Question

given the inverse demand function P = 40 - Q and a constant marginal cost of 10, what is the profit maximizing price?

please show step by step to solve

Answer 1

If the firm is a competitive firm:

Given the inverse demand function P = 40 - Q and marginal cost 10, the profit-maximizing price can be determined by equating P and MC.

40 - Q = 10

Q = 30.

Now put Q = 30 in the demand function P = 40 - 30 = 10.

So, if the firm is a competitive firm then the profit-maximizing price is 10.

If the firm is a monopolist:

For a monopolist, profit maximizes when MR = MC.

Given P = 40 - Q

TR = P * Q = 40Q - Q²

MR = 40 - 2Q

Now, 40 - 2Q = 10

2Q = 30

Q = 15.

So, P = 40 - 15 = 25.

So, if the firm is a monopolist then the profit-maximizing price is 25.