9.2: The Monopoly Model

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Learning Objective

Explain the relationship between price and marginal revenue when a firm faces a downward-sloping demand curve.
Explain the relationship between marginal revenue and elasticity along a linear demand curve.
Apply the marginal decision rule to explain how a monopoly maximizes profit.

Analyzing choices is a more complex challenge for a monopoly firm than for a perfectly competitive firm. After all, a competitive firm takes the market price as given and determines its profit-maximizing output. Because a monopoly has its market all to itself, it can determine not only its output but its price as well. What kinds of price and output choices will such a firm make?

We will answer that question in the context of the marginal decision rule: a firm will produce additional units of a good until marginal revenue equals marginal cost. To apply that rule to a monopoly firm, we must first investigate the special relationship between demand and marginal revenue for a monopoly.

Monopoly and Market Demand

Because a monopoly firm has its market all to itself, it faces the market demand curve. Figure 9.2 compares the demand situations faced by a monopoly and a perfectly competitive firm. In Panel (a), the equilibrium price for a perfectly competitive firm is determined by the intersection of the demand and supply curves. The market supply curve is found simply by summing the supply curves of individual firms. Those, in turn, consist of the portions of marginal cost curves that lie above the average variable cost curves. The marginal cost curve, MC, for a single firm is illustrated. Notice the break in the horizontal axis indicating that the quantity produced by a single firm is a trivially small fraction of the whole. In the perfectly competitive model, one firm has nothing to do with the determination of the market price. Each firm in a perfectly competitive industry faces a horizontal demand curve defined by the market price.

Figure 9.2 Perfect Competition Versus Monopoly Panel (a) shows the determination of equilibrium price and output in a perfectly competitive market. A typical firm with marginal cost curve MC is a price taker, choosing to produce quantity q at the equilibrium price P. In Panel (b) a monopoly faces a downward-sloping market demand curve. As a profit maximizer, it determines its profit-maximizing output. Once it determines that quantity, however, the price at which it can sell that output is found from the demand curve. The monopoly firm can sell additional units only by lowering price. The perfectly competitive firm, by contrast, can sell any quantity it wants at the market price.

Contrast the situation shown in Panel (a) with the one faced by the monopoly firm in Panel (b). Because it is the only supplier in the industry, the monopolist faces the downward-sloping market demand curve alone. It may choose to produce any quantity. But, unlike the perfectly competitive firm, which can sell all it wants at the going market price, a monopolist can sell a greater quantity only by cutting its price.

Suppose, for example, that a monopoly firm can sell quantity Q₁ units at a price P₁ in Panel (b). If it wants to increase its output to Q₂ units—and sell that quantity—it must reduce its price to P₂. To sell quantity Q₃ it would have to reduce the price to P₃. The monopoly firm may choose its price and output, but it is restricted to a combination of price and output that lies on the demand curve. It could not, for example, charge price P₁ and sell quantity Q₃. To be a price setter, a firm must face a downward-sloping demand curve.

Demand and Marginal Revenue

In the perfectly competitive case, the additional revenue a firm gains from selling an additional unit—its marginal revenue—is equal to the market price. The firm’s demand curve, which is a horizontal line at the market price, is also its marginal revenue curve. But a monopoly firm can sell an additional unit only by lowering the price. That fact complicates the relationship between the monopoly’s demand curve and its marginal revenue.

Examine figure 9.3 when firm sells 2 units it charges a price of $8 per unit. Its total revenue is $16. Now it wants to sell a third unit and wants to know the marginal revenue of that unit. To sell 3 units rather than 2, the firm must lower its price to $7 per unit. Total revenue rises to $21. The marginal revenue of the third unit is thus $5. But the price at which the firm sells 3 units is $7. Marginal revenue is less than price.

To see why the marginal revenue of the third unit is less than its price, we need to examine more carefully how the sale of that unit affects the firm’s revenues. The firm brings in $7 from the sale of the third unit. But selling the third unit required the firm to charge a price of $7 instead of the $8 the firm was charging for 2 units. Now the firm receives less for the first 2 units. The marginal revenue of the third unit is the $7 the firm receives for that unit minus the $1 reduction in revenue for each of the first two units. The marginal revenue of the third unit is thus $5. (In this chapter we assume that the monopoly firm sells all units of output at the same price)

Marginal revenue is less than price for the monopoly firm. Figure 9.3 shows the relationship between demand and marginal revenue.

Figure 9.3 Demand and Marginal Revenue The marginal revenue curve for the monopoly firm lies below its demand curve. It shows the additional revenue gained from selling an additional unit. Notice that, as always, marginal values are plotted at the midpoints of the respective intervals.

When the demand curve is linear, as in Figure 9.3, the marginal revenue curve can be placed according to the following rules: the marginal revenue curve is always below the demand curve and the marginal revenue curve will bisect any horizontal line drawn between the vertical axis and the demand curve. To put it another way, the marginal revenue curve will be twice as steep as the demand curve.

The marginal revenue and demand curves in Figure 9.3 follow these rules. The marginal revenue curve lies below the demand curve, and it bisects any horizontal line drawn from the vertical axis to the demand curve. At a price of $6, for example, the quantity demanded is 4. The marginal revenue curve passes through 2 units at this price. At a price of 0, the quantity demanded is 10; the marginal revenue curve passes through 5 units at this point.

Monopoly Equilibrium: Applying the Marginal Decision Rule

Profit-maximizing behavior is always based on the marginal decision rule: Additional units of a good should be produced as long as the marginal revenue of an additional unit exceeds the marginal cost. The maximizing solution occurs where marginal revenue equals marginal cost. As always, firms seek to maximize economic profit, and costs are measured in the economic sense of opportunity cost.

Figure 9.4 shows a demand curve and an associated marginal revenue curve facing a monopoly firm. The marginal cost curve is like those we derived earlier; it falls over the range of output in which the firm experiences increasing marginal returns, then rises as the firm experiences diminishing marginal returns.

Figure 9.4 The Monopoly Solution The monopoly firm maximizes profit by producing an output Q_m at point G, where the marginal revenue and marginal cost curves intersect. It sells this output at price P_m.

To determine the profit-maximizing output, we note the quantity at which the firm’s marginal revenue and marginal cost curves intersect (Q_m in Figure 9.4). We read up from Q_m to the demand curve to find the price P_m at which the firm can sell Q_m units per period. The profit-maximizing price and output are given by point E on the demand curve.

Thus we can determine a monopoly firm’s profit-maximizing price and output by following three steps:

Determine the demand, marginal revenue, and marginal cost curves.
Select the output level at which the marginal revenue and marginal cost curves intersect.
Determine from the demand curve the price at which that output can be sold.

Figure 9.5 Computing Monopoly Profit A monopoly firm’s profit per unit is the difference between price and average total cost. Total profit equals profit per unit times the quantity produced. Total profit is given by the area of the shaded rectangle *ATC*_mP_mEF.

Once we have determined the monopoly firm’s price and output, we can determine its economic profit by adding the firm’s average total cost curve to the graph showing demand, marginal revenue, and marginal cost, as shown in Figure 9.5. The average total cost (ATC) at an output of Q_m units is ATC_m. The firm’s profit per unit is thus P_m – ATC_m. Total profit is found by multiplying the firm’s output, Q_m, by profit per unit, so total profit equals Q_m(P_m – ATC_m)—the area of the shaded rectangle in Figure 9.5.

Heads Up!

Dispelling Myths About Monopoly

Three common misconceptions about monopoly are:

Because there are no rivals selling the products of monopoly firms, they can charge whatever they want.
Monopolists will charge whatever the market will bear.
Because monopoly firms have the market to themselves, they are guaranteed huge profits.

As Figure 9.4 shows, once the monopoly firm decides on the number of units of output that will maximize profit, the price at which it can sell that many units is found by “reading off” the demand curve the price associated with that many units. If it tries to sell Q_m units of output for more than P_m, some of its output will go unsold. The monopoly firm can set its price, but is restricted to price and output combinations that lie on its demand curve. It cannot just “charge whatever it wants.” And if it charges “all the market will bear,” it will sell either 0 or, at most, 1 unit of output.

Neither is the monopoly firm guaranteed a profit. Consider Figure 9.5 Suppose the average total cost curve, instead of lying below the demand curve for some output levels as shown, were instead everywhere above the demand curve. In that case, the monopoly will incur losses no matter what price it chooses, since average total cost will always be greater than any price it might charge. As is the case for perfect competition, the monopoly firm can keep producing in the short run so long as price exceeds average variable cost. In the long run, it will stay in business only if it can cover all of its costs.

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