A monopolist faces a demand curve given by: P = 105 - 3Q, where P is the price of the good and Q is the quantity demanded. The marginal cost of production is constant and is equal to $15. There are no fixed costs of production. How much output should the monopolist produce in order to maximize profit?

Question

Business

Bryan Curry

8 December, 07:16

A monopolist faces a demand curve given by: P = 105 - 3Q, where P is the price of the good and Q is the quantity demanded. The marginal cost of production is constant and is equal to $15. There are no fixed costs of production. How much output should the monopolist produce in order to maximize profit?

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Answers (1)

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Brenda Hayes · Answer 1

Answer: 15

Explanation:

For profit to be maximized by a monopolist, the marginal revenue and marginal cost must be gotten.

P = 105-3Q

MC = 15

Since total revenue is price * quantity, TR = P*Q = (105-3Q) Q

= 105Q-3Q^2

MR = 105-6Q

Since we've gotten marginal revenue and marginal cost, we equate both together.

MR=MC

105-6Q = 15

6Q = 105-15

6Q=90

Divide both side by 6

6Q/6 = 90/6

Q = 15

The quantity that will maximise profit is 15