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ECMC02S
Prof. G. Cleveland
Problem Set for Imperfect Competition
1. An industry consists of two firms, each of which have variable costs of $10 per unit but no
fixed costs. The industry demand curve is P = 70 - Q.
a) Solve for the Cournot equilibrium. In doing so, derive the reaction function of each firm (call
Q1 and Q2 the output of each firm). Solve for each firm's output, the market price, and each
firm's profits.
b) Suppose that firm 1 begins by producing 30 units of output (the monopoly solution if there is
only one firm). Trace the path to equilibrium by assuming that the two firms alternate choosing
output (thus the second firm chooses its level of output given that the first firm has chosen Q1 =
30; then the first firm chooses its level of output given whatever the first firm has just chosen,
and so on). Show your result as follows:
Q1=30 ----> Q2=? ----> Q1=? ----> Q2=? ----> Q1=? ----> etc.
Repeat if firm 1 begins by producing 0 units of output.
c) Graph the reaction functions of each firm. Show the process described in part b by starting at
Q1 = 30 (or 0) and then showing each firm's sequential actions.
d) Now suppose that firm 1 is a Stackelberg leader while firm 2 is a follower. Assume, as usual,
that the follower behaves like a Cournot duopolist (that is, assumes that the leader's output is
fixed). How will each firm behave (in terms of reaction functions)? What will each firm
produce, what will the price be, and what profits will each firm earn?
e) What will happen if this market is "contestable"?
f) Compare the Cournot and Stackelberg outcomes with the outcomes if the firms collude and
split the market, and with the outcome if the firms compete as price takers and split the market.
Compare the four outcomes in terms of price, output, and each firm's profits. On a graph of the
demand curve, show price and output for each outcome. Draw the industry's marginal cost curve.
Compute the efficiency loss relative to competition for the other three outcomes.
2. Return to the bridge problem (#4 in the previous problem set). Suppose now that the bridge is
being operated by a profit-maximizing monopolist, but that the market is contestable. Describe
the outcome. What kinds of assumptions would you have to make in order for contestability to
be a real possibility?
3. An industry consists of three firms: one, a dominant firm, sets the price for the industry (price
leadership); the other two, small firms, supply all they want at the price set by the dominant firm;
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the dominant firm then supplies whatever more consumers wish to buy at the established price.
Each small firm has total costs given by TCi (i=1,2), while the dominant firm has total costs of
TC0:
TCi = 6qi + (1/2)qi2
TC0 = 3q0 + (1/24)q02Total market demand for the good can be expressed as:
P = 24 - (1/4)QT
(note: QT = q0 + q1 + q2)
a) Determine the quantity supplied by each firm and the equilibrium price, and each firm's
profits. Show your solution graphically.
b) Now suppose that three more small firms with identical cost curves to those of firms 1 and 2
enter the industry. Solve again for price and each firm's output and profit.
c) Now return to the case of two small firms. Suppose that all three firms acted as price takers
(the competitive result). Derive market price and each firm's output and profit. What is the
efficiency loss involved with having a dominant firm?
4. A description of the short run situation for eighteen different firms is presented below. No
account is taken of long run adjustments.
Firm A: P = MR = MC = ATC
Firm C: P > MR > MC < ATC = P
Firm E: P > MR > MC > ATC > P
Firm G: P = MR < MC < ATC
Firm I: P > MR = MC < ATC > P
Firm K: P = MR = MC > ATC
Firm M: P = MR < MC > ATC > P
Firm O: P > MR = MC < ATC = P
Firm Q: P = MR > MC > ATC
Firm B:
Firm D:
Firm F:
Firm H:
Firm J:
Firm L:
Firm N:
Firm P:
Firm R:
P > MR = MC > ATC
P > MR < MC = ATC < P
P = MR > MC = ATC
P > MR > MC < ATC > P
P > MR < MC < ATC > P
P = MR > MC < ATC = P
P > MR = MC < ATC < P
P = MR = MC < ATC
P > MR > MC = ATC
Which of the firms fall into each of the following categories. Explain your reasoning. (Drawing
sketches corresponding to the above conditions for each firm may help in this problem) (Hint:
one of the firms may not exist).
a) firms which are perfect competitors;
b) firms which are either monopolists or imperfect competitors;
c) firms which are maximizing profits;
d) firms which could increase profits (or reduce losses) by increasing output;
e) firms which could increase profits (or reduce losses) by reducing output;
f) firms which are making positive economic profits;
g) firms which are taking economic losses;
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h) firms which are breaking even;
i) firms operating at the minimum point on their short run average cost curves;
i) firms operating at the minimum point on their short run average cost curves which could
increase profits (or reduce losses) by increasing output;
j) firms which are operating with excess capacity (which could increase output without
increasing average cost)