Answers to End-of-Chapter 6 Exercises
7. MPK = 200
10. a. K = 4 → q = 660.22
K
= 5 → q = 789.25 → MPK = 129.03
K
= 6 → q = 913.19 → MPK = 123.94
K
= 7 → q = 1033.04 → MPK = 119.85
L
= 49 → q = 660.22
L
= 50 → q = 662.89 → MPL = 2.67
L
= 51 → q = 665.52 → MPL = 2.63
L
= 52 → q = 668.11 → MPL = 2.59
b. Constant returns to scale
Answers to End-of-Chapter 7 Exercises
9. a. FC = 200
b. AVC = $55,000
c. MC = $55,000
d. AFC = $2000
e. C = 250 + 45q + 3i
Answers to End-of-Chapter 8 Exercises
3. a. The firm will produce 8 or
more units depending on the market price and will not produce in the 0 – 7
units because in this range MC is less than AVC.
b. When P = 38,
each firm will produce 8 units.
Therefore when P =38, Q = 800 units.
When P = 45, Q = 900. When P =55,
Q = 1000. When P =65 and Q = 1100.
4. a. q = 25
b. Profit = $1050
c. MC = 4q.
AVC = 2q. MC is greater than AVC
for any quantity greater than 0. The
firm produces in the SR as long as P is positive.
7. a. VC = 4q2
FC = 16
AC = 4q + 16/q
AVC = 4q
AFC = 16/q
b. Graph
c. Minimum average cost occurs where MC =
AC
q = 2
d. MC is above AC at all output levels, so
the firm will supply positive output at any positive price.
e. When P less than AC, firm earns negative
profit. Minimum AC occurs where q =
2. Plug this in average cost function to
find AC = 16. The firm will earn
negative profit if P is below 16.
f. When P is above 16.
9. a. C(q)
= 4000q2/81 + 1000
b. P = 987654q or q = .010125P
c. q =
.010125(1000) = 10.125
Profit = $4062.50
10. a. P = 5, Q = 6000
q = 500 Profit = 528
b. Entry. Because firms
are making economic profit. Entry
will equilibrium price to fall. Firm’s output will fall. Profits will fall to zero, no further entry.
c. P = $3.80
13. a. 100
b. No, P will be $1.50
c. 26
d. P = 2
e. $2
Answers to End-of-Chapter 9 Exercises
3. Japanese farmers would be
indifferent between the subsidy and the tariff because the increase in producer
surplus is the same under both policies.
The government may prefer the tariff because it does not require any
government spending.
5. a. If both demand
and supply are very elastic then the program could cost more than $50 million
per year. If both are relatively price
inelastic then it could cost less than $50 million per year.
b. If demand is perfectly inelastic then
the loss in consumer surplus will be exactly $50 million. Otherwise, it would cost less than $50
million per year.
6. a. Slope is rise over run
10-16/15-12 = -2
Constant, use point (15,10)
10 = constant - 2(15), or constant = 40
So QD = 40 -2P
Similarly, for supply function, slope is rise
over run (4-2)/(6-3) = 2/3
4 = constant + (2/3)(6),
or constant = 0
So QS = (2/3)P
b. Pw = 9
QS = 6 million pounds
QD = 22 million pounds
Imports = 22 – 6 = 16 million pounds
c. PUS = 9 + 3 = 12
QS = 8 million pounds
QD = 16 million pounds
Imports = 16 – 8 = 8 million pounds
Government collects 3(8) = $24 million
Deadweight loss = 0.5(12-9)(8-6) + 0.5(12-9)(22-16) = $12 million
d. With import quota of 8 million pounds, PUS
= 12
Cost to consumers is reduction in
consumer surplus = (12-9)(16) + (0.5)(12-9)(22-16) = $
57 million
Gain to producers is increase in
producer surplus = (12-9)(6) + (0.5)(8-6)(12-9) = $ 21
million
7. a. No tariff Price is 8 + 2 =
10. QD = 150
b. With tariff Price is 10 + 2 = 12. QD
= 130
c. (12-10)(130) +
0.5(12-10)(150-130) = $280 million
d. $2 (130) = $260
million
e. Net loss because the gain of $260
million is less than the loss of $280 million.
9. a. Fraction of tax borne by
consumers is ES/(ES – ED)
= 4/(4-(-0.2)) = 4/4.2 = 0.95
b. Demand for beer will increase. If supply of beer is infinitely elastic,
equilibrium price of beer will not change, and the quantity of beer consumed
will increase.
Answers to End-of-Chapter 10 Exercises
8. a. AR is the demand curve, P
= 700 – 5Q
MR = 700 – 10Q
MC1 = dC1/dQ1
= 20 Q1
MC2 = dC2/dQ2
= 40 Q2
Q = Q1 + Q2 = MC1/20
+ MC2/40 = 3MCT/40 or MCT = 40Q/3
Profit maximization occurs when MCT
= MR
b. 40Q/3 = 700 –
10Q, or Q = 30
MR = 700 – (10)(30)
= 400.
MC1 = 400 = 20Q1,
or Q1 = 20
MC2 = 400 = 40Q2,
or Q2 = 10
P = 700 – 5(30) = $550.
c. MC1 shifts left, causing MCT
to shift left, which will intersect MR curve at a lower total quantity and
higher MR. At a higher level of MR, Q2
is greater. Since QT falls
and Q2 rises, Q1 must fall. Since QT falls, P must rise.
9. Only MC2 is relevant
because the other MC lies above the demand curve. So demand curve is just P = 20 – 3Q2
MR then is equal to 20 – 6Q2
MR = MC2 means 20 – 6Q2
= 10 + 5Q2 or Q2 = 0.91.
Q1 = 0 Therefore P = 20 –
3(0.91) = $17.27.
12. a. SRMC = 5
P = 100Q-1/2
TR = PQ = 100Q1/2
MR = dTR/dQ = 50Q-1/2
Set SRMC = MR, or 5 = 50Q-1/2,
gives Q = 100, P = 100(100-1/2) = $10.
Profit = TR – SRTC = -$1500.
b. LRMC = 6
Following the same procedure as above,
we get Q = 69.44 to find P = 12
Profit = TR - LRTC = $833.33 – 416.66
= $416.67. The firm should remain in
business in the long run.
Answers to End-of-Chapter 11 Exercises
5. (i) MR1 = MC = 3, Q1 = 6
MR2 = MC = 3, Q2
= 5.5
P1 = 15 – 6 = $9
P2 = 25 – 2(5.5) = $14
Profit = 9(6) + 14(5.5) – [5 + 3
(11.5)] = $91.50
DWL1 = (0.5)(12-6)(9-3) = $18
DWL2 = (0.5)(11-5.5)(14-3) = $30.25
Total DWL = $48.25
(ii) P = 25 – 2Q if Q ≤ 5
18.33 – 0.67Q if Q > 5
MR = 25 – 4Q if Q ≤ 5
18.33 – 1.33Q if Q > 5
With MC = 3, 18.33 – 1.33Q is
relevant.
Equating MR and MC:
18.33 – 1.33Q = 3, or Q = 11.5
P = 18.33 – (0.67)(11.5)
= $10.67
With this price, Q1 = 4.33
and Q2 = 7.17
Profit is 10.67(11.5) – [5 + 3(11.5)]
= $83.21
DWL1 = (0.5)(12 – 4.33)(10.67 – 3) = $29.41
DWL2 = (0.5)(11 – 7.17)(10.67 – 3) = $14.69
Total DWL = $44.10
Answers to End-of-Chapter 12 Exercises
4. a. Firm 2’s reaction curve is:
Q2
= 24 – (Q1/2)
Firm
1 does not have a reaction function because it makes its output decision before
Firm 2, so there is nothing to react to.
b. Firm 1 chooses output Q1 to
maximize its profits subject to Firm 2’s reaction function:
Q1
= 24
Substituting
Q1 into Firm 2’s reaction function gives Q2
Q2
= 24 – (24/2) = 12
Substituting
Q1 and Q2 into the demand equation to find price
P
= 53 – 24 – 12 = $17
Profits
for each firm equal TR minus TC or:
Π1
= (17)(24) – (5)(24) = $288
Π2
= (17)(12) – (5)(12) = $144
Total
industry profit = $288 + $144 = $432
Compared
to Cournot equilibrium, total output has increased
from 32 to 36, price has fallen from $21 to $17, and total profits have fallen
from $512 to $432. Profits for Firm 1
have risen from $256 to $288, while Firm 2’s profits have declined sharply from
$256 to $144.
6. a. Q1 = Q2 = 80
P
= $140
Π1
= $6400 = Π2
b. Q = 120, P = $180, each will produce 60
units and profit for each firm is $7200.
c. If Firm 1 were the only firm, it would
produce the entire 120 units and earn a profit of $14,400.
d. Firm 2 cheats
by substituting Q1 = 60 into its reaction function:
Q2
= 120 – (60/2) = 90
Total
industry output is equal to Q1 + Q2 = 150
P
= 300 – 150 = $150
Π1
= (150)(60) – (60)(60) = $5400
Π2
= (150)(90) – (60)(90) = $8100
8. a. Texas Air’s reaction function:
Q1
= 30 – (Q2/2)
American’s
reaction function:
Q2
= 30 – (Q1/2)
Substituting:
Q1
= Q2 = 20
Q
= Q1 + Q2 = 40
P
= $60
Π1
= Π2 = $400
b. Texas Air’s reaction function:
Q1
= 37.5 – (Q2/2)
American’s
reaction function is same as before.
Q1
= 30, Q2 = 15
Q
= Q1 + Q2 = 45
Compared
to (a) equilibrium quantity has risen slightly.
c. P = 100- 30- 15 = $55
Texas
Air’s profits would be:
(55)(30)
– (25)(30) = $900
Difference
is $500. So Texas Air should be willing
to invest up to $500 to lower costs from 40 to 25 per unit.
Without
investment, American’s profits would be:
(55)(15)
– (40)(15) = $225
With
investment:
Q1
= 25 = Q2
P
= 100 – 50 = $50
American’s
profits are:
(50)(25)
– (25)(25) = $625
Difference
in profits for American is $400 so American would be willing to invest up to
$400 to reduce its MC to 25 if Texas Air also has MC of 25
10. a. q1 = q2 = 22.5
Q
= q1 + q2 = 45
P
= 300 – 3(45) = $165
Profit
for both firms will be equal:
Π
= $2278.13
b. Each firm should produce half the
quantity that maximizes industry profits (i.e. half the monopoly output). If they
have different cost functions, then it would not be optimal for them to split
the monopoly output evenly.
Joint
profits will be maximized at Q = 36.
Each firm will produce 18 and the optimal price to charge is P = 300 –
3(36) = $192
Profits
for each firm will be $2430.
c. We already know the profits if both
choose the Cournot output or both choose the cartel
output. If WW produces the Cournot output (22.5) and BBBS produces the collusive level
(18), then Q = 22.5 + 18 = 40.5, P = 300 – 3(40.5) = $178.50
Profit
for WW = $2581.88 and profit for BBBS = $2187
If
WW choose collusive output and BBBS chooses Cournot
output, profits will be reversed.
d. WW will use Stackelberg
strategy. WW’s profits will be: $2316.86
and BBBS’s profits will be $2067.24
Answers to End-of-Chapter 15 Exercises
1.
FV = $110 one year
from now
FV = $121 two
years from now
FV = $161.05
after five years
PDV = $90.91
one year from now
PDV = $82.64
two years from now
PDV = $62.09 five
years from now
4.
Find i such that
966
= (100)(1+i)-1 + (1100)(1+i)-2
Using the
quadratic formula to solve for i
i = 0.12 or -2.017
Since
negative interest rate does not make economic sense, the effective yield is 12
percent.
6.
a. PDV of $500 today is $500. The
present value of $540 next year is $514.29.
Should take $540 next year
b. If take $500 loan, can invest for 4 years and pay back
$500. Future value of $500 is 500(1.05)4
= $607.75
After paying back the loan you will have
$107.75 to keep. The future value of
$100 gift is 100(1.05)4 = $121.55.
Take $100 gift.
c.
Interest rate is 0 percent, which is 5 percent less than market rate. You save $400 = (0.05)($8000)
one year from now. PDV of this $400 is
$400/1.05 = $380.95, which is greater than $350. Take the financing.
d.
PDV = 50,000 + 50,000/1.05 + 50,000/(1.05)2
+ …+ 50,000/(1.05)19 = $654,266.04
e.
PDV of $60,000 perpetuity is $60,000/0.05 = $1,200,000. Take the $60,000 per year payment.
f.
Any gift of $N from parent to child could be made without taxation by lending
the child $N(1+r)/r.
To avoid taxes on $50,000 gift, parent would lend child $550,000,
assuming a 10
percent interest
rate. With that money child can earn
$55,000 in interest after one year and still have $500,000 to pay back to
parent. PV of $55,000 one year from now
is $50,000.
People of more moderate incomes find these
rules unfair because they might be able to give child $50,000 directly, but it
would not be tax free.
7. After
sixth year, Ralph’s income will be same with or without graduate education, so
we can ignore all income after first six years.
With graduate school, PV of income for next six years
-
$15,000/(1.1)1 - $15,000/(1.1)2
+ $60,000/(1.1)3 + $60,000/(1.1)4 +$60,000/(1.1)5
+$60,000/(1.1)6 = $131,150.35
Without
graduate school, PV for next six years is
$30,000/(1.1)1 + $30,000/(1.1)2 +
$30,000/(1.1)3 + $45,000/(1.1)4 + $45,000/(1.1)5
+ $45,000/(1.1)6 = $158,683.95
Payoff
from graduate school is not large enough to justify foregone income and tuition
expense while Ralph is in school.
11. a. NPV of buying car
is -20,000 + (12,000/(1.04)6) = -10,516.23
NPV of leasing is -3,600 – (3,600/(1.04)) - (3,600/(1.04)2) = -10,389.94
Better off leasing car
b. NPV of buying car
is -13,920.43
NPV of leasing is -9,684.18
Still better off leasing
car.
c. Indifferent if
NPV’s are equal or
-20,000 + (12,000/(1+r)6)
= -3,600 – (3,600/(1+r)) - (3,600/(1+r)2)
Solve for r. Easiest way is use spreadsheet
and calculate NPV’s for different values of r. Interest rate will be in neighborhood of
3.8%.
Answers to End-of-Chapter 14 Exercises
10. a. L = 64
b. q = 64
c. $4800
d.
L = 64, q = 64, profits = $3840
e.
L = 64, q = 64, profits = $3840