Econ-UA 353 HW #3

Econ-UA 353 HW #3
Due at the beginning of class on Monday Dec 8
Late homeworks will NOT be accepted
Question 1. Firm A is the sole producer of a sport drink.
A’s marginal cost
equals average cost MC = AC = 30, and it faces market demand
given by
inverse demand function P = 120 ? 0.5Q.
(a) Suppose A produces quantity q = 120 units at price p =
60. Is there any
dead weight loss at current price and quantity? If yes, how
much is the DWL?
(b) What is the monopoly price? What is the monopoly DWL?
Question 2. The inverse market demand for mineral water is P
= 200 ? 10Q,
where Q is total market output and P is the market price.
Two firms have
complete control of the supply of mineral water and both
have zero costs.
(a) Find the Cournot quantity, price, and each firm’s
profit.
(b) Denote the Cournot quantity for each firm by qa, and
denote half of the
monopoly quantity by qb. Suppose that the two firms interact
with each other
for infinite periods, and in each period they choose
quantities simultaneously.
Consider the following collusive strategy, the same as
discussed in class: produce
qb only if no one has cheated so far, and to produce qa
forever if some
has cheated before. Assume each firm acts to maximize its
sum of discounted
profits where the interest rate is r. Find the values for r
such that this collusive
strategy is a Nash equilibrium, namely, for what values of r
can the monopoly
profits be sustained through collusion?
(c) Find the Bertrand price, quantity, and each firm’s
profit.
(d) Denote the Bertrand price by pa, and denote the monopoly
price by pb.
Suppose that the two firms interact with each other for
infinite periods, and
in each period they set prices simultaneously. Consider the
following collusive
strategy, the same as discussed in class: set price pb only
if no one has cheated
so far, and to set price pa forever if some has cheated
before. Assume each firm
acts to maximize its sum of discounted profits where the
interest rate is r. Find
the values for r such that this collusive strategy is a Nash
equilibrium, namely,
for what values of r can the monopoly profits be sustained
through collusion?
Compare your answer to (b) and explain.
1Question 3. Two firms produce candies that are imperfect
substitutes. This
is reflected in the demand curves of the two firms’ candies,
D1(p1, p2) = 100 ?
p1 + 0.5p2 and D2(p1, p2) = 100 ? p2 + 0.5p1. Suppose each
firm has constant
marginal cost of 20.
(a) Interpret the demand curves, in particular, explain from
the demand curves
why the candies produced by the two firms are imperfect
substitutes.
(b) Suppose the two firms compete by making simultaneous
price decisions.
Calculate the equilibrium price, quantity and profit for
each firm.
(c) Suppose the two firms compete by making sequential price
decisions, where
firm 1 is the leader. Calculate the equilibrium price,
quantity and profit for
each firm. Compare the profits of the leader vs. the
follower and explain.
Question 4. Suppose an industry has ten firms. The market
shares of each
firm are: 25%, 15%, 10%, 10%, 8%, 8%, 7%, 7%, 5% and 5%.
(a) What is the four-firm concentration ratio?
(b) What is the Herfindahl-Hirschman Index?
(c) According to the merger guidelines, if the HHI is in the
range of 1000-1800
after a merger, you will not allow the merger if it
increased the HHI by 100
points or more. Would you allow a merger between the 2 firms
that had 5%
market share each? Would you allow a merger between the 2
firms that had 8%
market share each?
(d) Suppose the ten firms compete in a Cournot oligopoly in
this industry, and
the current price elasticity of demand is -0.8. What are the
profit margins for
each of the four biggest firms? What is the average profit
margin (weighted by
each firm’s market share) of this industry?
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