In a market with the inverse demand curve P = 10 - Q, Brand X is a monopolist with no fixed costs and with a marginal cost of $2.If marginal cost rises to $4, by how much will the price of Brand X rise?
A)$2.
B)$1.
C)$3.
D)$0; the firm is already charging the monopoly price.
E)None of the above.

Question

Quizplus · Accepted Answer

To find the monopoly price, we need to set marginal revenue equal to marginal cost. The marginal revenue for a monopolist is given by the derivative of the inverse demand curve.

MR = d/dQ (P) = d/dQ (10 - Q) = 10 - 2Q

Setting MR = MC:

10 - 2Q = 2

Q = 4

So, the monopoly price is P = 10 - 4 = $6.

If the marginal cost increases to $4, the monopoly price will increase. The new equilibrium quantity is found by setting the new marginal cost equal to the new marginal revenue:

10 - 2Q = 4

Q = 3

The new monopoly price is P = 10 - 3 = $7. So, the price of Brand X will rise by $1. Thus, the correct answer is (B).

In a Market with the Inverse Demand Curve P =