ECON461 - INDUSTRIAL ORGANIZATION
CONCORDIA UNIVERSITY
WINTER 2021
PROBLEM SET #2
1. Consider the following variant of the Dixit model that we discussed in class: In the market for microwaves, there
is an incumbent (firm 1) and a potential entrant(firm 2). The demand function is given by: P = 60−0.01(q1+q2)
where q1 is the output of the incumbent and q2 is the output of the entrant. Firms need two units of labou
and one unit of capital to produce one unit of output. Labour costs w = 10 per unit and capital costs
= 15 per unit. In addition, the entrant has to pay a fixed cost of F2 to enter this market. At period T = 1, the
incumbent chooses a level of capital investment K̄1 and at time T = 2, firms compete in quantities by buying
inputs and producing outputs
a. What is the range of possible levels of investment for firm 1 that could be a part of the equili
ium for this
game? That is, what is the lowest K̄1 that could be an optimal choice for firm 1 for some values of firm 2’s
fixed cost F2? What is the highest K̄1 that firm 1 could optimally choose? (8 pts)
. What is the equili
ium outcome and profits of this game if the entrant has fixed costs F2 = 1000? (4 pts)
c. What is the equili
ium outcome and profits of this game if the entrant has fixed costs F2 = 2500? (4 pts)
d. What is the equili
ium outcome and profits of this game if the entrant has fixed costs F2 = 4000? (4 pts)
2. Suppose there is a monopoly in the market whose consumers are one of two types (A and B). The (inverse)
demand of type A consumers is given by P = 80− 2QA and the (inverse) demand for type B consumers is given
y P = 140 − 2QB . The monopolist cannot price discriminate in this market.
a. Solve for the monopolist’s aggregate demand curve in this market and the associated marginal revenue curve
(10 pts)
. Suppose that the monopolist has a constant marginal cost of MC(q) = 30. Solve for the equili
ium price
and quantity in this market. How much of this output is sold to type A consumers and how much is sold
to type B consumers? (5 pts)
c. Suppose that the monopolist has a constant marginal cost of MC(q) = 50. Solve for the equili
ium price
and quantity in this market. How much of this output is sold to type A consumers and how much is sold
to type B consumers? (5 pts)
3. Suppose the monopolist in the previous problem can now price discriminate between type A and type B consumers
using a third degree price discrimination scheme (group pricing)
a. Suppose that this monopolist has a constant marginal cost of production of MC(q) = 50. Solve for the
equili
ium price charged to each type of consumer and the equili
ium quantity sold to each type of
consumer. Calculate total monopolist profits. How does this compare to the profit that the monopoly
earned when it could not price discriminate? Is price discrimination welfare improving in this case? (5 pts)
. Suppose that this monopolist has an increasing marginal cost of production of MC(q) = 20 + Q2 . Solve fo
the equili
ium price charged to each type of consumer and the equili
ium quantity sold to each type of
consumer. Calculate total monopolist profits. (10 pts)
1
4. Suppose that there are two individuals A and B. A’s (inverse) demand is given by PA = 50−2QA and B’s (inverse)
demand is given by PB = 70− 4QB . Suppose that the monopolist can first degree price discriminate.
a. What are the conditions that would have to be true in order for the monopolist to be able to first-degree
price discriminate in this market? (5 pts)
. Suppose the monopolist has costs given by C(Q) = 10Q. What is the optimal two-part tariff that he would
charge each consumer? What is the optimal block pricing scheme for each of the consumers? Calculate
total monopolist profits. (5 pts)
c. Suppose now that the monopolist has costs given by C(Q) = Q
2
5 . What is the optimal two-part tariff that
he would charge each consumer? What is the optimal block pricing scheme for each of the consumers?
Calculate total monopolist profits.(10 pts)
d. Suppose that the monopolist has costs of C(Q) = Q
2
5 . Suppose that there is one individual of type A and
three individuals of type B. What is the optimal block pricing scheme for each type of consumer? Calculate
total monopolist profits. (5 pts)
5. The market for a monopolist’s good consists of two types of consumers: the first has a demand given by
PA = 180− 5QA and the second has demand given by PB = 130− 6QB . To begin with there is one of each type
of consumer. The monopolist’s cost function is C(Q) = 10Q which means the monopolist has a marginal cost of
10
a. If the monopolist can first degree price discriminate, what is the optimal two part tariff to charge each type
of consumer? What are the optimal block pricing bundles to sell to each type of consumer? (5 pts)
. Suppose that the monopolist cannot tell the two groups apart and can only use second degree price dis-
crimination. What is the optimal menu of bundle(s) to offer to the consumers? (10 pts)
c. Now suppose that the monopolist is still restricted to second degree price discrimination, but instead of
having one of each type of consumer, there is one of type B and X of type A. What does X have to be
efore it’s better for the monopolist only to sell to A types. (Note: X is not necessarily an integer) (5 pts)
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ECON461: INDUSTRIAL ORGANIZATION
Lecture 11
Jan Victor Dee
Winter 2021
Concordia University
1 / 29
Price Discrimination
I So far, we have assumed that firms are restricted to uniform pricing
schemes
I Uniform Pricing: All consumers purchasing the good pay the same
price for every unit of the good
I Price Discrimination: Different consumer pay different prices for the
same good (or different quantities of the good)
I First degree (personalized pricing): extract the maximum amount that
each consumer is willing to pay
I Second degree (menu pricing): using different menu prices to sort
different types of consumers
I Third degree (group pricing): different groups of consumers pay different
prices
I To keep our analysis simple, we will look at price discrimination from
the perspective of a monopolist
2 / 29
Price Discrimination
I Why should firms price discriminate?
I Produce/sell more output to different market segments without reducing
per-unit price in other segments
I Transfer surplus from consumers to producers
I Given these benefits, why don’t we see firms do this more often?
3 / 29
Price Discrimination - Challenges
I There are two practical hurdles to price discrimination
I Identification: figuring out who the consumers are in order to charge
the right amount to each consume
I Estimating consumer demand isn’t so easy in practice - especially at the
individual level
I Especially difficult when individuals demand multiple units -
heterogeneity in consumer preferences, different marginal WTP for each
unit
I A
itrage: preventing people who buy at the lower price from reselling
the good
I Easier to price discriminate for services versus goods (legal services vs
law textbooks)
I May depend on legal status (prescription medicine)
4 / 29
Third Degree Price Discrimination
I Third degree price discrimination: different groups of people pay
different prices for the same good
I Examples include:
I Movie tickets - Seniors discount
I Metro pass, Restaurants - Student discounts
I Free
educed price lunches for low income families
I Domestic/International textbooks
I Prescription Drugs in US/Canada
I Groups are based on (easily) observable characteristics
I or group members want to identify themselves
I Monopolist can restrict a
itrage across groups
I Within group uniform unit prices
I ”Linear Pricing” within the group: you can buy as much as you want at
the group price (average price = marginal price within the group)
5 / 29
Third Degree Price Discrimination - Example
I Consider two separate geographic markets for a textbook (US and
Canada)
I Recall elasticity of demand: how responsive are consumers to a price
change
I We should expect that the group with more inelastic demand will be
charged a higher price than the group with more elastic demand
6 / 29
Third Degree Price Discrimination - Example
I Suppose that the (inverse) demand is given by
PU = 100− 2QU
PC = 50− 2QC
I The monopolist has a constant unit cost of production c = 5
I First, suppose that goods can flow freely across the two markets and
the monopolist can only set one price (no price discrimination)
I This is a standard pricing problem for a firm facing a segmented
demand curve
7 / 29
Uniform Pricing
I No price discrimination so PU = PC = P
I From the inverse demand functions we can derive each market’s
demand curve
PU = 100− 2QU ⇐⇒ QU = 50−
1
2
PU
PC = 50− 2QC ⇐⇒ QC = 25−
1
2
PC
I From the demand functions we can see that
I Canadians will only buy if P < 50
I Americans will only buy if P < 100
8 / 29
Uniform Pricing
I Deriving the aggregate demand curve:
I If P ∈ [50, 100] then only US buys and Q = 50− 0.5P or P = 100− 2Q
I If P ≤ 50 then both markets will have positive demand for the good
Q = QU + QC
= (50− 0.5P) + (25− 0.5P)
= 75− P
or P = 75− Q
I For profit maximization we set MR = MC . We can derive the marginal
evenue using the ”twice as steep” rule
I MR(US) = 100− 4Q
I MR(Both) = 75− 2Q
9 / 29
Uniform Pricing
I Two possibilities: either sell to both markets or sell to US market only
I Why do we not consider selling to Canada only?
I Suppose that the monopolist chooses to sell to the US only
I Setting MR(US) = MC we get Q = 23.75
I Which implies a price of P = 52.5 and profits of
π = (52.5− XXXXXXXXXX = XXXXXXXXXX
I Suppose that the monopolist chooses to sell to both markets
I Setting MR(both) = MC we get Q = 35
I This implies a price of P = 40 and profits of π = (40− 5)35 = 1225
I In our case, is is more profitable to sell to both markets. The additional
marginal revenue from the Canadian units make up for the lower price
on the US units
10 / 29
Third Degree Price Discrimination
I Now suppose that the firm can charge different prices in the two
markets
I The monopolist wants to maximize total profits and it needs to conside
how producing one output to sell in one market impacts the costs of
producing output to sell in the other market
I Special case: If the firm has a constant marginal cost of production,
then the firm can simply treat the two markets separately and optimize
separately for each market
I This approach will only work if the costs of production