Monopoly Profit-Maximization by Analyzing a Table

Consider the following table with cost and revenue data for a hypothetical monopolist:

Quantity TFC TVC TC AVC ATC MC Price Total Revenue Marginal Revenue
0 5,000 0 5,000 – – – 38 0 –
100 5,000 3,000 8,000 30 80 30 37 3,700 37
200 5,000 5,000 10,000 25 50 20 36 7,200 35
300 5,000 6,000 11,000 20 36.67 10 35 10,500 33
400 5,000 6,800 11,800 17 29.50 8 34 13,600 31
500 5,000 8,000 13,000 16 26 12 33 16,500 29
600 5,000 10,000 15,000 16.67 25 20 32 19,200 27
700 5,000 13,000 18,000 18.57 25.71 30 31 21,700 25
800 5,000 16,500 21,500 20.63 26.88 35 30 24,000 23
900 5,000 22,000 27,000 24.44 30 55 29 26,100 21

Problem: What are the profit-maximizing output and price for the above monopolist? What is the profit at this output? What is the average profit at this output?

Solution: Like the purely competitive firm, a monopolist maximizes profits at the quantity where marginal cost and marginal revenue are equal, or where marginal cost comes closest to marginal revenue, as long as marginal cost does not exceed marginal revenue, marginal cost is not falling, and price exceeds average variable cost.

Applying the profit-maximizing rule, we conclude that the firm maximizes profits at

Quantity = 600 units
Price = $32
Profit (TR-TC) = $19,200-$15,000 = $4,200
Average Profit (TP / Q) = $7 ($4,200 / 600)

Video Explanation
For a video explanation of a monopoly firm’s profit maximization using a table, please watch:

Monopoly Profit-Maximization by Analyzing a Graph
In a table, we find the profit-maximizing output by identifying the point at which marginal cost and marginal revenue are equal, as long as marginal cost does not exceed marginal revenue, marginal cost is not falling, and price exceeds average variable cost.

The graph below indicates that at output Qpm, marginal cost equals marginal revenue in the upward sloping portion of the marginal cost curve. At this output, the price is Ppm. For a monopolist, the marginal revenue curve and the demand (price) curve are different. Therefore, marginal revenue and price at the profit-maximizing output are different. From the MC=MR point, go straight up to the demand curve in order to identify the profit-maximizing price. This price is greater than the firm’s average variable cost, so the company will not need to shut down. The price is also greater than the firm’s average total cost, so the company is making an economic (above-normal) profit. Because there are barriers to entry into this industry, it is possible that the firm can continue to make economic profits in the long run, as well.

Video Explanation

For a video explanation of a monopolist’s profit-maximizing quantity and price using a graph, please watch: