Question

Problem 1. Second Degree price discrimination Suppose all consumers are identical and market demand given by p = 100-q. The monopoly's cost function is C(q) q2. (a) Suppose the monopolist cannot discriminate prices and must set a uniform price. Compute price and quantity set by the monopolist. Compute the profit of the monopoly. b) Suppose now that the monopoly can set a two-part tariff. Find the optimal two-part tariff. Compute the profit of the monopolist

Answer 1

(Problem 1)

Marginal cost (MC) = dC(q)/dq = 2q

(a) A single price monopolist will maximize profit by equating Marginal Revenue (MR) with MC.

Total revenue (TR) = p x q = 100q - q2

MR = dTR/dq = 100 - 2q

100 - 2q = 2q

4q = 100

q = 25

p = 100 - 25 = 75

TR = 75 x 25 = 1875

C(q) = 25 x 25 = 625

Profit = TR - C(q) = 1875 - 625 = 1250

(b) With two-part tariff, price equals MC and Profit equals consumer surplus (CS).

100 - q = 2q

3q = 100

q = 33.33

p = 100 - 33.33 = 66.67

From demand function, when q = 0, p = 100 (Vertical intercept of demand curve).

Profit = CS = Area between demand curve & price = (1/2) x (100 - 66.67) x 33.33 = (1/2) x 33.33 x 33.33 = 555.44

NOTE: As per Answering Policy, 1st question is answered.