Question

Consider a monopolist whose total cost function is TC = 20 + 5Q + 0.5Q² and whose marginal cost function is MC = 5 + Q. The demand function for the firm's good is P = 80 - 0.25Q. The firm optimizes by producing the level of output that maximizes profit or minimizes loss. If the firm uses a uniform pricing strategy, then the firm will:

Answer 1

The monopolist will equate marginal revenue to marginal cost to find the profit-maximizing output level and charge a uniform price based on the demand curve at that output level. If this price exceeds average cost, the monopolist earns positive profits.

Step-by-step explanation:

Profit Maximization for a Monopolist

A monopolist determines the profit-maximizing level of output by setting marginal revenue (MR) equal to marginal cost (MC). The given total cost function TC = 20 + 5Q + 0.5Q² can be used to derive the MC function, which is given as MC = 5 + Q. Given the demand function P = 80 - 0.25Q, we can calculate the marginal revenue function by doubling the slope of the demand function, leading to MR = 80 - 0.5Q. By equating MR to MC, the monopolist can find the quantity that maximizes profit. This quantity, when plugged into the demand function, gives the price the monopolist will charge.

The firm uses a uniform pricing strategy and will therefore charge every customer the same price, which is the price corresponding to the quantity where MR = MC on the demand curve. If this price is greater than the average cost, then the firm will earn positive profits.