1) y = – x3 + 8×2- 5x + 3
a) Graph “y”. Be sure to label all maximum and minimum points and
intercepts.
b) Graph the slope of “y” directly below y. Line up the graphs so that the x
values of the two graphs coincide.
(11)
(112)
Econ 3410
FINAL
SPRING 2020
Professor Rones page 2
2) y = ( 2×3 – 8x)4
Find dy/dx when X = – 72
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*
