Question

Given the demand function P=150 -0.5Q and the total Cost function TC=8Q

A. Maximize profit for a monopoly firm

B. Maximize profit for a perfectly competitive firm

C. Calculate the profit that monopolist lost to act as a perfectly competitive firm

Answer 1

A. Maximize profit for a monopoly firm

The profit for the monopoly will be at the point where MR=MC

Given the above demand curve, and we know that the marginal revenue is twice as the demand curve, the marginal revenue is equal to

$MR=150-Q$

The marginal cost from the cost function is

$MC=8$

Equating MC and MR and solving for Q, we get

$150-Q=8\\[0.3cm] Q=142$

The price that the monopoly will charge is equal to

$P=150-0.4(142)\\[0.3cm] P=\$79$

The profit for the firm is equal to

$\rm Profit=(76-8)142=\$10,082$

B. Maximize profit for a perfectly competitive firm

For a perfectly competitive firm, profit will be maximized when P=MC. Therefore

$150-0.5Q=8\\[0.3cm] 0.5Q=142\\[0.3cm] Q=284$

The maximum profit for perfectly competitive firm is equal to

$\rm Profit=(8-8)84=\$0$

C. Calculate the profit that monopolist lost to act as a perfectly competitive firm

The profit lost by the monopolist is equal to

$0-10082=\$10,082$