Question

For the following total-revenue and total-cost functions of a firm:

TR = 22Q - 0.5Q ^ 2 ,

TC=\ Q^ 2 -8.5Q^ 2 +50Q+90

(a) Determine the level of output at which the firm maximizes its total profit. (b) Determine the

Answer 1

A) $TR=22Q-0.5Q^2$

Differentiating TR yields;

$TR'=MR=22-Q$

$TC=Q^2-8.5Q^2+50Q+90$

$TC=-7.5Q^2+50Q+90$

Differentiating TC yields;

$TC'=MC=-15Q+50$

The level of output at which the firm maximizes its total profit is;

$MR=MC$ MR=MC

$22-Q=-15Q+50$

$Q+15Q=50-22$

$16Q=28$

$Q=28/16$

$Q=1.75 units$