Question

. The demand for mysterious good X in Lansing is Q = 12 ? P, where P is the price of good X per pound and Q is the quantity demanded in pounds. The marginal cost of producing the good is $2 per pound. There is no fixed cost of producing the good. There is only one firm, Alice, who can produce the good. Alice can perfectly price discriminate. Rather than naming the price for each quantity sold, Alice uses two-part tariff that names a per-unit price and a fixed-fee to maximize his profit. (a) What are the per-unit price and the fixed fee in his optimal two-part tariff? (b) How much is the consumer surplus? (c) How much is the producer surplus?

Answer 1

Demand: Q = 12 - P

Inverse demand: P = 12 - Q

Marginal cost = $2

(a) Under two-part tariff, Price equals Marginal cost and fixed fee equals consumer surplus.

12 - Q = 2

Q = 12 - 2 = 10

P = MC = $2

From inverse demand function we get, when Q = 0, P = $12 (Maximum willingness to pay)

Consumer surplus (CS) = Area between demand curve and price = (1/2) x $(12 - 2) x 10 = 5 x $10 = $50

Fixed fee = CS = $50

(b) As computed above, consumer surplus is $50.

(b) Producer surplus is the area between MC curve and market price. Since price and MC are equal, producer surplus is zero.