The demand for a monopolist's output is 10,000 divided by the square of the price it charges.The monopolist produces at a constant marginal cost of $5.If the government imposes a sales tax of $10 per unit on the monopolist's output, the monopolist price will rise by
A)$5.
B)$10.
C)$20.
D)$12.
E)None of the above.

Question

Quizplus · Accepted Answer

The monopolist's demand function can be written as:
Q = 10,000 / P^2
where Q is the quantity demanded and P is the price.
The monopolist's marginal revenue (MR) is the derivative of the demand function, which is:
MR = 20,000 / P^3
Setting MR equal to MC (marginal cost) gives us the monopolist's profit-maximizing price:
20,000 / P^3 = 5
P = (20,000 / 5)^(1/3) = 20
So the monopolist's price without the sales tax is $20.
When the government imposes a sales tax of $10 per unit, the monopolist's effective marginal cost increases by $10, so the new profit-maximizing price is:
20,000 / (P+10)^3 = 15
Solving for P gives:
P = 20.93
So the monopolist's new price is $20.93.
The price increase is therefore:
$20.93 - $20 = $0.93, which is closest to $1, or choice C.

The Demand for a Monopolist's Output Is 10,000 Divided by the Square