Page 591 - Microeconomics, Fourth Edition

c13marketstructureandcompetition.qxd 7/30/10 10:44 AM Page 565

PROBLEMS 565
from these stores typically live outside of town. Often, f ) What is the Bertrand equilibrium price in this market?
they will purchase from a store in the town closest to g) What are the Cournot equilibrium quantities and in-
them, but if farmers learn through word of mouth that dustry price when one firm has a marginal cost of 100 but
a feed retailer in a more distant town is selling feed the other firm has a marginal cost of 90?
at a lower price, they will sometimes go to that store to
obtain feed. 13.6. Zack and Andon compete in the peanut market.
The countrywide market shares of the largest feed Zack is very efficient at producing nuts, with a low
stores in Outer Baldonia are shown in the following marginal cost c Z 1; Andon, however, has a constant
table: marginal cost c A 10. If the market demand for nuts is
P 100 Q, find the Cournot equilibrium price and the
Firm Market Share quantity and profit level for each competitor.
Ben’s Feed and Supplies 2% 13.7. Let’s consider a market in which two firms com-
Joe’s Hog and Cattle Supply 1% pete as quantity setters, and the market demand curve is
Hogwarts 1% given by Q 4000 40P. Firm 1 has a constant marginal
Dave’s Livestock and Tools 0.50% cost equal to MC 1 20, while Firm 2 has a constant mar-
Ron’s Supply Shed 0.25% ginal cost equal to MC 2 40.
Eddie’s Feed Coop 0.25% a) Find each firm’s reaction function.
a) What is the 4CR concentration ratio for the livestock b) Find the Cournot equilibrium quantities and the
feed store market in Outer Baldonia? Cournot equilibrium price.
b) What is the HHI for this industry? 13.8. In a homogeneous products duopoly, each firm
c) Of the market structures described in Table 13.1, has a marginal cost curve MC 10 Q i , i 1, 2. The
which one best describes the livestock feed market in market demand curve is P 50 Q, where Q Q 1 Q 2 .
Outer Baldonia? a) What are the Cournot equilibrium quantities and
13.4. In the following, let the market demand curve be price in this market?
P 70 2Q, and assume all sellers can produce at a b) What would be the equilibrium price in this market if
constant marginal cost of c 10, with zero fixed costs. the two firms acted as a profit-maximizing cartel?
a) If the market is perfectly competitive, what is the c) What would be the equilibrium price in this market if
equilibrium price and quantity? firms acted as price-taking firms?
b) If the market is controlled by a monopolist, what is 13.9. Suppose that demand for cruise ship vacations is
the equilibrium price and quantity? How much profit given by P 1200 5Q, where Q is the total number of
does the monopolist earn?
passengers when the market price is P.
c) Now suppose that Amy and Beau compete as Cournot a) The market initially consists of only three sellers,
duopolists. What is the Cournot equilibrium price? Alpha Travel, Beta Worldwide, and Chi Cruiseline. Each
What is total market output, and how much profit does seller has the same marginal cost of $300 per passenger.
each seller earn?
Find the symmetric Cournot equilibrium price and output
13.5. A homogeneous products duopoly faces a for each seller.
market demand function given by P 300 3Q, where b) Now suppose that Beta Worldwide and Chi
Q Q 1 Q 2 . Both firms have a constant marginal cost Cruiseline announce their intention to merge into a single
MC 100. firm. They claim that their merger will allow them to
a) What is Firm 1’s profit-maximizing quantity, given achieve cost savings so that their marginal cost is less
that Firm 2 produces an output of 50 units per year? than $300 per passenger. Supposing that the merged
What is Firm 1’s profit-maximizing quantity when Firm firm, BetaChi, has a marginal cost of c $300, while
2 produces 20 units per year? Alpha Travel’s marginal cost remains at $300, for what
b) Derive the equation of each firm’s reaction curve and values of c would the merger raise consumer surplus
then graph these curves. relative to part (a)?
c) What is the Cournot equilibrium quantity per firm 13.10. A homogeneous products oligopoly consists of
and price in this market? four firms, each of which has a constant marginal cost
d) What would the equilibrium price in this market be if MC 5. The market demand curve is given by P 15 Q.
it were perfectly competitive? a) What are the Cournot equilibrium quantities and
e) What would the equilibrium price in this market be if price? Assuming that each firm has zero fixed costs, what
the two firms colluded to set the monopoly price? is the profit earned by each firm in equilibrium?