Suppose a monopolist faces the demand curve P = 164 - 1Q. The monopolist's marginal costs are a constant $22 and they have fixed costs equal to $132.

Given this information, what will the profit-maximizing price be for this monopolist? Round answer to two decimal places.

Let us determine the total revenue function.

[Math Processing Error]TR=P×QTR=(164−1Q)×QTR=164Q−Q2

Next, we determine the marginal revenue. It is the derivative of the total revenue function.

[Math Processing Error]TR=164Q−Q2MR=164−2Q

At maximum profit, the output produces where the marginal revenue is equal to the marginal cost. Let us determine the profit-maximizing quantity (Q).

[Math Processing Error]MR=MC164−2Q=222Q=164−22=142Q=142÷2Q=71

We substitute the profit-maximizing quantity to the demand function. Let us compute the profit-maximizing price.

[Math Processing Error]P=164−1QP=164−1(71)P=93.00(roundedofftotwodecimalplaces)

The profit-maximizing price for the monopolist is $93.00.