Homework 3
Managerial Economics
Due: May 6
1.In 2004, U.S. consumer products manufacturers distributed 27.548 billion coupons,
with a face value of over $280 billion, of which a mere 1.2% were redeemed by
consumers. Why do manufacturers spend millions of dollars to distribute coupons
when the redemption rate is so low? Why don’t they manufacturers directly cut the
wholesale prices of the products, which would be much cheaper to administer?
(A)Some say that retailers would absorb a direct wholesale price cut instead of
passing it on to consumers. They argue that, by contrast, retailers cannot absorb the
value of coupons. Suppose that the retail sector is perfectly competitive. Compare
the demand-supply equilibrium in the retail market with (i) a wholesale price cut of
50 cents and (ii) widespread distribution of 50-cent coupons. For this part, you
may assume that all consumers use coupons.
(B) Would there be any difference between the wholesale price cut and using
coupons if the retailer were a monopoly?
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2.For many years, the NBA had a monopoly over basketball and, consequently,
monopsonized the market for players. This monopsony over players began to erode in
1967 with the formation of the ABA. Finally, in 1983, basketball team owners agreed
to allow free agency, which removed the restrictions against players moving between
teams. An analysis of earnings showed that a player who scored 10% more points
would have earned 2.05% more salary between 1968 and 1975, but 3.21% more
salary between 1984 and 1988.
(A)Explain the connection between having a monopoly over basketball and a
monopsony over basketball players.
(B)Compare the wage rate when the demand side of the market is a monopsony with
the perfectly competitive wage.
(C)Explain the differences in player earnings between 1968-75 as compared with
1984-88.
(D)When the ABA and NBA proposed to merge, the basketball players opposed the
proposal. Explain why.
(A) The only seller of basketball games is the only buyer for basketball players.
(B)
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wage
ME
S
WC
Wm
comparative
monopsony
Qm
MB
players
QC
(C)1968-75: Monoposony; 1984-88: More competitive. Therefore, the player earnings
were higher between 1984-88.
(D) When both merge, the basketball player's earnings may decrease.
3.Hong Kong Director-General of Telecommunications Anthony Wong expressed
concern about the effect of license auctions on the price of telecommunications:
“There’s good and bad in auctioning off spectrum … it may raise costs for telecoms
providers” (“Telecoms chief sees further fall in long-distance tariffs”, South China
Morning Post, December 31, 1999, Business 1.)
(A)Typically, licenses are transferable, but the one-time license fee, once paid, is not
refundable. From an operational standpoint, how does the cost of a license depend
on the price, if any, that the owner paid for it?
(B)How does the one-time license fee affect the marginal cost of providing
telecommunications service? How does it affect the profit-maximizing scale of
operations?
(C)Suppose that the one-time license fee is changed to an annual charge based on the
telecommunications provider’s revenue. How would the new policy affect the
service provider’s profit-maximizing scale of operations?
Answer
(A) The cost of a license depends on the prevailing market price of licenses,
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which may have little or no relation to the price that the owner paid for
it at an earlier time.
(B) The one-time license fee is a fixed cost with respect to the scale of
operations and does not affect the marginal cost. Hence it does not
affect the profit-maximizing scale of operations.
(C)The annual charge based on the telecommunications provider’s revenue would
raise the provider’s marginal cost, and hence reduce the profit-maximizing scale.
4.Suppose that Iron Music has the copyright to the latest CD of the heavy Iron band.
The market demand curve for the CD is Q=800-100P, where Q represents quantity
demanded in thousands and P represents the price in dollars. Production requires a
fixed cost of $100,000 and a constant marginal cost of $2 per unit.
(A)What price will maximize profits?
(B)At that price, how will be the sales?
(C)What is the maximum profit?
(D)Calculate the Lerner Index at the profit-maximizing scale of production.
(E)Suppose that the fixed cost rises to $200,000. How would this affect the
profit-maximizing price?
Answer
(a) Since demand, Q = 800 - 100p, the price is p = 8 - Q/100.
Hence, total revenue,
R(Q) = pQ = (8 - Q/100) Q = 8Q - Q2/100.
Differentiating, the marginal revenue is
8 - Q/50.
Since the marginal cost is $2, by equating marginal revenue with marginal
cost, we have
8 - Q/50 = 2,
which implies that, at the profit maximum,
Q = 6 x 50 = 300.
By the demand equation, the profit-maximizing price is 8 - 300/100
= $5 per unit.
(b) At the profit-maximizing price of $5 per unit, Q = 300. The question
states that Q represents the quantity demanded in thousands, hence the
profit-maximizing sales is 300,000 units.
(c) The maximum profit is R(Q) - 100,000 - (Q x 2) = (5 x 300,000) 100,000 - (2 x 300,000) = $800,000.
(d) At the profit-maximizing scale, the Lerner Index is (p - 2)/p = 3/5 =
5
0.6.
(e) The increase in fixed cost would not affect the profit-maximizing price.
5.Referring to the following figure, suppose that Mercury Airlines’ marginal revenue
and demand curves cross the marginal cost curve at quantities of 3,000 and 6,000
seats a week, respectively. All other data remain the same.
(A)Calculate the profit under policies of (i) uniform pricing, and (ii) complete price
discrimination.
(B)Suppose that Mercury implements complete price discrimination. Explain why it
should sell up to the quantity where the buyer’s marginal benefit equals Mercury’s
marginal cost.
(C)Explain why Mercury’s profit is higher with complete price discrimination than
with uniform pricing.
4000
p
800
0
3000
quantity (seats per week)
6
6000
Answer:
(i) Under uniform pricing, the profit-maximizing quantity is where
MR=MC or Q=3000. Referring to the figure, at that Q, the price p
on the demand curve must be halfway between 800 and 4000.
Hence, p = 2400, and profit = (2400 – 800) x 3000 = 4.8 million
dirhams a week.
(ii) Under complete price discrimination, the seller should sell the
quantity where MB = MC. Referring to the Figure, that quantity is
Q = 6000. Then, total revenue is the area under the demand
curve up to Q = 6000, hence TR = [(4000 + 800)/2] x 6000 = 14.4
million dirhams a week. Now total cost, TC = 800 x 6000 = 4.8
million dirhams, hence the profit = 14.4 – 4.8 = 9.6 million dirhams a week.
(b) Mercury maximizes its profit by producing the quantity where the buyer’s
marginal benefit equals Mercury’s marginal cost. If it sold a larger
quantity, so that the marginal benefit is less than the marginal cost, then
its profit would be lower. By contrast, if it sold a smaller quantity, it could increase
profit by selling more.
(c) Complete price discrimination yields more profit than uniform pricing
because it extracts a higher price from existing buyers and extends sales to new
buyers who would not be served under uniform pricing.
6.The National Collegiate Athletic Association(NCAA) restricts the amount that
colleges and universities may pay their student athletes. Suppose that there are just
two colleges in the NCAA: Ivy and State. Each must choose between paying athletes
according to NCAA rules and paying more. If both Ivy and State follow the NCAA
salaries, then each would earn $3 million. If one follows the NCAA salaries and the
other pays more than NCAA salaries, then the college paying more can attract better
players and would earn $5 million, while the college following NCAA would earn just
$1 million. If both colleges pay more than NCAA salaries, they would increase their
costs but not get better players, so both would earn 2 million.
(A) Construct a game in strategic form to analyze the choices of Ivy and State, and
identify the equilibrium/equilibria?
(B)With government backing, the NCAA can punish colleges that pay more than the
NCAA permitted salaries. How would this affect the equilibrium/equilibria?
(C)Which of the following concepts best describes the NCAA rules on player
salaries:(i) monopoly;(ii) monopsony;(iii) economies of scale;(iv) economies of scope.
Explain your answer.
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Answer:
(a) The key to this question is constructing the game in strategic form. The
NCAA functions as a buyer cartel in the market for college athletes. If both
Ivy and State pay according to NCAA rules, then they succeed as a cartel –
they receive 3 each. If Ivy breaks the cartel and pays more, while State
keeps to the cartel, then Ivy will benefit and State will lose – Ivy gets 4, and
State gets 1. Similarly, if Ivy keeps to the cartel and State breaks it, Ivy gets
1 and State gets 4. Finally, if they both pay more, then both will be worse
off – each receives 2.
State College
Ivy College
Pay by NCAA
Pay by NCAA rule
Pay more
I: 3,
I: 1,
S: 3
S: 4
Pay more
I: 4,
I: 2,
S: 1
S: 2
(b) The Nash equilibrium is both colleges will pay more than the NCAA allows.
(c) If the NCAA has government backing, then both colleges will follow the
NCAA recruiting rules, and achieve the highest combined profit.
7.Dial-up Internet users need modems to convert digital data into analog signals and
Internet access providers (IAPs) need matching modems to convert the analog signals
back to digital data. In the mid-1990s, the dominant standard for modems was the
V.34, providing a speed of 28.8 or 36.6 kilobits per second (kbps). In Autumn 1996,
two incompatible technologies for 56 kbps modems – Rockwell’s K56Flex and U.S.
Robotics’s X2 -- were launched.
(A)Construct the following game in strategic form. End-users choose among the
three alternatives of buying K56Flex, buying X2, or remaining with the old
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technology, while IAPs have the same choice. If both end-users and IAPs choose
K56Flex, each group receives a net benefit of 100, and similarly, if both groups
choose X2. If end-users or IAPs buy K56Flex or X2, while the other does not buy
the matching technology, the buyer receives a net benefit of –50. Anyone that
remains with the old technology receives 0. Identify the equilibrium/equilibria in
pure strategies.
(B)In February 1998, Rockwell and U.S. Robotics agreed on a common V.90
standard. How did this affect the game and its equilibrium/equilibria?
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