Question

A firm has the following revenue and cost functions.

TR = 60 Q - Q2

TC = 12 Q2 +30 Q + 30

Determine the quantity level at which the firm maximizes its total profit.

(Hint: use marginal revenue = marginal cost rule)

Answer 1

By the definition of the marginal revenue:

$$MR=\dfrac{d}{dQ}(TR)=\dfrac{d}{dQ}(60Q-Q^2)=60-2Q.$$

By the definition the marginal cost:

$$MC=\dfrac{d}{dQ}(TC)=\dfrac{d}{dQ}(12Q^2+30Q+30)=24Q+30.$$

The firm maximizes its total profit when MR=MC:

$$60-2Q=24Q+30,$$ $$26Q=30,$$ $$Q=1.15$$