Question

TR = 120 Q – Q2

TC = 12 Q2 +30 Q + 10

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

Answer 1

By the definition of the marginal revenue:

$$MR=\dfrac{d}{dQ}(TR)=\dfrac{d}{dQ}(120Q-Q^2)=120-2Q.$$

By the definition the marginal cost:

$$MC=\dfrac{d}{dQ}(TC)=\dfrac{d}{dQ}(12Q^2+30Q+10)=24Q+30.$$

The firm maximizes its total profit when MR=MC:

$$120-2Q=24Q+30,$$ $$26Q=90,$$ $$Q=3.46$$