Question

1. A single firm produces widgets, with a cost function and inverse demand function as follows, C(q) = 150 + 2q P(Qd) = 10 ? 0.08Qd (a) Calculate the monopolist’s profit-maximizing price, quantity, and profit if he can charge a single price in the market (single price monopolist). (b) Suppose the firm can sell units after your answer to (a) at a lower price (2nd-degree price discrimination, timed-release). What quantity will be sold for what price in this second-tier market? Calculate the monopolist’s profit. (c) Suppose each new tier of pricing the monopolist introduces increases fixed costs by $2 (quantities can be irrational). What is the profit-maximizing quantity, number of prices, monopolist’s profit, and deadweight loss? (d) Suppose the firm can perfectly price discriminate (1st-degree) with a 40% increase in marginal cost; calculate the profit-maximizing quantity, monopolist’s profit, and deadweight loss? (e) Between (c) and (d), which is socially preferred? Which would the monopolist choose to do?

Answer 1

a) Under monopoly, equilibrium is attained where MR = MC

TR = P.Q = (10 - 0.08Q)Q = 10Q - 0.08Q²

MR = 10 - 0.16Q

TC = 150 + 2Q

MC = 2

It implies, MR = MC

10 - 0.16Q = 2

0.16Q = 8

Q = 800/16 = 100/2

Q = 50 units

P = 10 - 0.08(50) = 10 - 4 = $ 6

Profit = TR - TC = P.Q - (150 + 2X50) = 6 X 50 - 150 - 100 = 300 - 250 = $ 50

b) When monopoly firm perfectly price discriminate then equilibrium is where Demand = MC

P = MC

10 - 0.08Q = 2

8 = 0.08Q

Q = 800/8

Q = 100 units

P = 10 - 0.08(100) = $ 2

Monopolist profit = 2 X 100 = $ 200

c) Two-Part Pricing:

TR = P.Q = (10 - 0.08Q)Q = 10Q - 0.08Q²

MR = 10 - 0.16Q

TC = 150 + 2Q

MC = 2

It implies, MR = MC

10 - 0.16Q = 2

0.16Q = 8

Q = 800/16 = 100/2

Q = 50 units

P = 10 - 0.08(50) = 10 - 4 = $ 6

Entry fee = Area of shaded region = 1/2 X 50 X (10 - 6) = 25 X 4 = $ 100

Profit = 2 Entry Fee + (P - MC)Q = 2(100) + (6 - 2)50 = 200 + 200 = $ 400