(Industrial Organization Theory and Practice, 4e Don Waldman, Elizabeth Jensen)
(Solution Manual all Chapters)
Solutions to Even Numbered Problems
Chapter 2
Problem 2:
a. S = 1.196. There are a number of ways to calculate S. The easiest is to use the formula
S = AC(q)/MC(q). Doing so, gives you S = 256/214 = 1.196. Similarly, using the
elasticity formula from Application 2.6, you get (1/8)/(214/2048) = .125/.1045 = 1.196.
b. The firm is experiencing economies of scale. The value of S is greater than one. Also,
the AC falls from 262 to 256 while q increases from 7 to 8.
c. The value of S can be interpreted to read that for every one percentage increase in
costs, output will increase by 1.196 percent.
Problem 4:
a. The production of shampoo exhibits economies of scale up until 2 units of output.
After that, the production of shampoo exhibits diseconomies of scale. There are two ways
to see this. One way is to simply graph AC for different values of q. For example,
qS AC
1 5
2 4
4 5
8 8.5
You can see that at first, AC falls as q increases from 1 to 2, but then AC increases after
that. Another way is more mathematical. If you set AC= 4/qs +qs equal to MC = 2qs, you
will find that when AC=MC, qs=2. This implies, that AC is at a minimum when qs=2.
(Also, finding the first derivative of AC and setting it equal to zero gives the same
outcome.)
b. Yes, it does exhibit economies of scale. For example,
qT AC
1 5
4 1.5
9 .778
16 .5
100 .14
As q increase, AC falls.
c. Yes. No matter what combination, it will always be $1 less expensive to make the
products. Notice that C(qs,qT) is $1 less than C(qs,0) + C(0,qT). Note as the quantities
become larger, this $1 difference, as a percentage of total costs, becomes somewhat
trivial.
Chapter 2
Page 1
, Waldman/Jensen – Industrial Organization Theory and Practice, Fourth Edition
Solutions to Even Numbered Problems
Chapter 3
Problem 2:
a. The firm sets P = MC. 50 = 2q+30; q=10. Because we only are given one of many
SRTC functions, we don’t know the LRTC function, and therefore, we cannot determine
the LR equilibrium price. It’s probably not $50, but we can’t know for sure what it is
from the information given in this question.
b. The short-run supply function is simply the MC curve above minimum AVC. AVC =
q+30. This curve hits a minimum when q=0. Thus, the firm’s short-run supply function is
simply: P = 2q + 30.
Problem 4:
a. Firm sets P = MC. 2q=60; q = 30
b. Profits = TR – TC = 60*30 – (302 +100) = 1800 – 1000 = 800
c. Short-run supply is MC above minimum AVC. In this case, P = 2q
d. The industry supply curve is calculated by summing each individual firm’s short-run
supply curve. qi = P/2. Q = 100 (P/2) = 50P. The formula for the industry supply curve
is: P = Q/50.
Problem 6:
a. Set QD = QS. 100 – P = -50 + 2P; 3P = 150; Pe = 50; Qe = 50
b. Consumer Surplus = ½ (100-50)*50 = 1250
Producer Surplus = ½ (50-25) * 50 = 625
Problem 8:
a. MR = 55 – 4Q
b. set MR = MC; 55 – 4Q = 2Q – 5; Q = 10; P = 55 – 2(10) = 35
c. Profits = 35(10) – [102 – 5(10) + 100] = 350 – 150 = 200
d. Consumer Surplus is shown graphically in Figure 3A.1 as triangle area ABC
Consumer Surplus = ½ (55-35) (10) = 100
e. P = MC; 55-2Q = 2Q – 5; Q = 15; P = 25
f. Profits under perfect competition = 25(15) – [152 – 5(15) +100] = 375 – 250 = 125
Consumer Surplus under perfect competition is shown graphically in Figure 3A.1 as
triangle area AEG. Consumer Surplus = ½ (55-25) *15 = 225
Chapter 3
Page 2
, Waldman/Jensen – Industrial Organization Theory and Practice, Fourth Edition
Solutions to Even Numbered Problems
g. Deadweight Loss is shown graphically in Figure 3A.1 as the triangle BEF.
Deadweight Loss = ½ (35-15) * (15-10) =50
FIGURE 3A.1
Problem 10:
As indicated in Figure Problem 3A.2, without trade the equilibrium price and quantity
are:
Demand = 100 - qUS = 25 + qUS = Supply
solving for qUS yields qUS = 37.5
P=100-qUS=62.5
Chapter 3
Page 3
, Waldman/Jensen – Industrial Organization Theory and Practice, Fourth Edition
Solutions to Even Numbered Problems
Figure 3A.2
With trade the total supply curve is the sum of the US supply and the foreign
supply in the United States:
1
qUS = P - 25 and q f = P - 12.5
2
1 3
⇒ qtotal = qUS + q f = (P - 25) + ( P - 12.5) = P - 37.5
2 2
3 2
⇒ P = 37.5 + qtotal ⇒ P = 25 + qtotal
2 3
Chapter 3
Page 4
(Solution Manual all Chapters)
Solutions to Even Numbered Problems
Chapter 2
Problem 2:
a. S = 1.196. There are a number of ways to calculate S. The easiest is to use the formula
S = AC(q)/MC(q). Doing so, gives you S = 256/214 = 1.196. Similarly, using the
elasticity formula from Application 2.6, you get (1/8)/(214/2048) = .125/.1045 = 1.196.
b. The firm is experiencing economies of scale. The value of S is greater than one. Also,
the AC falls from 262 to 256 while q increases from 7 to 8.
c. The value of S can be interpreted to read that for every one percentage increase in
costs, output will increase by 1.196 percent.
Problem 4:
a. The production of shampoo exhibits economies of scale up until 2 units of output.
After that, the production of shampoo exhibits diseconomies of scale. There are two ways
to see this. One way is to simply graph AC for different values of q. For example,
qS AC
1 5
2 4
4 5
8 8.5
You can see that at first, AC falls as q increases from 1 to 2, but then AC increases after
that. Another way is more mathematical. If you set AC= 4/qs +qs equal to MC = 2qs, you
will find that when AC=MC, qs=2. This implies, that AC is at a minimum when qs=2.
(Also, finding the first derivative of AC and setting it equal to zero gives the same
outcome.)
b. Yes, it does exhibit economies of scale. For example,
qT AC
1 5
4 1.5
9 .778
16 .5
100 .14
As q increase, AC falls.
c. Yes. No matter what combination, it will always be $1 less expensive to make the
products. Notice that C(qs,qT) is $1 less than C(qs,0) + C(0,qT). Note as the quantities
become larger, this $1 difference, as a percentage of total costs, becomes somewhat
trivial.
Chapter 2
Page 1
, Waldman/Jensen – Industrial Organization Theory and Practice, Fourth Edition
Solutions to Even Numbered Problems
Chapter 3
Problem 2:
a. The firm sets P = MC. 50 = 2q+30; q=10. Because we only are given one of many
SRTC functions, we don’t know the LRTC function, and therefore, we cannot determine
the LR equilibrium price. It’s probably not $50, but we can’t know for sure what it is
from the information given in this question.
b. The short-run supply function is simply the MC curve above minimum AVC. AVC =
q+30. This curve hits a minimum when q=0. Thus, the firm’s short-run supply function is
simply: P = 2q + 30.
Problem 4:
a. Firm sets P = MC. 2q=60; q = 30
b. Profits = TR – TC = 60*30 – (302 +100) = 1800 – 1000 = 800
c. Short-run supply is MC above minimum AVC. In this case, P = 2q
d. The industry supply curve is calculated by summing each individual firm’s short-run
supply curve. qi = P/2. Q = 100 (P/2) = 50P. The formula for the industry supply curve
is: P = Q/50.
Problem 6:
a. Set QD = QS. 100 – P = -50 + 2P; 3P = 150; Pe = 50; Qe = 50
b. Consumer Surplus = ½ (100-50)*50 = 1250
Producer Surplus = ½ (50-25) * 50 = 625
Problem 8:
a. MR = 55 – 4Q
b. set MR = MC; 55 – 4Q = 2Q – 5; Q = 10; P = 55 – 2(10) = 35
c. Profits = 35(10) – [102 – 5(10) + 100] = 350 – 150 = 200
d. Consumer Surplus is shown graphically in Figure 3A.1 as triangle area ABC
Consumer Surplus = ½ (55-35) (10) = 100
e. P = MC; 55-2Q = 2Q – 5; Q = 15; P = 25
f. Profits under perfect competition = 25(15) – [152 – 5(15) +100] = 375 – 250 = 125
Consumer Surplus under perfect competition is shown graphically in Figure 3A.1 as
triangle area AEG. Consumer Surplus = ½ (55-25) *15 = 225
Chapter 3
Page 2
, Waldman/Jensen – Industrial Organization Theory and Practice, Fourth Edition
Solutions to Even Numbered Problems
g. Deadweight Loss is shown graphically in Figure 3A.1 as the triangle BEF.
Deadweight Loss = ½ (35-15) * (15-10) =50
FIGURE 3A.1
Problem 10:
As indicated in Figure Problem 3A.2, without trade the equilibrium price and quantity
are:
Demand = 100 - qUS = 25 + qUS = Supply
solving for qUS yields qUS = 37.5
P=100-qUS=62.5
Chapter 3
Page 3
, Waldman/Jensen – Industrial Organization Theory and Practice, Fourth Edition
Solutions to Even Numbered Problems
Figure 3A.2
With trade the total supply curve is the sum of the US supply and the foreign
supply in the United States:
1
qUS = P - 25 and q f = P - 12.5
2
1 3
⇒ qtotal = qUS + q f = (P - 25) + ( P - 12.5) = P - 37.5
2 2
3 2
⇒ P = 37.5 + qtotal ⇒ P = 25 + qtotal
2 3
Chapter 3
Page 4
