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Unformatted text preview: ARE [0% Spring 2008
' M.Whitney Intermediate Microeconomic Theory
Homework 2
Due Thursday, Ma} 81'”, at start of class
1. (18) Suppose each ﬁrm in an industry has the following cost function: TCr= f +g*qj “1*ch where f, g and h are positive constants. a. In terms of f, g, and h, what quantity minimizes average total cost? (Hint: take the derivative of ATC) b. Under perfect competition in the long run, marginal cost equals average total cost. Explain why this is
true. Now solve for longrun ﬁrm output, qi *, in terms of f, g, and h. How does your answer
compare to the answer in part a? c. Now let each ﬁrm’s cost function be TCi= 40,000 + 100"'qi + qi 2
Under competition in the long run, how much will each ﬁrm produce, and at what price? If market
demand for this good is Qd = 3000  2P, how many units are sold, and what is the long—run
equilibrium number of ﬁrms? What is consumer surplus in this market? And what is the proﬁt or
loss per ﬁrm? d. Suppose that the ﬁrms’ cost functions and market demand are the same as in part c, and the number of
ﬁrms is equal to that in part c. However, the ﬁrms are monopolistically competitive. Find each ﬁrm’s
optimal output; market price and quantity; marginal cost and average cost per unit, and consumer
surplus. What is the proﬁt or loss per ﬁrm? Will additional ﬁrms enter or exit this market? 2. (l6) Demand for home theater systems is Q = 1800  P. The two ﬁrms that produce these systems have the
following cost functions: Tc,= 100,000 + 300*ql + .5 ql 2
TC2 = 50,000 + 200*q2 + q2 2 For each market structure below, ﬁnd (i) output of each ﬁrm; (ii) market quantity; (iii) market price; (iv) proﬁt
for each ﬁrm; (v) producer surplus and consumer surplus. (Hint: remember producer surplus for an industry
equals total industry proﬁts, plus ﬁxed costs) a). The ﬁrms are Coumot oligopolists b) The ﬁrms are Bertrand oligopolists. c) Firm 1 is a Stackelberg leader, and Firm 2 is a follower.
d) The two ﬁrms form a cartel. 3. (4) Four identical Coumot oligopolists each have total cost functions of : TCi = 30 + 5*qi + .1in
Inverse market demand for their product is: P = 100  2Q a. What quantity should each ﬁrm produce? What is the market quantity and price? What is each ﬁrm's
proﬁt or loss? b. The managers of these ﬁrms collude to form a cartel. Now, what is the equilibrium market quantity?
What is the equilibrium price? How much is sold by each ﬁrm, and what is each ﬁrm's proﬁt or loss? 4. (4) Collegetown Hardware and Big Barn Supply are two rival home improvement stores. Each is
considering expanding by additing one or two new stores to the existing locations. The expected impact on proﬁts of these proposals are shown below. —
m
m a. Does either player have a dominant strategy? Why or why not? b. If each store adopts a maximin approach, what strategy will it choose ﬁrst? What are the payoffs? Is this
solution a Nash equilibrium? If not, what will happen next? c. If the 2 stores cooperated, what strategy would be optimal? Is this a Nash equilibrium point? 5.(4) The payoff matrix belowshows outcomes for a zerosum game: If each store adopts a maximin approach, what strategy will it choose ﬁrst? What are the payoffs? Is this
solution a Nash equilibrium? If not, what will happen next? 6. (4) Three oligopolists produce breakfast cereal. Each is considering whether to introduce a new “healthy”
cereal, or a “sweet” cereal. The a 011' matrix below shows the 0 c ssible outcomes of their decisions: a. If each ﬁrm adopts a maximin approach, what strategy will it choose ﬁrst, and what are the payoffs? Is this
outcome 3 Nash equilibrium? b. What set of strategies would provide the best cooperative outcome for the industry? Is this solution a Nash I
equilibrium? ...
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This note was uploaded on 05/03/2008 for the course ARE 100B taught by Professor Whitney during the Spring '08 term at UC Davis.
 Spring '08
 WHITNEY

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