay
Silent
–5
0
0
–5
–1
–1
If Duncan stays silent, Larry gets 0 if he squeals and
−1 (a year in jail) if he stays silent. If Duncan confesses, Larry gets −2 if he squeals and −5 if he does
not. Thus, Larry is better off squealing in either case,
so squealing is his dominant strategy. By the same
reasoning, squealing is also Duncan’s dominant
strategy. As a result, the Nash equilibrium is for both
to confess.
3. No strategies are dominant, so we use the bestresponse approach to determine the pure-strategy
Nash equilibria. First, identify each firm’s best
N-15
responses given each of the other firms’ strategies (as
we did in Solved Problem 13.1). This game has two
Nash equilibria: (a) Firm 1 medium and Firm 2 low,
and (b) Firm 1 low and Firm 2 medium.
19. We start by checking for dominant strategies. Given
the payoff matrix, Toyota always does at least as
well by entering the market. If GM enters, Toyota
earns 10 by entering and 0 by staying out of the market. If GM does not enter, Toyota earns 250 if it
enters and 0 otherwise. Thus, entering is Toyota’s
dominant strategy. GM does not have a dominant
strategy. It wants to enter if Toyota does not enter
(earning 200 rather than 0), and it wants to stay out
if Toyota enters (earning 0 rather than −40). Because
GM knows that Toyota will enter (entering is
Toyota’s dominant strategy), GM stays out. Toyota’s
entering and GM’s not entering is a Nash equilibrium. Given the other firm’s strategy, neither firm
wants to change its strategy. Next, we examine how
the subsidy affects the payoff matrix and dominant
strategies. The subsidy does not affect Toyota’s payoff, so Toyota still has a dominant strategy: It enters
the market. With the subsidy, GM’s payoff if it enters
increases by 50: GM earns 10 if both enter and 250
if it enters and Toyota does not. With the subsidy,
entering is a dominant strategy for GM. Thus, both
firms’ entering is a Nash equilibrium.
22. The game tree illustrates why the incumbent may
install the robotic arms to discourage entry even
though its total cost rises. If the incumbent fears that
a rival is poised to enter, it invests to discourage
entry. The incumbent can invest in equipment that
lowers its marginal cost. With the lowered marginal
cost, it is credible that the incumbent will produce
larger quantities of output, which discourages entry.
The incumbent’s monopoly (no-entry) profit drops
from $900 to $500 if it makes the investment
because the investment raises its total cost. If the
incumbent doesn’t buy the robotic arms, the rival
enters because it makes $300 by entering and nothing if it stays out of the market. With entry, the
incumbent’s profit is $400. With the investment, the
rival loses $36 if it enters, so it stays out of the market, losing nothing. Because of the investment, the
incumbent earns $500. Nonetheless, earning $500 is
better than earning $400, so the incumbent invests.
23. The incumbent firm has a first-mover advantage, as
the game tree illustrates. Moving first allows the
incumbent or leader firm to commit to producing a
relatively large quantity. If the incumbent does not
make a commitment before its rival enters, entry
occurs and the incumbent earns a relatively low
profit. By committing to produce such a large output
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Answers to Selected Problems
For Chapter 14, Problem 22
First stage
Profits (πi , πe )
Second stage
Do not enter
Do not invest
Entrant
Enter
Incumbent
Do not enter
Invest
($900, $0)
($400, $300)
($500, $0)
Entrant
Enter
level that the potential entrant decides not to enter
because it cannot make a positive profit, the incumbent’s commitment discourages entry. Moving backward in time (moving to the left in the diagram), we
examine the incumbent’s choice. If the incumbent
commits to the small quantity, its rival enters and the
incumbent earns $450. If the incumbent commits to
the larger quantity, its rival does not enter and the
incumbent earns $800. Clearly, the incumbent
should commit to the larger quantity because it earns
a larger profit and the potential entrant chooses to
stay out of the market. Their chosen paths are identified by the darker blue in the figure.
($132, – $36)
24. It is worth more to the monopoly to keep the potential entrant out than it is worth to the potential
entrant to enter, as the figure shows. Before the
pollution-control device requirement, the entrant
would pay up to $3 to enter, whereas the incumbent
would pay up to πi − πd = $7 to exclude the potential entrant. The incumbent’s profit is $6 if entry does
not occur, and its loss is $1 if entry occurs. Because
the new firm would lose $1 if it enters, it does not
enter. Thus, the incumbent has an incentive to raise
costs by $4 to both firms. The incumbent’s profit is
$6 if it raises costs rather than $3 if it does not.
For Chapter 14, Problem 23
First stage
Second stage
Accommodate (q i small)
Profits (π i , πe )
Do not enter
($900, $0)
Entrant
Enter
Incumbent
($450, $125)
Do not enter
Deter (q i large)
($800, $0)
Entrant
Enter
($400, $0)
For Chapter 14, Problem 24
First stage
Second stage
Do not raise costs
Profits (πi , πe )
Do not enter
($10, $0)
Entrant
Enter
Incumbent
Do not enter
Raise costs $4
($3, $3)
($6, $0)
Entrant
Enter
(–$1, –$1)
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Answers to Selected Problems
26. Let the probability that a firm sets a low price be θ1
for Firm 1 and θ2 for Firm 2. If the firms choose their
prices independently, then θ1θ2 is the probability that
both set a low price, (1 − θ1)(1 − θ2) is the probability that both set a high price, θ1(1 − θ2) is the probability that Firm 1 prices low and Firm 2 prices high,
and (1 − θ1)θ2 is the probability that Firm 1 prices
high and Firm 2 prices low. Firm 2’s expected payoff
is E(π2) = 2θ1θ2 + (0)θ1(1−θ2) + (1 − θ1)θ2 + 6(1− θ1)
(1 − θ2) = (6 − 6θ1) − (5 − 7θ1)θ2. Similarly, Firm 1’s
expected payoff is E(π1) = (0)θ1θ2 + 7θ1(1 − θ2) +
2(1−θ1)θ2 +6(1− θ1)(1 − θ2) = (6 − 4θ2) − (1 − 3θ2)θ1.
Each firm forms a belief about its rival’s behavior.
For example, suppose that Firm 1 believes that Firm
2 will choose a low price with a probability θ̂2. If θ̂2
is less than 1_3 (Firm 2 is relatively unlikely to choose
a low price), it pays for Firm 1 to choose the low
price because the second term in E(π1), (1 − 3θ̂2)θ1,
is positive, so as θ1 increases, E(π1) increases.
Because the highest possible θ1 is 1, Firm 1 chooses
the low price with certainty. Similarly, if Firm 1
believes θ̂2 is greater than 13_, it sets a high price with
certainty (θ1 = 0). If Firm 2 believes that Firm 1
thinks θ̂2 is slightly below 13_, Firm 2 believes that Firm
1 will choose a low price with certainty, and hence
Firm 2 will also choose a low price. That outcome,
θ2 = 1, however, is not consistent with Firm 1’s expectation that θ̂2 is a fraction. Indeed, it is only rational
for Firm 2 to believe that Firm 1 believes Firm 2 will
use a mixed strategy if Firm 1’s belief about Firm 2
makes Firm 1 unpredictable. That is, Firm 1 uses a
mixed strategy only if it is indifferent between setting
a high or a low price. It is indifferent only if it believes
θ̂2 is exactly 13_. By similar reasoning, Firm 2 will use a
mixed strategy only if its belief is that Firm 1 chooses
a low price with probability θ̂1 = 75_. Thus, the only
possible Nash equilibrium is θ2 = 57_ and θ2 = 13_
Chapter 14
2. The monopoly will make more profit than the
duopoly will, so the monopoly is willing to pay the
college more rent. Although granting monopoly
rights may be attractive to the college in terms of
higher rent, students will suffer (lose consumer surplus) because of the higher textbook prices.
16. Given that the duopolies produce identical goods,
the equilibrium price is lower if the duopolies set
price rather than quantity. If the goods are heterogeneous, we cannot answer this question definitively.
17. By differentiating its product, a firm makes the residual demand curve it faces less elastic everywhere. For
example, no consumer will buy from that firm if its
N-17
rival charges less and the goods are homogeneous. In
contrast, some consumers who prefer this firm’s
product to that of its rival will still buy from this
firm even if its rival charges less. As the chapter
shows, a firm sets a higher price the lower the elasticity of demand at the equilibrium.
22. The inverse demand curve is p = 1 − 0.001Q. The
first firm’s profit is π1 = [1 − 0.001(q1 + q2)]q1 −
0.28q1. Its first-order condition is dπ1/dq1 = 1 −
0.001(2q1 + q2) − 0.28 = 0. If we rearrange the
terms, the first firm’s best-response function is q1 =
360 − 1_2q2. Similarly, the second firm’s best-response
function is q2 = 360 − 1_2q1 By substituting one of
these best-response functions into the other, we learn
that the Nash-Cournot equilibrium occurs at q1 = q2
= 240, so the equilibrium price is 52¢.
24. Given that the firm’s after-tax marginal cost is
m + τ, the Nash-Cournot equilibrium price is p =
(a + n[m + τ])/(n + 1), using Equation 14.17. Thus,
the consumer incidence of the tax is dp/dτ = n/(n + 1)
< 1 (= 100%).
25. See Solved Problem 14.2. The equilibrium quantities
are q1 = (a − 2m1 + m2)/3b = (90 + 30)/6 = 20 and
q2 = (90 − 60)/6 = 5. As a result, the equilibrium
price is p = 90 − (2 × 20) − (2 × 5) = 40.
28. Firm 1 wants to maximize its profit:
π1 = (p1 − 10)q1 = (p1 − 10)(100 − 2p1 + p2).
Its first-order condition is dπ1/dp1 = 100 − 4p1 + p2
+ 20 = 0, so its best-response function is p1 = 30 +
1_
p . Similarly, Firm 2’s best-response function is p2
4 2
= 30 + 1_4 p1. Solving, the Nash-Bertrand equilibrium
prices are p1 = p2 = 40. Each firm produces 60 units.
31. One approach is to show that a rise in marginal cost
or a fall in the number of firms tends to cause the
price to rise. Solved Problem 14.4 shows the effect of
a decrease in marginal cost due to a subsidy (the
opposite effect). The section titled “The Cournot
Equilibrium with Two or More Firms” shows that as
the number of firms falls, market power increases
and the markup of price over marginal cost
increases. The two effects reinforce each other.
Suppose that the market demand curve has a constant elasticity of ε. We can rewrite Equation 14.10
as p = m/[1 + 1/(nε)] = mμ, where μ = 1/[1 + 1/(nε)]
is the markup factor. Suppose that marginal cost
increases to (1 + α)m and that the drop in the number of firms causes the markup factor to rise to
(1 + β)μ; then the change in price is [(1 + α)m ×
(1 + β)μ] − mμ = (α + β + αβ)mμ. That is, price
increases by the fractional increase in the marginal
cost, α, plus the fractional increase in the markup
factor, β, plus the interaction of the two, αβ.
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Answers to Selected Problems
38. You can solve this problem using calculus or the formulas for the linear demand and constant marginal
cost Cournot model from the chapter.
a. For the duopoly, q1 = (15 − 2 + 2)/3 = 5, q2 =
(15 − 4 + 1)/3 = 4, pd = 6, π1 = (6 − 1)5 = 25,
π2 = (6 − 2)4 = 16. Total output is Qd = 5 + 4
= 9. Total profit is πd = 25 + 16 = 41. Consumer
surplus is CSd = 1/2(15 − 6)9 = 81/2 = 40.5. At
the efficient price (equal to marginal cost of 1),
the output is 14. The deadweight loss is DWLd =
1/2(6 − 1)(14 − 9) = 25/2 = 12.5.
b. A monopoly equates its marginal revenue and
marginal cost: MR = 15 − 2Qm = 1 = MC. Thus,
Qm = 7, pm = 8, πm = (8 − 1)7 = 49. Consumer
surplus is CSm = 1/2 (15 − 8)7 = 49/2 = 24.5.
The deadweight loss is DWLm = 1/2 (8 − 1)
(14 − 7) = 49/2 = 24.5.
c. The average cost of production for the duopoly is
[(5 × 1) + (4 × 2)]/(5 + 4) = 1.44, whereas the
average cost of production for the monopoly is 1.
The increase in market power effect swamps the
efficiency gain, so consumer surplus falls while
deadweight loss nearly doubles.
39. a. In the Cournot equilibrium, qi = (a − m)/(3b) =
(150 − 60)/3 = 30, Q = 60, p = 90.
26. If a firm has a monopoly in the output market and is
a monopsony in the labor market, its profit is
π = p(Q(L))Q(L) − w (L)L,
where Q(L) is the production function, p(Q)Q is its
revenue, and w(L)L—the wage times the number of
workers—is its cost of production. The firm maximizes its profit by setting the derivative of profit
with respect to labor equal to zero (if the secondorder condition holds):
⎛
⎞
⎜⎜ p + Q(L) dp ⎟⎟ dQ − w (L) − dw L = 0.
⎟
⎜⎝
dQ ⎟⎠ dL
dL
Rearranging terms in the first-order condition, we
find that the maximization condition is that the
marginal revenue product of labor,
⎛
d p ⎞⎟ d Q
⎟⎟
MRPL = MR × MPL = ⎜⎜⎜ p + Q(L)
d Q ⎟⎠ d L
⎝
⎛
1⎞ d Q
= p⎜⎜1 + ⎟⎟⎟
,
⎜⎝
ε ⎟⎠ d L
equals the marginal expenditure,
ME = w (L) +
⎛
dw
L = w (L)⎜⎜1 +
⎜⎝
dL
⎛
= w (L)⎜⎜1 +
⎜⎝
L d w ⎞⎟
⎟
w d L ⎟⎟⎠
1 ⎞⎟
⎟,
η ⎟⎠⎟
b. In the Stackelberg equilibrium in which Firm 1
moves first, q1 = (a − m)/(2b) = 50 − 60)/2 = 45,
q2 = (a − m)/(4b) = (150 − 60)/4 = 22.5, Q =
67.5, and p = 82.5.
where ε is the elasticity of demand in the output market and η is the supply elasticity of labor.
40. a. The Cournot equilibrium in the absence of gov-
34. Solving for irr, we find that irr equals 1 or 9. This
ernment intervention is q1 = 30, q2 = 40, p = 50,
π1= 900, and π2 = 1,600.
b. The Cournot equilibrium is now q1 = 33.3, q2 =
33.3, p = 53.3, π1 = 1,108.9, and π2 = 1,108.9.
c. Because Firm 2’s profit was 1,600 in part a, a fixed
cost slightly greater than 1,600 will prevent entry.
Chapter 15
2. Before the tax, the competitive firm’s labor demand
was p × MPL. After the tax, the firm’s effective price
is (1 − α)p, so its labor demand becomes (1 − α)p ×
MPL.
15. An individual with a zero discount rate views current
and future consumption as equally attractive. An
individual with an infinite discount rate cares only
about current consumption and puts no value on
future consumption.
21. The competitive firm’s marginal revenue of labor is
MRPL = p(1 + 2K).
approach fails to give us a unique solution, so we
should use the NPV approach instead. The NPV = 1
− 12/1.07 + 20/1.072 ≈ 7.254, which is positive, so
that the firm should invest.
40. Currently, you are buying 600 gallons of gas at a cost
of $1,200 per year. With a more gas-efficient car, you
would spend only $600 per year, saving $600 per
year in gas payments. If we assume that these payments are made at the end of each year, the present
value of these savings for five years is $2,580 at a 5%
annual interest rate and $2,280 at 10%. The present
value of the amount you must spend to buy the car in
five years is $6,240 at 5% and $4,960 at 10%. Thus,
the present value of the additional cost of buying now
rather than later is $1,760 (= $8,000 − $6,240) at
5% and $3,040 at 10%. The benefit from buying
now is the present value of the reduced gas payments.
The cost is the present value of the additional cost of
buying the car sooner rather than later. At 5%, the
benefit is $2,580 and the cost is $1,760, so you
should buy now. However, at 10%, the benefit,
$2,280, is less than the cost, $3,040, so you should
buy later.
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Answers to Selected Problems
43. Because the first contract is paid immediately, its
present value equals the contract payment of $1 million. Our pro can use Equation 15.19 and a calculator to determine the present value of the second
contract (or hire you to do the job for him). The
present value of a $2 million payment 10 years
from now is $2,000,000/(1.05)10 ≈ $1,227,827 at
5% and $2,000,000/(1.2)10 ≈ $323,011 at 20%.
Consequently, the present values are as shown in the
table.
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24. Assuming that the painting is not insured against
fire, its expected value is
$550 = (0.2 × $1,000) + (0.1 × $0)
+ (0.7 × $500).
Chapter 17
3. As Figure 17.3 shows, a specific tax of $84 per ton
Present Value
at 20%
of output or per unit of emissions (gunk) leads to the
social optimum.
$50,000
$500,000
6. Granting the chemical company the right to dump 1
$2 million in 10 years
$1,227,827
$323,011
Total
$1,727,827
$823,011
Payment
$500,000 today
Present Value
at 5%
Thus, at 5%, he should accept Contract B, with a
present value of $1,727,827, which is much greater
than the present value of Contract A, $1 million. At
20%, he should sign Contract A.
ton per day results in that firm’s dumping 1 ton and
the boat rental company’s maintaining one boat,
which maximizes joint profit at $20.
19. As the figure shows, the government uses its
expected marginal benefit curve to set a standard at
S or a fee at f. If the true marginal benefit curve is
MB1, the optimal standard is S1 and the optimal fee
is f1. The deadweight loss from setting either the fee
or the standard too high is the same, DWL1.
Similarly, if the true marginal benefit curve is MB2,
both the fee and the standard are set too low, but
both have the same deadweight loss, DWL2. Thus,
the deadweight loss from a mistaken belief about the
marginal benefit does not depend on whether the
government uses a fee or a standard. When the government sets an emissions fee or standard, the
amount of gunk actually produced depends only on
the marginal cost of abatement and not on the
marginal benefit. Because the fee and standard lead
to the same level of abatement at e, they cause the
same deadweight loss.
Chapter 16
3. As Figure 16.2 shows, Irma’s expected utility of 133
at point f (where her expected wealth is $64) is the
same as her utility from a certain wealth of Y.
5. The expected punishment for violating traffic laws is
18. If they were married, Andy would receive half the
potential earnings whether they stayed married or
not. As a result, Andy will receive $12,000 in
present-value terms from Kim’s additional earnings.
Because the returns to the investment exceed the
cost, Andy will make this investment (unless a better investment is available). However, if they stay
unmarried and split, Andy’s expected return on the
investment is the probability of their staying
together, 1/2, times Kim’s half of the returns if they
stay together, $12,000. Thus, Andy’s expected
return on the investment, $6,000, is less than the
cost of the education, so Andy is unwilling to make
that investment (regardless of other investment
opportunities).
For Chapter 17, Problem 19
Fee, marginal benefit,
marginal cost, $
θV, where θ is the probability of being caught and
fined and V is the fine. If people care only about the
expected punishment (that is, there’s no additional
psychological pain from the experience), increasing
the expected punishment by increasing θ or V works
equally well in discouraging bad behavior. The government prefers to increase the fine, V, which is costless, rather than to raise θ, which is costly due to the
extra police, district attorneys, and courts required.
MC of abatement
DWL2
f2
e
f
MB 2
DWL1
f1
Expected MB
of abatement
MB 1
S1
S
S2
Units of gunk abated per day
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Answers to Selected Problems
21. We care only about the marginal harm of gunk at the
social optimum, which we know is MCg = $84
(because it is the same at every level of output).
Thus, the social optimum is the same as in our
graphical example (and no algebra is necessary). We
can also solve the problem using algebra. Using the
equations from the chapter, we set the inverse
demand function, p = 450 − 2Q, equal to the new
social marginal cost, MCs = MCp + 84 = 30 + 2Q
+ 84 = 114 + 2Q, and we find that the socially optimal quantity is Qs = (450 − 114)/(2 + 2) = 84.
Chapter 18
2. Because insurance costs do not vary with soil type,
buying insurance is unattractive for houses on good
soil and relatively attractive for houses on bad soil.
These incentives create a moral hazard problem:
Relatively more homeowners with houses on poor
soil buy insurance, so the state insurance agency will
face disproportionately many bad outcomes in the
next earthquake.
6. Brand names allow consumers to identify a particular company’s product in the future. If a mushroom
company expects to remain in business over time, it
would be foolish for it to brand its product if its
mushrooms are of inferior quality. (Just ask Babar’s
grandfather.) Thus, all else the same, we would
expect branded mushrooms to be of higher quality
than unbranded ones.
15. Because buyers are risk neutral, if they believe that
the probability of getting a lemon is θ, the most they
are willing to pay for a car of unknown quality is p
= p1(1 − θ) + p2θ. If p is greater than both v1 and v2,
all cars are sold. If v1 > p > v2, only lemons are sold.
If p is less than both v1 and v2, no cars are sold.
However, we know that v2 < p2 and that p2 < p, so
owners of lemons are certainly willing to sell them.
(If sellers bear a transaction cost of c and p < v2 + c,
no cars are sold.)
Chapter 19
1. If Paula pays Arthur a fixed-fee salary of $168,
Arthur has no incentive to buy any carvings for
resale, given that the $12 per carving cost comes out
of his pocket. Thus, Arthur sells no carvings if he
receives a fixed salary and can sell as many or as few
carvings as he wants. The contract is not incentive
compatible. For Arthur to behave efficiently, this
fixed-fee contract must be modified. For example,
the contract could specify that Arthur gets a salary of
$168 and that he must obtain and sell 12 carvings.
Paula must monitor his behavior. (Paula’s residual
profit is the joint profit minus $168, so she gets the
marginal profit from each additional sale and wants
to sell the joint-profit-maximizing number of carvings.) Arthur makes $24 = $168 − $144, so he is
willing to participate. Joint profit is maximized at
$72, and Paula gets the maximum possible residual
profit of $48.
6. By making this commitment, a company may be trying to assure customers who cannot judge how
quickly a product will deteriorate that the product is
durable enough to maintain at least a certain value in
the future. The firm is trying to eliminate asymmetric
information to increase the demand for its product.
9. Presumably, the promoter collects a percentage of
the revenue of each restaurant. If customers can pay
cash, the restaurants may not report the total
amount of food they sell. The scrip makes such
opportunistic behavior difficult.
13. A partner who works an extra hour bears the full
opportunity cost of this extra hour but gets only half
the marginal benefit from the extra business profit.
The opportunity cost of extra time spent at the store
is the partner’s best alternative use of time. A partner
could earn money working for someone else or use
the time to have fun. Because a partner bears the full
marginal cost but gets only half the marginal benefit
(the extra business profit) from an extra hour of
work, each partner works only up to the point at
which the marginal cost equals half the marginal
benefit. Thus, each has an incentive to put in less
effort than the level that maximizes their joint profit,
where the marginal cost equals the marginal benefit.
14. This agreement led to very long conversations.
Whichever of them was enjoying the call more
apparently figured that he or she would get the full
marginal benefit of one more minute of talking
while having to pay only half the marginal cost.
From this experience, I learned not to open our
phone bill so as to avoid being shocked by the
amount due (back in an era when long-distance
phone calls were expensive).
21. The minimum bond that deters stealing is $2,500.