Question

A firm has the following revenue and cost functions.

TR = 120 Q – Q²

TC =  1/2Q² +30 Q + 10

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

(Hint: use marginal revenue = marginal cost rule)       

Answer 1

$TR=120Q-Q^2$

$MR=120-2Q$

$TC=\frac {1}{2Q^2}+30Q+10$

$MC=\frac {-1}{Q}+30$

At the level at which the firm maximizes profit,

$MR=MC$

$120-2Q=\frac{-1}{Q}+30$

$2Q^2-90Q-1=0$

Solving quadratic equation above:

$Q=\frac{90+/-(8108)^\frac{1}{2}}{2\times2}$

$Q=45$

The quantity level Q=45