What is the profit maximization condition for a monopolist

Question

Assignment:

Part A

1. Monopoly and price discrimination:

(a) What is the profit maximization condition for a (single-price) monopolist in the short-run? How about in the long-run? Is it efficient to have monopoly in the society? Why or why not? When does the government allow monopoly?

(b) If a monopolist is allowed to price-discriminate, what are the three broad categories of discrimination? Explain each one of them with example.

2. A monopolist faces the following demand curve: P = 1200 3Q; its total cost is given by: T C = 5000 + Q₂.

(a) If it is a single price monopolist, what is its profit maximizing price and quantity? How much is the profit? How much are consumer surplus, producer surplus and dead-weight loss? Compare these to the efficient outcome where the social surplus is maximized.

(b) Suppose it is a first degree price discriminator instead of a single price monopolist. What is the lowest price that the monopolist will charge? How much will be the profit (loss) of the form? How much are consumer surplus, producer surplus and dead-weight loss? Compare these to the ecient outcome.

Part B

3. Third degree price discrimination:

During the war, the same arms merchant often sells weapons to both sides of the conáict. In this situation, a different price could be offered to each side because there is no danger of resale. Suppose a US arms merchant has a monopoly of a special air-to-sea missiles and is willing to sell them to both India and China. India's demand for missiles is P₁ = 840-2x and Chinaís is P₂ = 1040-2.5y, where P₁ and P₂ are in millions of dollars. The marginal cost of missiles is MC = 2Q; where Q = x + y: How many missiles will be sold to each country and what price will be charged to each country?

4. Multi-plant monopolist:

A monopolist has access to two production processes with the following marginal cost curves: MC₁ = 2x and MC₂ = 60 + y, where output in production process 1 is x, output in production process 2 is y and hence total output produced is Q = x + y:

(a) During peak season, the monopolist faces the following demand curve: P = 160-2/3Q: How much should he produce at each facility to maximize profits?

(b) During off season, the monopolist faces a reduced demand given by: P = 70-2/3Q: How much should he produce at each facility to maximize profits?