Question

Suppose that Total revenue of the firm is
TR = 5Q + 3Q2 and TC is TC = Q + 4Q2.
Obtain the quantity that maximizes profit and hence maximum profit.

Answer 1

Maximum profit occurs when:

$$MR = MC$$

and

$$MR = 5 + 6Q$$ $$MC = 1+ 8Q$$

For maximum profit:

$$5+6Q =1+8Q ;$$

$$5-1 =8Q-6Q$$

$$2Q =4$$

$$\therefore Q=2$$

Maximum profit = TR- TC

$$5(10)+3(2^2 )- (2+4(2^2))=$$

$$62-18=44$$ $$Max Profit = 44$$