Microeconomics Question from Walter E. Williams:[]
Given two isolated markets supplied by a single monopolist, let the two corresponding demand functions be:
and .
The monopolist’s total cost function is:
.
(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?
Answer[]
(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, , which implies . The same procedure gives . From the total cost function, we can derive .
By setting , we arrive at the solution for (b): , which implies ; implies .
With these market quantities, we can now determine respective market prices: , .
(b) From (a) above: ; .
(c) Profits will equal the aggregate revenues less total cost: .
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