Question

A monopoly’s demand function is Q=1280p-2A0.5, where Q is it s quantity, p is its price and A is the level of advertising. Its constant marginal and average cost of production is 8, and its cost of a unit of advertising is 1. What are the firm’s profit-maximizing price, quantity and level of advertising?

Answer 1

This means that, as p increases, Q increases. So, in order to sell more, raise the price.

At the same time, when Advertisement increases, q decreases. That, is to sell more, decrease the advertisement.

(This function certainly do not look like a demand function)

Revenue,

Profit,

Last equation is 0 only when either A =0 or 16 = 2p (that is, p=8)

If A = 0,

If 16=2p (that is p=8),

But P=8 is clearly not a point of maximum. (It could be a minimum or point of inflection)

Therefore, this equation do not have a maximum. You can keep on increasing the profit (theoretically) by increasing p (and thereby Q)