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.
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

Solution:

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

$$MC=TC'=1+4\times2Q=1+8Q$$

$$MR=TR'=5+3\times2Q=5+6Q$$

$$2Q=4$$

$$Q=2$$ $$Pr=TR-TC$$

$$Pr=5Q+3Q^2-Q-4Q^2=4Q-Q^2$$

$$Pr=4\times2-4$$

$$Pr=4$$

Answer Q=2, profit = 4