Answer to Question #161720 in Economics of Enterprise for Tharindu Jayasinghe

Question

A firm has the following revenue and cost functions. TR = 60 Q – Q^2

TC = 1 /2 Q^2 +30Q + 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:

$MC=\dfrac{d}{dQ}(TC)=\dfrac{d}{dQ}(0.5Q^2+30Q+30)=Q+30.$

The firm maximizes its total profit when MR=MC:

$60-2Q=Q+30,$ $3Q=30,$ $Q=10.$