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

QuantityTFCTVCTCAVCATCMCPriceTotal RevenueMarginal Revenue
05,00005,000380
1005,0003,0008,000308030373,70037
2005,0005,00010,000255020367,20035
3005,0006,00011,0002036.67103510,50033
4005,0006,80011,8001729.5083413,60031
5005,0008,00013,0001626123316,50029
6005,00010,00015,00016.6725203219,20027
7005,00013,00018,00018.5725.71303121,70025
8005,00016,50021,50020.6326.88353024,00023
9005,00022,00027,00024.4430552926,10021

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.

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

Monopoly Profit-Maximization by Analyzing a GraphIn 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.

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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.

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Video Explanation

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