Question

Suppose a firm has its TR and TC functions estimated as follows:

TR = 300Q-3Q2

TC = 500 + 50Q + 2Q2

Find (a) profit function of the firm, (b) the quantity of output (Q) that maximizes the firm's profit.

Answer 1

a)

$PF=TR-TC=-500+250Q-5Q^2,$

b)

$PF'=250-10Q,$

$Q=25,$

$PF=2625.$