A profit-maximizing monopolist faces a downward-sloping demand curve that has a constant elasticity of 4.The firm finds it optimal to charge a price of $24 for its output.What is its marginal cost at this level of output?

A) $55
B) $18
C) $48
D) $10
E) $24

We know that the demand curve has a constant elasticity, so we can use the formula:

E = (% change in quantity demanded) / (% change in price) = (dQ/Q) / (dP/P)

where E is the elasticity, Q is the quantity demanded, and P is the price.

We also know that the firm is maximizing profit, which means that it is producing at the point where marginal revenue (MR) equals marginal cost (MC). Therefore, we can use the following formula for Marginal Revenue:

MR = P (1 + 1/E)

At the profit-maximizing level of output, we have P = $24, and E = 4.

Solving for MR, we get:

MR = $24 (1 + 1/ 4)

Next, we need to find MC at this level of output. We know that MR = MC, so:

$24 (1 + 1/ 4) = MC

Solving for MC, we get:

MC = $18

Therefore, the answer is B) $18.