Question

Suppose that monopolist has a demand function p1= 100-Q1 , p1=80-Q1 , C=6Q1+6Q2. How much should be sold in the market? What are corresponding prices? Find total profit?

Answer 1

$$MR_1=100-Q_1,$$

$$MR_2=80-Q_2,$$

Set $MR_1=MR_2=MC$

$$C=6Q_1+6Q_2=6(Q_1+Q_2)$$

$Q_1+Q_2=Q$

$$C=6Q$$

$$MC=6$$

$$MR_1=6=>100-Q_1=6$$

$$Q_1=94$$

$$p_1=100-94=6$$

$$MR_2=6=>80-Q_2=6$$

$$Q_2=74$$

$$p_2=80-74=6$$

Profits are the difference between the sum of the revenues generated in both market segments and the total cost of producing the output:

$$\pi=p_1(MR_1)+p_2(MR_2)-C$$

$$\pi=6(6)+6(6)-6(6+6)=0$$