Question

Suppose that the (inverse) market demand curve for a new drug is given as follows: P = 400 - 10Q and their marginal revenues is MR = 400 - 20Q. Suppose also that there is a single supplier of the drug who faces a total cost curve as TC = 10 + 10Q and its marginal cost is MC = 20Q.

What are the monopolist's profit-maximizing output and price?

Answer 1

The monopolist's profit-maximizing output is 10 units and the price is $300.

Step-by-step explanation:

In order to find the monopolist's profit-maximizing output and price, we need to equate the marginal revenue (MR) and marginal cost (MC). By setting MR equal to MC, we can find the quantity at which the monopolist maximizes their profit.

In this case, the MR is given as MR = 400 - 20Q and the MC is given as MC = 20Q. Setting MR = MC, we can solve for the quantity:

400 - 20Q = 20Q → 400 = 40Q → Q = 10

So, the monopolist's profit-maximizing output is 10 units.

To find the price, we can substitute the quantity into the demand curve equation P = 400 - 10Q:

P = 400 - 10(10) = 400 - 100 = 300

Therefore, the monopolist's profit-maximizing output is 10 units and the price is $300.