Question

A firm faces the following demand curve for one of its products: Q = 50P^-2 I^1.3 R^.0001 A^.2 where Q=output, P=own price, I=income, R =price of related good, and A=Advertising Expenditures The firm has average monthly sales from this product of $1,000,000, it should set quarterly Advertising Budget at __________________. Correct! $100,000 $300,000 $1,000,000 monopolies shouldn't advertise The correct answer is 100,000 but could someone show how you get that? And why you don't times the 100,000 by 3 because it is quarterly advertising?

Answer 1

Demand function is Q = 50P^-2 I^1.3 R^.0001 A^.2

Advertising elasticity = 0.2

Price elasticity = -2

Advertising elasticity / price elasticity =0.2/2 = 1/10.

Optimum advertising expenditure requires advertising / sales revenue = Advertising elasticity / price elasticity

Hence we have advertising / 1,000,000 = 1/10

This gives advertising expenditure = 1,000,000/10 = 100,000

(I presume the advertising is done on quarterly basis in this question. Perhaps because firms do not advertise monthly in general since it then raises the cost of production and also advertising takes time to reach and affect consumers)