A monopolist sells a product in two separate markets at different prices; i.e., he price discriminates. The demand curves in these markets are: PA= 100 - QA and Pg = 60 - 0.5 QB His average cost function (ATC) is: ATC = Q + 100/Q where Q = QA + QB In your calculations, let it be defined as profit. (Hint: Find an equation for it. Then replace with QA+ Qe. Then, maximize with respect to QA and QB.) a) Use Cramer's Rule to find the profit maximizing quantities QA* and Q8*. (If you absolutely do not remember Cramer's rule, do it any way you can.) You do NOT have to check second derivative conditions for a maximum. b) Find the maximum profit, T* c) Find ATC*(Q) where Q*= QA*+ QB*
A monopolist sells a product in two separate markets at different prices; i.e., he
discriminates.
PA= 100 - QA and Pg = 60 - 0.5 QB His average cost function (
In your calculations, let it be defined as profit.
(Hint: Find an equation for it. Then replace with QA+ Qe. Then, maximize with respect to QA and QB.)
a) Use Cramer's Rule to find the profit maximizing quantities QA* and Q8*.
(If you absolutely do not remember Cramer's rule, do it any way you can.)
You do NOT have to check second derivative conditions for a maximum.
b) Find the maximum profit, T*
c) Find ATC*(Q) where Q*= QA*+ QB*
d) Graph the solution, as we did in HW6. You should have two graphs of demand curves
and one graph of cost curves. The following page has a sample set of graphs that you can use as a guide, with all labels and coordinates missing.
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