Economics 5321 - what is the optimal two part tariff when

Question

QUESTION 1:

Let's say the cost function and the demand function of a monopolistic firm are as follows

C = 10 + Q²

P = 20 - Q

(a) What is the price and output this monopolistic firm will produce?

(b) What will be the price and quantity if the monopolist decided to act as a perfect competitor?

(c) What is the PS, CS, and total welfare when in perfect competition? (d)What is the PS, CS, and Total welfare is monopoly?

(e) What is the deadweight loss when you move from perfect competition to monopoly?

(f) If the government sets a price of p=10, how does this decision affect price, quantity?

QUESTION 2:

Consider the market for a product with two types of potential users: those in proportion λ have inverse demand schedule P_λ = 5 - 0.5*Q_λ while the remaining (1-λ) have inverse demand P_1-λ = 10 - Q_1-λ. Normalize the total number of consumers to 1 and let MC = 2 be the constant marginal cost of the monopolist.

(a) What is the optinal (profit-maximizing) two-part tariff as a function of λ that induces both types of consumers to buy?

(Hint: If the inverse demand looks like P=a-bQ, when the consumer surplus at price P has the form CS = (1/2b)(a-P)²)

(b) What is the optimal two part tariff when only high demand consumers purchase the good?

(c) If λ= 0.5, which of the pricing schemes yields a higher total profit?

(d) If λ= 0.75, which of the pricing schemes yields a higher total profit?