Question

Suppose that the demand and the total cost functions of a monopolist are P=24-3Q and C=Q²+8Q respectively, find the optimum quantity, price and profit on these levels.

Answer 1

$P=MR=24-3Q$

Integrating MR yields;

$TR=24Q-\frac{3}{2}Q^2$

$TC=Q^2+8Q$

Differentiating TC yield;

$MC=2Q+8$

$MR=MC$

$2Q+8=24-3Q$

$5Q=16$

$Q=3.2 units$

Optimum quantity= 3.2units

 $P=24-3(3.2)$

$P=24-9.6$

$price=14.4 dollars$

$Profit=TR-TC$

$TR=(24(3.2)-\frac{3}{2}(3.2)^2)$

$TR=64.44 dollars$

$TC=35.84 dollars$

 $TC=3.2^2+8(3.2)=35.84$

 $Profit=64.44-35.84$

$Profit=28.6 dollars$