Answer to Question #142338 in Finance for Mr. Dinesh Pal Singh

Question

39. The Inquiry Club at Jefferson University has compiled a book, which expose the private lives of many of the professors on campus. Economics majors in the club estimate that total revenue from sales of books is given by the equation
TR = 120Q – 0.1Q3
i) Over what output range is demanded elastic?
ii) Initially, the price is set at $71.60. To maximize total revenue, should the price be increased or decreased? Explain.

Answer 1

i) Total revenue (TR) is maximized when $MR = TR'(Q) = 120 - 0.3Q^2 = 0,$

Q = 20.

So, the demand is elastic over the output of 20 units.

ii) The demand equation is $P = 120 - 0.1Q^2,$ so if the price is set at $71.60, then:

$120 - 0.1Q^2 = 71.6,$

Q = 22 units, the demand is elastic at this level of output.

So, to maximize total revenue the price should be decreased.