Question

Find the Profit Maximizing output and total profit from the information

Demand Function :Q=20-0.4P and 

Cost function:TC (C) =25+Q+0.2Q²

Answer 1

At optimal point, marginal revenue is equal to marginal cost.

MR=MC;

$Revenue=Price\times Demand$

$Revenue=(50-2.5Q)\times Q=50Q-2.5Q ^2$

$MR=50-5Q$

Cost function

C=25+Q+0.2Q²; MC=1+0.4Q

So, equate MC and MR to find optimal quantity and price.

MC=MR; 1+0.4Q=$50-5Q$

5.4 Q=49; Q=9.07 units

But Price =50-2.5Q=50-22.67=27.31

Profit = Revenue- Cost

$Profit=(50Q-2.5Q ^2)-(25+0.2Q ^2+Q);$

$Profit=(50\times9.07-2.5\times9.07 ^2)-(25+0.2\times9.07 ^2+9.07)=197.3$

Optimal quantity=9.07 units

Optimal price=27.31

Optimal profit=197.3.