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Suppose a monopolist faces one market with the following demand curve: ?2(?2) = 1000 − 2?2...

Suppose a monopolist faces one market with the following demand curve:

?2(?2) = 1000 − 2?2

Let the marginal cost be $20 per unit.

  1. What is the firm’s optimal output? What is the profit-maximizing price?

  2. Suppose the government requires the monopolist to charge a price that is equal to the socially optimal price. What is this price? What is the socially optimal level of output?

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Answer #1

Socially optimal price:P=MC

500-(1/2Q2)=20

1/2Q2=480

Q2=960

P2=500-(1/2)*960

P2=20

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