Answer to Question #312220 in Microeconomics for Pat

Question

The Inquiry Club at Jefferson University has compiled a book that exposes the private lives of many of the professors on campus. Economics majors in the club estimate that total revenue from sales of the book is given by the equation:

TR =120Q - 0.1Q³

a. Over what output range is demand elastic?

b. Initially, the price is set at $71.60. To maximize total revenue, should the price be increased or decreased? Explain.

Answer 1

a)    Over what output range is demand elastic?

By taking derivative of TR

dTR/dQ=120Q-0.1Q³

0       =    120 – 0.3Q²

120   =    0.3Q²

Q²      =    120/0.3          

Q²      =    400

Q       =    20

We know that

TR   =   PxQ

P   =   TR/Q

P   =   120 – 0.1Q²

P   =   120 – 0.1(20)²

P   =   120 – 0.1(400)

P   =   120 - 40

P   =   80

Q = 20 demand is elast

b)   Initially, the price is set at $71.6. To maximize total revenue should the price be increased or decreased? Explain

If price is 80, then TR

TR      =   120(20) – 0.1(20)²

TR      =   2,400 – 800

TR      =   1,600

If price is set to 71.6, then TR becomes

TR      =    20 x 71.6

TR      =    143

This clearly indicate that price should be increased from 71.6 to 80 in order to get maximum Total revenue