Question

given total cost function (TC)= Q2+2Q+2 and total revenue function (TR)= 8Q-3, then calculate the A. profit maximizing level of output? B. maximum profit?

Answer 1

A) Let's f[nd MC and MR:

$$MC=\dfrac{dTC}{dQ}=2Q+2,$$ $$MR=\dfrac{dTR}{dQ}=8.$$

The profit maximizing level of output occurs when MC=MR:

$$2Q+2=8,$$ $$2Q=6,$$ $$Q=3.$$

B) By the definition, maximum profit can be found as follows:

$$\pi=TR-TC,$$ $$\pi=8Q-3-(Q^2+2Q+2)=8Q-3-Q^2-2Q-2,$$ $$\pi=-Q^2+6Q-5.$$ $$\pi_{max}=-(3)^2+6\cdot3-5=\$4.$$