Economics 3551
Mansfield, et. al., 7e
Answers to assignments 9 and 10
Chapter 10
1. The Bergen Company and the Gutenberg Company are the only two firms that produce and sell a
particular kind of machinery. The demand curve for their product is
P = 580 - 3Q
where P is the price (in dollars) of the product, and Q is the total amount demanded. The total cost function
of the Bergen Company is
TCB = 410QB
where TCB is its total cost (in dollars) and QB is its output. The total cost function of the Gutenberg
Company is
TCG = 460QG
where TCG is its total cost (in dollars) and QG is its output.
a. If these two firms collude and they want to maximize their combined profit, how much will the Bergen
Company produce?
b. How much will the Gutenberg Company produce?
c. Will the Gutenberg Company agree to such an arrangement? Why or why not?
Solution:
a. Bergen’s marginal cost (410) is always less than Gutenberg’s marginal cost (460). Therefore Bergen
would produce all the combination’s output. Setting Bergen’s marginal cost equal to the marginal revenue
derived from the demand function (MRB = 580 – 6QB) yields
410 = 580 - 6QB so QB = 170/6 and QG = 0. Bergen’s price will be $495.00 and profit = $2,408.33
b. As discussed in part a, Gutenberg’s marginal cost is always greater than Bergen’s. If Gutenberg were to
produce 1 unit and Bergen 1 unit less, it would reduce their combined profits by the difference in their
marginal costs. If Gutenberg were to produce 1 unit without any reduction in Bergen’s output, it would
reduce their combined profits by the same amount.
c. If direct payments for output restrictions between the firms were legal, Gutenberg would accept the zero
output quota. But, if competition were to break out, Gutenberg would make zero profits and Bergen would
also earn $0 (since competition implies P = MC). Thus the most Bergen would pay for Gutenberg’s
cooperation is $2,408.32, and the least Gutenberg would accept to not produce is $.01.
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Economics 3551
Answers to assignments 9 and 10
2. The can industry is composed of two firms. Suppose that the demand curve for cans is
P = 100 - Q
where P is the price (in cents) of a can and Q is the quantity demanded of cans in millions per month.
Suppose the total cost function of each firm is
TC = 2 + 15q
where TC is total cost (in tens of thousands of dollars) per month and q is the quantity produced (in
millions) per month by the firm. (Note: there is some confusion about units. TC is in tens of thousands of
dollars per month. q is in millions of units per month. Suppose q = 1,000,000 so 15q = 15,000,000 cents.
That equals 150,000 dollars which translates to $15 x 10,000.
Thus total cost is 2 + 15 = $17 x 10,000 = $170,000. The units work, but it’s not immediately obvious.)
a. What are the price and output if managers set price equal to marginal cost?
b. What are the profit- maximizing price and output if the managers collude and act like a monopolist?
c. Do the managers make a higher combined profit if they collude than if they set price equal to marginal
cost? If so, how much higher is their combined profit?
Solution:
a. Since each firm has a constant marginal cost of $0.15, the price must also be $0.15 for price to equal
marginal cost. Since marginal cost equals price equals average variable cost in this case, each firm loses an
amount equal to their fixed costs, $20,000.
b. If they collude, they will produce where marginal revenue equals marginal cost. Marginal revenue is
given by MR = 100 - 2Q. Setting marginal revenue equal to marginal cost, the joint profit maximizing
combined output is Q = 42.5 and P = $57.50. Since the firms have constant marginal costs, only one firm
should operate; therefore they would avoid the fixed costs of the other firm. Their combined profits would
be
π = $57.50(42.5) - [2 + 15(42.5)] = $1,804.25, or $18,042,500. If they cannot avoid the fixed costs of one
of the firms by shutting it down, their combined profits would be $18,022,500.
c. Since they lose $40,000 if they compete and earn $18,022,500 if they collude, they earn $18,062,500
more if they collude than if they compete.
3. An oligopolistic industry selling a particular type of machine tool is composed of two firms. Managers at
the two firms set the same price and share the total market equally. The demand curve confronting each
firm (assuming that the other firm sets the same price) follows, as well as each firm’s total cost function.
P
Qd
Qs
TC
$10.00
5
5 $45.00
$9.00
6
6 $47.00
$8.00
7
7 $50.00
$7.00
8
8 $55.00
$6.00
9
9 $65.00
a. Assuming that each manager is correct in believing that managers at the other firm will charge the same
price as they do, what price should each charge?
b. Under the assumptions in part (a), what daily output rate should managers at each firm set?
Solution:
P
(1,000)
$10.00
$9.00
$8.00
$7.00
$6.00
Qd
Qs
5
6
7
8
9
5
6
7
8
9
TC
(1,000)
$45.00
$47.00
$50.00
$55.00
$65.00
MC
MR
$2.00
$3.00
$5.00
$10.00
$4.00
$2.00
$0.00
-$2.00
TR
$50.00
$54.00
$56.00
$56.00
$54.00
a. Each should charge a price of $9,000 since that is the last price for which MR > MC..
b. Each firm should produce 6 units.
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Economics 3551
Answers to assignments 9 and 10
9. In the 1960s Procter & Gamble recognized that disposable diapers could be made a mass- market
product and developed techniques to produce diapers at high speed and correspondingly low cost. The
result was that it dominated the market. According to Harvard’s Michael Porter, who made a careful study
of this industry, the following were some ways in which Procter & Gamble might have signaled other firms
to deter entry.
Tactic
1. Signal a commitment to defend
position in diapers through public
statements, comments to retailers, etc.
2. File a patent suit.
3. Announce planned capacity
expansion.
4. Announce a new generation of
diapers to be introduced in the future.
Cost to Procter
& Gamble
None
Legal fees
Cost to an Entrant
Raises expected cost of entry by increasing
probability and extent of retaliation.
Incurs legal fees plus the probability that P&G
wins the suit with subsequent cost to the
competitor.
Raises expected risk of price cutting and the
probability of P&G’s retaliation to entry.
Raises the expected cost of entry by forcing
entrant to bear possible product development
and changeover costs contingent on the
ultimate configuration of the new generation.
None
None
a. In considering these possible tactics, why should managers at Procter & Gamble be concerned about
their costs?
b. Why should managers be concerned with the costs to an entrant?
c. By the 1990s Procter & Gamble had to compete with high- quality, private- label diapers (as well as with
Kimberly- Clark, which successfully entered the market in the 1970s). In March, 1993 its Pampers brand
had about 30 percent of the market, and its Luvs brand had about 10 percent. The price of Luvs and
Pampers exceeded that of discount brands by over 30 percent. Should Procter & Gamble have cut its
prices?
d. In 1993 Procter & Gamble sued Paragon Trade Brands, a private-label producer, alleging infringement
of two patents. Are lawsuits of this kind part of the process of oligopolistic rivalry and struggle?
Solution:
a. Obviously, Procter & Gamble must be concerned with its own costs. If it adopts a tactic that is far more
costly to itself than to a potential entrant, it may cost more than it is worth.
b. The point of these tactics is to raise the cost to a potential entrant and thus discourage entry.
c. Whether Procter & Gamble should have cut its price depends on whether the discount brands (and
Kimberly-Clark, which has become a major rival) would cut their prices in response and by how much. In
fact, Procter & Gamble did reduce its price substantially (by 16 percent in the case of Luvs). According to
Edwin Artzt, chairman of Procter & Gamble, “We believe our profits are going to grow, because we’re
going to get volume back.”
d. Yes. Procter & Gamble wanted to reduce what it regarded as improper imitation of its technology. On
the other hand, firms that are sued often regard such suits as attempts to intimidate them.
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Economics 3551
Answers to assignments 9 and 10
12. Steve Win has purchased land from the city of Atlantic City in the Marina section. There are stories of a
new casino building boom in Atlantic City (MGeeM is also talking about entering, and Gump is opening
his fourth casino). Some talk is circulating that Win will subdivide his new land purchase and perhaps three
casinos will be built on the site.
Suppose Win subdivides his land into two parcels. He builds on one site and sells the other to another
gambling entrepreneur. Win estimates that the demand for gambling in the Marina area of Atlantic City
(after accounting for the presence of two existing casinos in the Marina and adjusting for the rest of the
casinos in Atlantic City) is
P = 750 - 5Q
where P is the price associated with gambling and Q is the quantity of gambling (think of P as the average
amount that a typical patron will net the casino, an amount paid for the entertainment of gambling, and Q as
the number of gamblers).
Win, of course, does not sell the other parcel until his casino is built (or is significantly far along); thus he
has a first- mover advantage. Win’s total cost (TCW) of producing gambling is
TCW = 20 + 40QW + 15.5QW2
where QW is the number of gamblers in Win’s casino, and the total cost (TCR) of producing gambling for
Win’s rival is
TCR = 10 + 50QR + 20QR2
where QR is the number of gamblers in the rival’s casino and
Q W + QR = Q
Would Atlantic City have done better to sell the land as two separate parcels rather than as a single parcel
to Win (given that Win was going to subdivide, Win and his rival could not collude, and Win did not have
the ability to produce as a monopolist)? You may assume that Win and his rival could have been Cournot
duopolists. If Atlantic City could do better, show why and by how much. Carry all calculations to the
thousandths decimal point.
Solution:
The monopoly solution for Win makes MR = 750 – 10QW = 40 + 31QW . Solving, Q =17.317 at
P =$663.42.
The last two questions involve the Cournot and Stackelberg models. I apologize for assigning them. The
answers are below and (if anyone cares) I will post the solution separately.
However, if Win and the rival produce as simultaneous-moving duopolists,
QW = 17.317 - 0.1220Qr
Qr = 14 - 0.1QW
Solving, QW = 15.80 and Qr = 12.42 for a total of Q = 28.22 and P = $608.90. If Win can act as a first
mover by selling the land parcel to the rival, QW = 16 and Qr = 12.4 for a total of Q = 28.40 and
P = $608.00.
The first-mover advantage is small in this case.
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Economics 3551
Answers to assignments 9 and 10
Chapter 11
1. Two soap producers, the Fortnum Company and the Maison Company, can
stress either newspapers or magazines in their forthcoming advertising campaigns.
The payoff matrix is as follows:
a. Is there a dominant strategy for each firm? If so, what is it?
b. What will be the profit of each firm?
c. Is this game an example of the prisoner’s dilemma?
Solution:
a. The dominant strategy for Maison is newspapers. The dominant strategy for Fortnum is magazines.
b. Maison’s profit will be $8 million. Fortnum’s profit will be $9 million.
c. This is not a prisoner’s dilemma game. The players do not end up with an outcome from which both
would be better off if they cooperated.
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Economics 3551
Answers to assignments 9 and 10
4. Two rival bookstores are trying to locate in one of two locations. The locations are near each other. Each
would like to avoid a bidding war because that will drive up both of their rents. Payoffs are given in the
following table:
Does either player have an incentive to bid higher for a location? If so, by how much?
Solution:
Neither store has a dominant strategy in this game. Therefore, they have no incentive to bid for a location.
When one firm makes a choice, the other firm’s best strategy is to choose the other location. BUT the
payoffs indicate that Location 1 is superior to location 2. Either firm would be willing to bid for that
location. In fact, Barnes & Noble (B&N) appears to be in a better position to exploit location 1. The total
payoff for B&N gets Location 1 and Borders gets Location 2 is 100, compared to 80 for the other Nash
equilibrium. B&N would be willing to pay Borders up to (60 – 25) = 35 to persuade Borders to select
Location 2.
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Economics 3551
Answers to assignments 9 and 10
5. Two soft drink producers, York Cola and Reno Cola, secretly collude to fix prices. Each firm must
decide whether to abide by the agreement or to cheat on it. The payoff matrix is as follows:
a. What strategy will each firm choose, and what will be each firm’s profit?
b. Does it matter whether this agreement is for one period or for three periods?
c. Is this game an example of the prisoner’s dilemma?
Solution:
a. Reno and York each have cheat as their dominant strategy, so they will each earn $28 million.
b. Since abiding by the agreement would raise their profits to $29 million each if this game were to be
played out an infinite number of times, the dominant strategy would be for both to abide if they thought
that a defection would be met with cheating by their opponents in all future rounds.
c. Yes, this is a prisoner’s dilemma since the firms are stuck in an outcome from which both could be made
better off by cooperation.
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