Answers to Even Problems for Waldman/Jensen 2nd Ed.
CHAPTER 2
2.
a.
SRMC = 2q + 30 = 50 =p
q
20
 10
2
It is not a long-run equilibrium because:
  TR  TC  (10  50)  (10 2  (30)(10)  400)
  500  (100  300  400)  300  0
b. Because the AVC=q+30, the short-run supply function is the SRMC curve
above the AVC curve, which is identical to the SRMC.
The short-run supply function is: S=2q+30
4.
a. MR=53-2Q
b.
MR  53  2Q  5  MC
48
Q
 24
2
P=53-24=29
c.
 =TR-TC=Q(P-AC)
=24(29)-24(5)=24(29-5)
=576
e. Perfectly Competitive Q=48
P= 5
h.
Monopoly Profits = 24(29-5)= 576
Consumer’s Surplus
= 288
Dead Weight Loss
= 288
Total = 1152
6. As indicated in Figure Problem 2.6, 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
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
The equilibrium with trade:
2
Demand = 100 - q = 25 + q = Supply
3
5
q = 75  q = 45
3
With trade, q=45, P=55.
Welfare changes to the United States as a result of free
trade are identified below.
Consumer surplus without trade was:
1
2
CS w/o trade = ( 37.5 ) = 703.125
2
Producer surplus without trade was:
1
2
PS w/o trade = (37.5 ) = 703.125
2
Without trade, CS + PS = 703.125 + 703.125 = 1406.25
Consumer surplus with trade is:
1
2
CS w/ trade = ( 45 ) = 1012.5
2
The domestic firms' producer surplus with trade is:
1
2
PS w/ trade = (30 ) = 450
2
With trade, CS + PS = 1012.5 + 450 = 1462.5
The net welfare gain to the United States from trade is:
1462.5 - 1406.25 = 56.25
CHAPTER 4
2.. a.. 4FCR=20+20+16+16=72
b.
HHI  20 2  20 2  16 2  16 2  9 2  8 2  6 2  5 2  1,518
4.
N
10,000
HHI
a.N 
10,000
 10
1,000
b.N 
10,000
8
1,250
c.N 
10,000
7
1,428
d .N 
10,000
4
2,500
The numbers equivalent tells us something about the meaning of a particular HHI
by informing us about how many equal size firms would “fit” in an industry with a given
HHI. Smaller values of N suggest less competition.
The numbers equivalent does not convey any information about the distribution of
market shares among firms.
6. DO NOT ASSIGN THIS PROBLEM UNLESS YOUR STUDENTS HAVE BEEN
INTRODUCED TO THE COURNOT-NASH EQUILIBRIUM WITH N FIRMS IN
A MICROECONOMICS COURSE. As we do on a number of occasions, we are
introducing a concept before we go through the material in depth later in the text
(chapter 7).
In this industry the perfectly competitive quantity is:
P = 200 - Q = 20 = MC
Q = 180 and P = 20
The Cournot-Nash equilibrium with linear demand, linear MC, and N=3 firms is:
QCN 
N
3
3
QPC = Q PC = 180 = 135
( N  1)
4
4
Therefore, p = 65
If two firms merge the Cournot-Nash equilibrium would be:
2
2
QCN = Q PC = 180 = 120
3
3
Therefore, p = 80
In Figure Problem 4.2, as a result of the merger, consumer surplus declines more
than profits increase, so economic welfare declines as a result of the merger.
Change in consumer surplus :
1
1
New CS - Old CS = (120)(120) - (135)(135) = 7200 - 9112.5 = -1912.5
2
2
Change in profits :
New Profits - Old Profits = 120(80 - 20) - 135(65 - 20) = 7200 - 6075 = 1125
The net change in consumer surplus plus profits is:
-1912.5+1125=-787.5
CHAPTER 6
2. The solution to the game is for Ben to “Enter” and Jerry to “Maintain Current Price.”
Perhaps Jerry could sign a contract with an independent lawyer stating that if Ben
entered, the lawyer would play “Aggressive if Entry.” Such a public contract might
deter entry.
CHAPTER 7
2. Note: Here we use the same concepts we introduced in chapter 4 problem
number 6, but now the concept of a Cournot-Nash equilibrium has been analyzed in
3
detail. With linear demand and linear marginal costs, the Cournot-Nash equilibrium is
4
of the perfectly competitive quantity, that is:
P  100  2Q pc  20  MC
Q pc 
80
 40
2
QCN 
3
(40)  30
4
For each firm, therefore, q1  q2  q3  10 .
4. The Bertrand equilibrium is identical to the competitive equilibrium.
P
1000
 20  MC
Q
Q
1000
 50
20
P
1000
 20
50
6. The Cournot-Nash equilibrium for the duopolists is obtained by finding the
intersection of the two reaction functions. Because of symmetry each firm has the same
reaction function. The American firm's reaction function is:
P = 100 - q J - qUS and MC US = 40
MRUS = (100 - q J ) - 2 qUS = 40
1
qUS = 30 - q J
2
By symmetry the Japanese firm's reaction function is:
1
q J = 30 - qUS
2
The Cournot-Nash equilibrium is:
1
1
1
1
qUS = 30 - q J = 30 - (30 - qUS ) = 15 + qUS
2
2
2
4
qUS =
15x4
= 20
3
By symmetry qJ=20 and total quantity q=40, and therefore, P=60.
a. With the tariff, the Japanese firm's reaction function changes to:
P = 100 - qUS - q J and MC J = 50
MR J = (100 - qUS ) - 2 q J = 50
1
q J = 25 - qUS
2
The American firm's Cournot-Nash output is then:
1
1
1
1
qUS = 30 - q J = 30 - (25 - qUS ) = 17.5 + qUS
2
2
2
4
qUS =
17.5x4
= 23.33
3
The Japanese firm's Cournot-Nash output is then:
1
1
q J = 25 - qUS = 25 - (23.33) = 25 - (11.67) = 13.33
2
2
b. Total output with the tariff is 23.33 + 13.33 = 36.66, and price P=63.34.
c. Before the tariff:
1
2
CS US = (40 ) = 800
2
 US = TR - TC = (20x60) - (250 + 20(40)) = 1200 - 1050 = 150
and CSUS + πUS = 800 + 150 = 950
After the tariff:
1
2
CSUS = (36.66 ) = 671.98
2
 US = TR - TC = (23.33x64.34) - [250 + 40(23.33)]
= (1501.05) - (1183.2) = 317.85
In addition, the government gains tax revenue equal to:
Tax Revenue = 10 x 13.33 = 133.33
CSUS + πUS + Tax Revenue = 671.98 + 317.85 + 133.33 = 1123.16
American welfare increases by 1123.16 - 950 = 173.16
CHAPTER 8
2. Neither Waldman or Jensen would ever defect.
4. It would be reasonably easy to maintain effective collusion in this case, because Firm
A would always prefer a high price.
Firm A appears to be the dominant firm in this industry.
High price is Firm A’s dominant solution.
Firm B does not have a dominant solution. Firm B should play “High Price” if
Firm A plays “High Price,” and Firm B should play “Low Price” if Firm A plays “Low
Price.”
CHAPTER 10
2. If  is “very small” (perhaps approaching zero), entry is virtually impossible and there
is no need to limit price.
If  is “very large,” limit pricing might be an attractive strategy if limit pricing
results in profits that are greater than zero. However, limit pricing would not be attractive
if profits equaled zero at the limit price.
Ceteris paribus, the higher the value of  , the greater is the likelihood of limit
pricing.
Of course even a high value of  would not result in a high probability of limit
pricing if there were very low profits to be earned at the limit price or if the firm had a
very high discount rate.
4. The Nash equilibrium E,{L, } is not a subgame perfect Nash equilibrium because it
requires that at the node DF1, the Dominant Firm would play limit price (L) if the
potential entrant stays out. But playing L is not a Nash equilibrium for the subgame
beginning at the node DF1.
6. To determine whether or not a pooling equilibrium exists, we must calculate the
expected value of IBM’s profits as follows:
 H  HI  (1   H ) LI  (.75)(75)  (.25)(300)  (56.25)  (75)  18.75  0
Because IBM’s expected profits are negative, a pooling equilibrium exists.
Regardless of whether Xerox has high costs or low costs, Xerox would charge the price it
prefers if it has low costs. Therefore, if Xerox has high costs, it would limit price in this
case.
8. a. As we saw in problem 6 above, a pooling equilibrium exists because:
 H  2H + (1 -  H ) 2L = 0.75(75) + 0.25(-300) = 56.25 - 75 = -18.75 < 0
Therefore, a high-cost monopolist would limit price and charge P=55, the optimal price
for a low-cost monopolist, in period 1.
b. A low-cost monopolist would charge its profit-maximizing price P=55 in period 1.
c. The high-cost monopolist limit prices in period 1 and charges its profit-maximizing
price in period 2, therefore, total profits for a high-cost monopolist would be:
 H = 45(55 - 25) +
37.5(62.5 - 25)
= 1,350 + 1,278.41 = 2,628.41
1.1
d. The low-cost monopolist charges its profit-maximizing price in period 1 and 2,
therefore, total profits for a low-cost monopolist would be:
 L = 45(55 - 10) +
45(55 - 10)
= 2,025 + 1,840.91 = 3,865.91
1.1
CHAPTER 11
2. The current solution is for the potential entrant to enter and the dominant firm to SR
profit maximize.
The incumbent would have to spend an amount on advertising greater than 250 to
prevent entry.
The new solution would be for the potential entrant to stay out and the dominant
firm to maximize profits. The dominant firm would earn a profit of just under 2,250,
which equals 2,500 minus the amount the dominant firm spends on advertising.
3. If the fixed costs of production of sickeningly sweet corn flakes were $225 instead of
$75, Big G would not enter the sickeningly sweet corn flakes market when demand
tripled because equation A1 would become:
18.75 225
= 187.5 - 204.5 = -17 < 0
.10 (1.1)1
 Gpv3d =
Because profits are negative with the higher fixed costs, Big G would stay out of the
market and there would be no need to use product proliferation to deter entry.
CHAPTER 12
2. Suppose there are three trucks, A, B, and C. Start with all three at the middle of the 10
mile stretch, i.e. at the 5-mile mark. Currently they each earn 33.3% of the profits.
If Truck A moves a “very small distance”  to the right or left of the 5-mile mark
it can capture 50% of the profits, leaving Trucks B and C to share the other 50%.
Suppose Truck A moved to the right, then both Trucks B and C have an incentive to
move a “very small distance”  to the left of the 5-mile mark. Suppose Truck B moves ”
 to the left of center. We now have A slightly right of center, B slightly left of center,
and C stuck earning almost nothing in the center.
Now Truck C has an incentive to move a “very small distance”  to the right of
A or the left of B. This shifting can go on indefinitely. Using such reasoning it is clear
that at no time will all three trucks be doing the best they can given the choices of the
other trucks. Therefore, there is no Nash equilibrium with 3 trucks.
1
4. a. The new introductory demand curve would be: P=(100-Q)(1-.75)=25- Q .
4
b. In Figure Problem 12.4, the new introductory demand curve would be the heavy
kinked line CBAE.
c. For informed consumers, the maximum amount they would pay to try the second
1
mover’s product is: P=(100-Q)(1-.75)=25- Q -S. The line OA traces out the maximum
4
amount each informed consumer would pay to try the second mover’s product. Note: The
second mover would have to pay the first consume approximately 25 to try the product.
37.5
3
Q  25  Q . Subtracting the line OA
Mathematically, the line OA is: P=-25+
50
4
from the line AE, the demand curve for the second mover is:
12.5
q =12.5-0.187q.
P=12.566.7
The highest price the second mover can charge to obtain any consumers is just under
12.5.
d. Yes. The increase in the risk-cost actor has substantially reduced the demand curve
faced by the second mover, thus making it even more difficult to enter.
CHAPTER 13
2. Before the cost-saving invention the monopolist’s profits were:
Demand was: P=50-q; so MR=50-2q.
To maximize profits set MR=MC:
MR=50-2q=25; so q=12.5 and P=50-12.5=37.5
Profits then are:
 M  TR  TC  Pq  ( LRAC )q  (37.5)(12.5)  (25)(12.5)  (468.75)  (312.5)  156.75
With the introduction of the cost-saving device the monopolist’s profits would be
calculated as follows:
MR=50-2q=20; so q=15 and P=50-15=35
Profits are then:
 M  TR  TC  Pq  ( LRAC )q  (35)(15)  (20)(15)  525  300  225
Profits for the monopolist increase by (225-156.75)=68.75 as a result of the
introduction of the cost-saving device.
If the industry were perfectly competitive patent holder could license the devise
for a royalty payment, R of 5 per unit. Price would remain at 25 and quantity sold would
remain at 25, but the patent holder could earn a total royalty of:
Royalty=qR=25(5)=125.
The patent holder has a greater incentive to introduce the device because the
patent holder can earn 125 compared to the monopolist’s increase in profits of only
68.75.5
CHAPTER 14
2. Note: We are ignoring the impact of fixed costs on profits in calculating the optimal
pricing policy.
Without discrimination the optimal policy would be to charge $1,000 for an
unrestricted ticket and sell one ticket. This yields a profit of
 w / o  $1,000  mc  $1,000  $100  $900
Compared to a profit with discrimination of:
 w /  ($1,000  $250)  $200  $1,250  $200  $1,050
The airline should discriminate and charge $1,000 for an unrestricted ticket and
$250 for a ticket with a two-week minimum stay. This yields total surplus of:
CS +  = $0 + $1,050= $1,050
Let’s make the same calculations with the new demand conditions.
Without discrimination the optimal policy would be to charge $650 for an
unrestricted ticket and sell two tickets. This yields a profit of
 w / o  $1,300  $200  $1,100
Compared to a profit with discrimination of:
 w /  ($1,000  $250)  $200  $1,250  $200  $1,050
Now to maximize profits the airline should not discriminate, but charge all
passengers $650 for an unrestricted ticket. This yields total surplus of:
CS +  = $350 + $1,100= $1,450
In this case, welfare is greater without discrimination.
4.
If discrimination is possible, the profit maximizing policy is to charge a price per
unit price equal to marginal cost of 10 and charge a fixed fee of 4050 to consumer 1 and a
fixed fee of 800 to consumer 2. Total profits would then be 4050+800=4850.
6.
The situation is depicted in Figure Problem 14.6 above. In this case, the monopolist
should charge a per copy fee equal to 20 and a fixed fee equal to 1600 to each consumer.
The fixed fee equals the consumer surplus for the low demand Type B consumer if the
per copy charge is 20. Profits then equal:
 =2(fixed fee)+ p(q A  qB ) -2(fixed costs)
=2(1600)+20(80+40)-2(500)
=(3200)+(2400)-(1000)=4600
Using a two-part tariff still increases profits. In this case from 4500 to 4600
despite the dramatic reduction in the monthly rental fee from 5000 to 1600. The price
ceiling, however, reduces profits for the monopolist from 4625 to 4600.
CHAPTER 15
2.
In the figure above, with bilateral monopoly (a monopolist wholesaler and a
monopolist retailer) the price to the consumer would be 80 and 20 units would be sold.
1
Consumer surplus would equal the small triangle A, which equals (20)( 20)  200 .
2
Producer surplus would be 20(80-20)=1200. Total surplus would equal 1400.
After a merger, the price would decline to 60 and quantity would increase to 40.
Consumer surplus would increase to the sum of the three areas A+B+C, which equals
1
(40)( 40)  800 . Producer surplus now equals 40(60-20)=1600. Total surplus is now
2
2400.
There is a gain of total surplus of 1000.
4.
It does not matter whether the tax is placed on the monopolist manufacturer or the
competitive retailers.
In the figure above, we’ve presented both ways of viewing the tax. If the
tax is placed on the monopolist manufacturer, it increases marginal cost from MC to
MCtax, where MCtax=MC+$1.00, but the demand curve and MR curves remain at D
and MR. The result is that quantity declines to qtax and price increases from P to Ptax.
If the tax is placed on the competitive retailers, it does not affect MC for
the monopolist, but reduces the demand curve to Dtax and the marginal revenue curve
to MRtax. Note that Dtax lies everywhere exactly $1.00 below the original demand
curve D. The new marginal revenue curve intersect the MC curve at qtax, so output is
the same in both cases.
We can use algebra to prove the same result. Consider any linear demand curve
P=a-Q and constant marginal cost curve, mc. A tax placed on the monopolist increases
marginal cost to mc+ 1. With P=a-Q; MR=a-2Q, so MR=MC implies:
MR=a-2Q=mc+1
2Q = a-(mc+1)=a-1-mc
(a  1)  mc
Q
2
A tax on the retailers leaves marginal cost constant at mc, but changes demand to
P=(a-1)-Q. Marginal revenue is then MR=(a-1)-2Q; so MR=MC implies:
MR=(a-1)-2Q=mc
2Q = a-(mc+1)=a-1-mc
(a  1)  mc
Q
2
The resulting output is the same regardless of who actually pays the tax.
CHAPTER 20
2.
The situation is shown above.
The price structure is allocatively efficient because Q=90. The last unit sold is
sold at marginal cost.
Profits are the sum of the two shaded rectangles. The average cost of producing
1800
 10  20  10  30 . For the first 60 units sold at p=40, profits are
each unit is AC=
90
positive and equal 60(p-AC)=60(40-30)=60(10)=600. For the next 30 units sold at p=10,
profits are negative and equal 30(p-AC)=30(10-30)=30(-20)=-600. The sum the two areas
equals (+600)+(-600)=0. So total profits are normal.