Question

Consider a monopoly with the following Inverse Demand and Marginal Cost/Supply Curves:

Inverse Demand: P = 40 - 1.5Q

Inverse Supply: P = 4 + 1.5Q

What is the price that a monopoly will charge in this market in order to maximize its profit?

Answer 1

A monopoly will charge a price of $21.25 in order to maximize its profit.

Step-by-step explanation:

A monopoly maximizes its profit by setting the quantity where marginal revenue (MR) equals marginal cost (MC).

In this case, the inverse demand curve is given by P = 40 - 1.5Q and the inverse supply curve is given by P = 4 + 1.5Q.

To find the profit-maximizing price and quantity, we need to equate MR and MC:

MR = change in total revenue / change in quantity = P x (1 - 1.5 / 40 - 1.5Q) = 40 - 3Q

MC = change in total cost / change in quantity = change in (4 + 1.5Q) / change in Q = 1.5

Setting MR = MC, we have 40 - 3Q = 1.5. Solving for Q, we get Q = 12.5

Substituting Q = 12.5 into the inverse demand curve, we find P = 40 - 1.5(12.5) = 21.25

Therefore, the monopoly will charge a price of $21.25 in order to maximize its profit.