Download Answers to Chapter 12 Problems

Econ 30010
Intermediate Microeconomic Theory
Answers for Chapter 12 Problem
14. a. Under third-degree price discrimination, the firm simultaneously (not independently)
solves for an optimal quantity and price in each market. That is, it equates marginal revenue in
each market with the marginal cost of total production. The firm’s marginal revenue in Europe
is defined by MRE = 70 – 2QE and in the United States it is defined by MRU = 110 – 2QU. The
firm’s marginal cost function is MC(QE+QU)=10. Thus, the two equations that define the firm’s
profit-maximizing third-degree price discrimination policy are
70-2QE = 110 – 2QU
And
70-2QE = 10.
Solving these equations simultaneously implies QE = 30 and QU = 50. To sell these quantities,
the firm should set PE = 40 and PU = 60. With these prices and quantities, firm profit will equal
3400.
b. If the firm can only set one price, the demand function faced by the firm changes to
0 if P  110


Q  QE  QU   110  P if 70  P  110
180  2 P if 0  P  70.

Notice that at a price of 70, the firm will only sell its drug in the United States and the quantity
demanded will be 40. This means that if the firm sells less than 40 units it is only selling in the
United States and if it sells more than 40 units, it is selling in both the United States and Europe.
Thus, if Q ≤ 40, inverse demand must be P(Q) = 110 – Q and MR(Q) = 110 – 2Q. However, if
Q > 40, inverse demand must be P(Q) = 90 – Q/2 and MR(Q) = 90 – Q. To find the profitmaximizing uniform price and quantity, we need to figure out if the marginal cost and marginal
revenues curves intersect at Q ≤ 40 or at Q > 40.
Let’s check Q ≤ 40 first. Equating marginal revenue with marginal cost implies 110-2Q = 10 or
Q = 50. Since this value contradicts the assumption that Q ≤ 40, we know that the profitmaximizing quantity must be greater than 40. With Q > 40, equating marginal revenue with
marginal cost implies 90-Q = 10 or QM = 80. Then firm’s profit-maximizing price will equal 50.
Notice that at a price of 50, the firm will sell 20 units in Europe and 60 units in the United States.
Firm profit will equal 3200.
c. First, let’s calculate CS and PS when the firm can price discriminate. Using each demand
curve, CSE = (70-40)(30)/2 = 450 and CSU = (110-60)(50)/2 = 1250. Thus, total consumer
surplus equals 1700. To calculate PS, recall that PS = π +FC = 3400 since FC = 0.
Second, let’s calculate CS and PS when the firm does not price discriminate. We can again use
each country’s demand curve to calculate CS so now CSE = (70-50)(20)/2 = 200 and
CSU = (110-50)(60)/2 = 1800. Thus, CS = 2000 and PS = 3200. Uniform pricing is worse for
the European customers but better for the US customers and for the firm.
From (a) and (b), the firm will serve both markets under either pricing policy.