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Industrial Economics
“Price Discrimination” and “Product Differentiation”
Review Questions
Q1. A monopolist sells in two markets. The demand curve for her product is given by
P1=137-2Q1 in the first market and P2=275-5Q2 in the second market, where Qi is the quantity
sold in market i and Pi is the price in market i. She has a constant marginal cost of production,
c=5 and no fixed costs. She can charge different prices in the two markets. What is the profit
maximazing combination of quantities for this monopolist?
Q2. Suppose that a monopoly can produce any level of output it wishes at a constant marginal
cost of $5 per unit. Assume that the monopoly sells its goods in two different markets that are
seperated by some distance. The demand curves in the first and second markets are Q1=55-P1
and Q2=70-2P2, respectively. If the monopolist can maintain the seperation between the two
markets, what level of output should be produced in each market? and what price will prevail
in each market? what are total profits?
Q3. A monopolist is deciding how to allocate output between two markets. The two markets
are seperated geographically. Demand for the two markets are: P1=15-Q1 and P2=25-2Q2. The
monopolist’s total cost is C(Q)=5+3(Q1+Q2). What are price, output and profits (i) if the
monopolist can price discriminate? (ii) if the law prohibits charging different prices in the two
regions?
Q4. F.Gasmi, Q.Voung and J.Laffont have used statistical methods to estimate demand curves
for Coke (Firm 1) and Pepsi (Firm 2).
Q1=64-4P1+2P2
Q2=50-5P2+P1
These demand functions imply that both goods are horizantally differentiated. Coca-cola and
Pepsi has marginal costs of $5 and $4, respectively.
a) what is Coca-cola’s profit-max price, given that Pepsi sets a price of $8?
b) what is Coca-cola’s profit-max price, when Pepsi sets an arbitrary price P2 (what is the
equation of Coca-cola’s reaction function)?
c) What is Pepsi’s best response to any arbitrary price P1 for Coke?
Q5. The total cost functions of two firms in a duopoly market that has product differentiation,
C1=12Q1 and C2=10Q2, respectively. The demand functions are Q1=250-5P1+2P2 and
Q2=280+P1-4P2. Find the Cournot equi. price, quantitiy and max. profits.
Q6. The total cost and inverse demand functions of a leader firm in a duopoly market that has
2
product differentiation are C1=4 Q and P1=364-2Q1-2Q2 , respectively. The second firm
1
wants to have and keep the market share of 0.2. Find the equi. quantity of outputs for each
firm.