Question

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?

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