A monopolist has a marginal cost of $10 and no fixed cost.It faces the following inverse demand curve: p = 80 - q.The monopolist can engage in an advertising campaign that leads to a new inverse demand curve represented by p = 100 - q.What is the maximum amount that the monopolist is willing to spend in this campaign?
A) $650
B) $800
C) $1,000
D) It cannot be determined.

Question

Quizplus · Accepted Answer

Under the original demand curve, the monopolist's profit-maximizing output q* is determined by equating marginal revenue to marginal cost:
MR = 80 - 2q* = MC = 10
Thus, q* = 35, and the corresponding price is p* = 80 - 35 = 45.
The monopolist's profit is (p* - MC) x q* = (45 - 10) x 35 = $1,225.
If the monopolist invests in advertising, the new demand curve implies that MR = 100 - 2q*. The monopolist will again equate MR to MC to determine the profit-maximizing output, q'. We have:
100 - 2q' = 10
Thus, q' = 45, and the corresponding price is p' = 100 - 45 = 55.
The monopolist's profit under the new demand curve is (p' - MC) x q' = (55 - 10) x 45 = $2,025.
The maximum amount that the monopolist is willing to spend on advertising is equal to the increase in profit due to advertising. In this case, the increase in profit is $2,025 - $1,225 = $800. Therefore, choice (B) is the correct answer.

A Monopolist Has a Marginal Cost of $10 and No