Only need the graphs 3) 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* 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.
Only need the graphs
3) A monopolist sells a product in two separate markets at different prices; i.e., he price
discriminates. The demand
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*
- 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.
Label the curves and lines in each graph. On the sample, I have labeled 19 points with plain numbers. Replace these numbers with the values from your solution. NOTICE that the graphs line up horizontally. For example, numbers 4, 11, and 16 should have the same value. Similarly, 3, 10, and 15 should have the same value.
Show the profit in each market on the graphs. (It is a rectangle.)
Calculate the profit in each market (show your calculations) and verify that it equals
QA = 22.5 units
QB = 5 units
Profit = $905
ATC* = 31.14
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