Economics of Competition and Strategy ECOS2201
Economics of Competition and Strategy
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Economics of Competition and Strategy
ECOS2201
1. THIS IS AN OPEN BOOK EXAM.
2. THIS PAPER HAS 5 QUESTIONS – EACH WORTH 20 MARKS.
3. ALL ANSWERS MUST BE HANDWRITTEN AND A PDF COPY OF YOUR HAND-
WRITTEN ANSWERS MUST BE UPLOADED ON THE CANVAS EXAM PORTAL.
MAKE SURE THAT YOU UPLOAD JUST ONE FILE WITH ALL OF YOUR AN-
SWERS TOGETHER AND THAT THE FILE IS A PDF FILE.
4. YOU ARE NOT ALLOWED TO TAKE SCREEN SHOTS OF QUESTIONS AND DIS-
CUSS THEM ON ED.
5. YOU WILL HAVE 2 HOURS (INCLUDES 10 MINUTES OF READING TIME) TO
COMPLETE THE EXAM AND WILL HAVE AN ADDITIONAL 30 MINUTES TO
UPLOAD THE EXAM ON THE CANVAS EXAM PORTAL.
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1. Suppose demand is given by Q = 200 − P . Also assume that there are no production
costs.
(a) Consider a monopolist. Graph the marginal revenue curve. What price and quantity
will the monopolist choose? (5 marks)
(b) Now consider a Cournot duopoly where firms choose quantities simultaneously. Let
q1 be the quantity chosen by firm 1 and q2 be the quantity chosen by firm 2. Plot
the best response functions for both firms with all of the intercepts clearly labeled.
(5 marks)
(c) On the same graph above, plot all the pairs (q1, q2) such that the sum of both firms’
quantities add up to the optimal monopoly quantity in part (a) above. (5 marks)
(d) Suppose both firms reach an agreement where they each produce half of the monopoly
output. Depict this point on the graph above. Is this agreement self enforcing? If
not, how much additional output (over and above the agreed value) does each firm
have an incentive to produce? (5 marks)
2. Suppose demand is given by Q = 200−P . Consider a Bertrand duopoly where two firms
choose prices simultaneously.
(a) Suppose there are no production costs. What is the Nash equilibrium of the game?
(5 marks)
(b) Now suppose there are production costs where firm 1 has a cost function given by
C1(q1) = 5q1 and firm 2 has a cost function given by C2(q2) = 10q2. Assume that in
the case of tie (where both firms set the same price), the low cost firm (i.e. firm 1)
gets all of the demand. What is the Nash Equilibrium of this game? (5 marks)
(c) Suppose there are no production costs as in part (a). Consider an infinitely repeated
version of the Bertrand duopoly. Construct grim trigger strategies that enable firms
to collude and charge the monopoly price each period. For what values of the interest
rate r is this a Nash Equilibrium? (10 marks)
3. (a) Suppose demand for a homogeneous good is given by Q = 200 − P . Also assume
that there are no production costs and no entry. Suppose firms choose quantities
sequentially (as in the Stackelberg model): firm 1 chooses its quantity q1 in the first
period and then firm 2 chooses its quantity q2 in the second period, after observing
q1. Find the Subgame Perfect Nash equilibrium and graphically depict it (include
the Cournot best response functions and firm 1’s isoprofit curve). (10 marks)
(b) Consider a first price sealed bid auction with two bidders whose private valuations
are uniformly distributed on [0, 1]. Suppose both of these bidders use strategies that
are linear in their values so that bi(vi) = avi. Find the value of a so that the bid
functions are a Bayesian Nash Equilibrium. (10 marks)
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4. Consider the location model of product differentiation from class. The city is of length
1 unit, firms have constant marginal costs of c per unit and no fixed costs, and each
consumer buys one unit of the good. Consumer i’s utility derived from buying product j
is given by
uij = u− t (xi − yj)2 − pj, for j = 1, 2.
where t is a taste cost for the consumer. Suppose that consumers are uniformly distributed
across the whole city (between 0 and 1) and that firm 1 is at one end of the city (y1 = 0)
while firm 2 is at the other end (y2 = 1).
(a) What is the demand for each firm’s product? (5 marks)
(b) Find the Nash equilibrium prices and profits. (5 marks)
(c) Consider the same set up as above but now assume that at the start of the game, one
of the firms – say Firm 2 – can influence the taste parameter t through advertising.
The cost of influencing t for firm 2 is 10t2. What is the optimal level of t that firm
2 chooses in a subgame perfect equilibrium? (5 points) (5 marks)
(d) Find the level of advertising that maximizes the joint profit of both firms. How is
this different from part (c)? Why? (5 marks)
5. Consider the following screening problem: A university writes a contract with a firm to
deliver q units of a good. The firm has constant marginal cost c, so that its profit is P−cq
where P denotes the payment for the transaction. The firm’s cost is private information
and may be either high (c = 10) or low (c = 5). The university believes that each of these
types of firms is equally likely, and it makes a take it or leave it offer to the firm (whose
default profit is 0). Let B(q) = 4q
1
2 denote the benefit to the university of obtaining q
units.
(a) Suppose the university could observe the firm’s costs. What is the optimal contract
offered by the university? Depict this contract graphically. (10 marks)
(b) Write down the constrained optimization problem for the university when costs are
not observable. Using a graph, explain which constraints bind. Keep your answer
short. (5 marks)
(c) Compute the optimal contract offered by the university. (5 marks)