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Microeconomics Question from Walter E. Williams:Edit

Given two isolated markets supplied by a single monopolist, let the two corresponding demand functions be:

P_1=12-Q_1 and P_2=20-3Q_2.

The monopolist’s total cost function is:

TC=3+2(Q_1+Q_2).

(a) What will the prices be in each market?

(b) What will be the quantity sold in each market?

(c) What will be the total profits earned by the monopolist?

AnswerEdit

(a) Since we have two isolated markets, we can assume the monopolist will engage in price discrimination to maximize profits. As we are given both inverse demand functions, R_1=P_1Q_1=(12-Q_1)Q_1=12Q_1-Q_1^2, which implies MR_1=12-2Q_1. The same procedure gives MR_2=20-6Q_2. From the total cost function, we can derive MC=MC_1=MC_2=2.

By setting MR_1=MR_2=MC, we arrive at the solution for (b): 12-2Q_1=MR_1=MC=2, which implies Q_1=5; 20-6Q_2=MR_2=MC=2 implies Q_2=3.

With these market quantities, we can now determine respective market prices: P_1=12-5=7, P_2=20-3(3)=11.

(b) From (a) above: Q_1=5; Q_2=3.

(c) Profits will equal the aggregate revenues less total cost: \mathit{\Pi}^M=\sum_{i=1}^2 p_iq_i-TC=7(5)+11(3)-3-2(5+3)=35+33-19=49.


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