Question

suppose that the demand and total cost function of a monoplist are P=24-3Q and C=Q²+8Q respectively, finde the optimum quality ,price and profit on these levels.

Answer 1

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

MR=MC;

$Revenue=Price\times Demand$

$Revenue=(24-3Q)\times Q=24Q-3Q ^2$

$MR=24-6Q$

Cost function

C=Q²+8Q; MC=2Q+8

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

MC=MR; 2Q+8=$24-6Q$

8 Q=16; Q=2

But Price =24-3Q=24-6=18

Profit = Revenue- Cost

$Profit=(24Q-3Q ^2)-(Q ^2+8Q);$

$Profit=(24\times2-3\times2 ^2)-(2 ^2+8\times2)=16$

Optimal quantity=2 units

Optimal price=18

Optimal profit=16.