Final Exam from Last Year (2021)
ECON 445
24 April 2021
The exam has a total of 100 points. Please answer all questions.
Students are not permitted to engage in group work or collaborate with
other students on this exam. Collaboration on exams is a violation of academic
integrity.
1 Short Questions (20 pts)
Provide brief answers to each of the following questions (ideally no more than
three to four sentences).
1. (4 pts) If marginal costs of production are decreasing over time (instead
of being constant over time), does that make it easier or harder for firms
to collude? Why?
2. (4 pts) Firms in an industry produce a homogeneous good. You have data
on prices P , quantity Q, a demand shifter y and a cost shifter w. The
demand curve and marginal cost curve are linear. Describe how you would
estimate the demand curve.
3. (4 pts) Explain in your own words the difference between entry deterrence
and entry accommodation.
4. (4 pts) Historically, prices in an industry were published on a quarterly
basis. In an effort to improve transparency for consumers, the industry
association launches a new digital platform that will allow prices to be
published on a daily basis. Describe how this change might affect the
sustainability of a collusive outcome, and explain the reasoning behind
your answer.
5. (4 pts) In the model of capacity deterrence we studied in class, the in-
cumbent invest in capacity first, and then the potential entrant decides
whether or not to enter. Suppose the order of this game were reversed: the
potential entrant first decides whether or not to enter, and following that
the incumbent invests in capacity. In this situation, can the incumbent
use the threat of capacity investment to deter the potental entrant from
entering? Explain why or why not.
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2 Longer Questions
2.1 Collusion with risk of discovery (18 pts)
Two firms both produce a homogeneous product. Suppose the market demand
is given by: P (Q) = 40 − Q/4. Each firm has the following cost function:
C(q) = 8q.
1. (2 pts) What would be the monopoly price, quantity, and profits in this
market?
2. (4 pts) Consider the following collusive agreement that uses a grim trigger
strategy to punish deviations.
(a) As long as every firm has cooperated in all past periods, each firm
charges p∗ = pM (the monopoly price), and enjoys half of the monopoly
profits.
(b) If any firm has ever charged a price of p < p∗ in the past, then
each firm will charge the Bertrand price, pB , today and in all future
periods.
Derive the discounted sum of lifetime profits for each firm if it (i) sticks to
the above collusive agreement (ii) deviates from the agreement. What is
the range of the firms’ common discount factor, δ, such that neither firm
has an incentive to deviate from the agreement?
3. (6 pts) The competition authority investigates the industry on a regular
basis. Because of limited data access and the difficulty of arguing anti-
trust cases in court, the investigation only succeeds with probability r.
Here’s how this affects the game played between the firms. In any pe-
riod where both firms charge the monopoly price pM , with probability
1− r the investigation fails and the firms continue earning the monopoly
profits. With probability r the investigation succeeds, in which case two
things happen: (i) first, firms are forced to give up any profits they earned
in that period (ii) in addition, each firm will be forced to pay a fine of F .
By contrast, if either firm sets a price lower than the monopoly price, then
the investigation will fail with a probability of 1, because the firms can
successfully argue in court that they were not colluding.
What is the discounted sum of lifetime expected profits for each firm (as
a function of r and F ) if it sticks to the collusive agreement from part
(2)? What is the range of the firms’ common discount factor, δ, such that
neither firm has an incentive to deviate from the agreement?
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4. (3 pts) Suppose r = 0.25 (i.e. the investigation has a 25% chance of suc-
ceeding). What is the minimum fine F the competition authority should
charge in order to ensure that firms would not wish to collude (for any
discount factor that lies strictly between 0 and 1)?
5. (3 pts) Would the minimum required fine F that you derived in part (4)
increase, decrease, or remain the same if:
ˆ Firms compete in quantities rather than prices?
ˆ Demand for the product is increasing over time?
ˆ Demand for the product became more elastic?
In each case, briefly explain the reasoning behind your answer.
2.2 Collusion with alternating demand (17 pts)
Consider a market with Bertrand competition between two firms who both pro-
duce a homogeneous good. Marginal costs for both firms are given by c = 4 and
firms discount the future at a rate δ.
Demand fluctuates predictably over time, and alternates between high and
low. In even-numbered periods (e.g, year 2, year 4, etc.), demand is high and
given by D(p) = 40 − 4p. In odd-numbered periods (e.g, year 1, year 3, etc.),
demand is low and given by D(p) = 20− 2p.
1. (2 pts) Derive the equilibrium prices and quantities under Bertrand com-
petition (i) when demand is high (even-numbered periods) and (ii) when
demand is low (odd-numbered periods). What are the profits earned by
each firm in even-numbered periods and odd-numbered periods?
2. (3 pts) Derive the equilibrium prices and quantities under collusion (i)
when demand is high (even-numbered periods) and (ii) when demand is
low (odd-numbered periods). What are the profits earned by each firm in
even-numbered periods and odd-numbered periods?
3. (3 pts) Carefully describe a grim trigger collusive strategy for the infinitely
repeated game.
4. (6 pts) Under the collusive strategy you specified in part (3), for what val-
ues of δ will collusion be viable? (Hint: remember to distinguish between
even-numbered and odd-numbered periods!)
5. (3 pts) Suppose that δ is too low by some small amount. Describe what
the two firms can do to preserve the collusive arrangement (you do not
need to work out the exact prices they should charge).
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2.3 Price Discrimination I (15 pts)
Air Canada has a monopoly on air service between Kingston and Toronto. There
are two types of customers who fly this route: business travelers and leisure
travelers. They’ve asked you to help think about pricing on that route, and
have provided you with the following estimates of annual demands, where QB
is the quantity of tickets demanded by business travellers, QL is the quantity of
tickets demanded by leisure travellers, PB is the price paid by business travellers,
and PL is the price paid by leisure travellers.
QB = 2000− 2PB (1)
QL = 10000− 20PL (2)
Annual costs are given by: C(Q) = 300, 000 + 40Q, where Q = QB +QL
1. (3 pts) If Air Canada sets a single uniform price for all tickets on the route,
what would be the profit-maximizing price that you would recommend?
What are total seats sold, total consumer surplus and Air Canada’s profits
at this price?
2. (4 pts) Air Canada told you it can charge different prices for different
groups, because all business travelers on the route are Air Canada fre-
quent flyers, but the leisure travelers are not. What would be the profit-
maximizing fares to charge for tickets bought by frequent flyers and tickets
bought by other travellers? If this segmentation is successful, how many
seats of each type would Air Canada sell? What are total consumer sur-
plus and Air Canada’s profits?
3. (4 pts) Would social welfare be higher under the prices in (2) or in (1)?
What intuition underlies this result?
4. (4 pts) Unfortunately, after implementing the price scheme in (2) where
Air Canada charged the business fare for passengers with frequent flyer
numbers and the leisure fare to passengers without a frequent flyer number,
you discover that there are no longer any frequent flyers on the route. Can
you think of an explanation for what has happened? How many leisure
tickets are being sold, and what are Air Canada’s profits?
2.4 Price Discrimination II (15 pts)
Suppose a grocery sells coffee to two types of people:
ˆ 150 college graduates, who value a bag of coffee at $20
ˆ 100 retirees, who value a bag of coffee at $10
Assume the marginal cost of producing a bag of coffee is 0.
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1. (3 pts) Initially the grocery has to charge a uniform price p per bag of cof-
fee. What price p should the grocery choose to maximize profits? What
are the grocery’s profits?
2. (6 pts) Now suppose that the grocery can offer coupons in a local mag-
azine. Coupons can be used to offset the cost of purchasing coffee. For
example if the grocery offers a $1 coupon, then any customer can cut out
the $1 coupon and bring it to the grocery to get a $1 discount when pur-
chasing a bag of coffee. Let d denote the discount offered in the coupon
(in the example above, d = 1).
It is time-consuming and annoying to flip through the magazine, find the
coupon and cut it out. College grads are in a hurry, and it costs them
$5.01 of time to sit down and cut coupons. However, retirees’ time is free,
and they incur no cost from cutting coupons.
What pricing strategy should the grocery adopt to maximize profits? In
other words, what is the price p the grocery should charge per bag of cof-
fee, and what is the discount d it should set when offering the coupon?
What profits will the grocery earn?
(Hint : think of whether the grocery can use the coupon to second-degree
price discriminate. Remember to check the incentive compatibility and
individual rationality conditions!)
3. (3 pts) What pricing strategy (i.e. price p, coupon discount d) should
the grocery adopt if there are 50 retirees (instead of 100) and 150 college
grads? What profits will the grocery earn?
4. (3 pts) If the cost of cutting coupons for college grads is $2.01 (instead of
$5.01), and there are 150 college graduates and 100 retirees, what pricing
strategy (i.e. price p, coupon discount d) should the grocery adopt? What
profits will the grocery earn?
2.5 Free entry (15 pts)
Suppose that demand is given by D(p) = 34 − p, and there are many firms
competing in quantities (i.e., Cournot). The fixed cost of entry is 6, and the
marginal cost of production is 10. There are infinitely many identical potential
entrants.
The potential entrants play a two stage game. First, each firm simultane-
ously decides whether or not to enter. Second, the firms that decide to enter
compete in quantities.
1. (3 pts) In general terms (i.e., without solving for anything yet), charac-
terize the free entry equilibrium conditions.
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2. (5 pts) Now for the demand system and costs above, what is the equilib-
rium number of firms?
3. (3 pts) With respect to social efficiency, do you expect that there are too
many or too few firms? Motivate your answer carefully. (Note: you do
not need to solve explicitly for the number of firms that would maximize
social surplus).
4. (4 pts) Now suppose that in the second stage of the game, instead of
competing in quantities, firms compete in prices. Derive the equilibrium
number of firms. With respect to social efficiency, do you expect that
there are too many or too few firms?
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