Question

The market price in a perfect competetive industry is P =RM 10. Suppose that the total cost function of an individual firm in the industry is given by: TC= 100+ 5Q+ 0.02Q²

a) at what price and output would the firm maximize its profit?
b) what is the firm total profit at the profit maximizing price?

Answer 1

a) at what price and output would the firm maximize its profit?

A firm in a perfect competitive firm will maximize their revenue when:

$\text{MR=MC}$

The marginal revenue of the firm will be as follows:

$\blue{\text{Revenue=Price * Quantity}}$

$\text{Revenue}=10Q$

The marginal revenue will therefore be:

$\text{Marginal revenue}=\dfrac{\delta\text{Revenue}}{\delta Q}=10$

The marginal cost on the other hand will be:

$\text{Marginal cost}=\dfrac{TC}{Q}=5+0.04Q$

Equating the MR=MC

$10=5+0.04Q$

$Q=\dfrac{10-5}{0.04}=125$

The profit maximizing quantity is 125.

The profit maximizing price will be equal to $10.

b) what is the firm total profit at the profit maximizing price?

The total profit will be equal to:

$\text{Profit function}=10-5-0.04Q$

$\text{Profit function}=10-5-0.04\times 125$

$\text{Profit function}=0$

The total profit at the price of 10 will be equal to 0.