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EconS 301, Spring 2015, Microeconomics with Calculus
Professor Rosenman
Homework 10
1. Shortly after deregulation in 1979 major airlines found themselves in a price war. One airline
reduced its fares, and others followed. The effects were staggering; many airlines suffered large
losses in 1982 and the first half of 1983. Airline executives recognized that they could not
support the low prices, and raised them, so in October 1983 they were the highest since
deregulation. Profits improved. Yet in December of 1983 Continental Airlines tried to start
another fare war. For the most part the airlines stood firm, and did not match the fare decrease
this time. Explain which model(s) of oligopoly best explains this sort of pricing behavior. (4
points)
2. Moscow, in order to gain new revenues, recently imposed a sales tax on restaurants
(monopolistic competition). Alternatively, it could have used a franchise fee (a license) which
the business must pay it if it intends to continue operating in Moscow.
a. Contrast the impacts of each tax on the restaurants, including the effect on individual
firms and the number of firms in the market. Treat the sales tax as a per unit tax, and
the license fee as a fixed amount, payable no matter how much was sold. (2 points)
b. Do the same analysis if instead the taxes were applied to the two hardware stores in
Moscow (an oligopoly). (2 points)
3. The following 1990 data shows market share for automobile rentals in airports
Firm
Share
Hertz
.295
Avis
.252
Budget
.186
National
.163
Dollar
.052
Alamo
.023
Other
.029
a. Calculate the C4 and H for the industry, treating “Other” as one firm. (1
point)
b. Compute the number of equal sized firms that will give the values you
compute. (2 points)
c. If the market elasticity of demand for rental cars at airports is -2, calculate
the Lerner’s index for Avis and the weighted average market Lerner’s Index.
(2 points)
4. Wild bird food is dominated by a few large firms. One manager of a company claims that an
increase in the minimum wage will severely impact the company’s profits because the nature of
competition in the industry prevents it from raising price. Using the kinked-demand curve
model of oligopoly, defend or refute the manager’s argument. (3 points)
5. Hotelling’s Beach helps us understand competition between two ice cream firms, but is less
successful for understanding competition between more than two firms. Look at slide 14 from
the lecture. When the businesses are located at points A and B we found that the indifferent
consumer is at point x where Pi is the price charged at each location and ice cream melts at a
rate t(x-L)2 where L is location A or B. We solved for x to find
𝑥=
𝐵+𝐴
2
𝑃 −𝑃
𝐵
𝐴
+ 2𝑡(𝐵−𝐴)
.
The Hotelling model assumes firms are Bertrand, so each wants to maximize market share.
a. Start with two firms that have no costs of production. If firms can move their location
on the beach, explain why we should expect that not only do they locate next to each
other, but they should charge the same price. (1 points)
b. Suppose the firms are making a profit. Where would the new firm locate and how
would its price compare? Explain? (2 points)
c. If firms can change location easily, what would you expect to happen with the market
dynamics? Do you think there is an equilibrium? Why or why not? (2 points)
6. Smith and Jones are playing a gambling game. Each chooses a “1” or a “2” and they have the
payoffs shown below
Jones
Smith
1
2
1
J=4,S=1
J=3,S=2
2
J=2,S=-50
J=1,S=-25
a. Find the dominant strategy for each player. Given both have a dominant strategy,
where do they end up? Explain your answer. (2 points)
b. Is it a Nash equilibrium? Explain why or why not. (2 points)
XC1: A market has two firms which produce identical goods.. Both face constant marginal and average
cost. Firm 1 has MC1=AC1=10 and firms 2 has MC2=AC2=8. Market demand is given by Q=500-20P.
a. Suppose both firms follow Cournot behavior. Find the market price and each firm’s
output and profit. (HINT: Find the reaction functions first) (2 points)
b. Now suppose firm 1 is a Stackelberg leader and firm two is a follower. Find market price
and each firm’s output and profit. (3 points)
XC2: An extension of the Hotelling’s Beach model is the Salop Circle. Now customers are located on a
circle, rather than in a line. Firms again can choose where to locate. Suppose customers always go to
the closest seller.
a. Using a picture, argue that with two firms, wherever they locate each gets ½ of the business.
(2 points)
b. Now add a third firm. Figure out how they will locate. Explain and defend your answer. (2
points)
c. If firms on the circle are making profits we would expect entry. Suppose when the number
of firms is K profits become zero. How will these K firms locate on the circle? Explain your
answer. (1 point)