Question

Given : TC=Q2+2Q+2 and TR=8Q-3 then
A. calculate profit maximizing level of output
B. maximum profit

Answer 1

Solution:

Profit is TR minus TC

FWe compose the profit function and find its derivative:

$$Profit=TR-TC$$

$$Profit=8Q-3-Q^2-2Q-2$$

$$Profit=-Q^2+6Q-5$$

$$Profit'=-2Q+6$$

$$-2Q+6=0$$

$$Q=3$$

Answer: profit maximizing level of output  Q=3

B.

$$Profit=-3^2+6\times 3-5=4$$

Answer: maximum profit 4