Read this chapter to learn the characteristics, workings, and effects of the monopoly model. Take a moment to read through the stated learning outcomes for this chapter of the text, which you can find at the beginning of each section. These outcomes should be your goals as you read through the chapter. Attempt the "Try It" problems at the end of each section before checking your answers.
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.
Because a monopoly firm has its market all to itself, it faces the market demand curve. Figure 10.2 "Perfect Competition Versus Monopoly" 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 10.2 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.
A firm's elasticity of demand with respect to price has important implications for assessing the impact of a price change on total revenue. Also, the price elasticity of demand can be different at different points on a firm's demand curve. In this section,
we shall see why a monopoly firm will always select a price in the elastic region of its demand curve.
Suppose the demand curve facing a monopoly firm is given by Equation 10.1, where Q is the quantity demanded per unit of time and P is the price per unit:
This demand equation implies the demand schedule shown in Figure 10.3 "Demand, Elasticity, and Total Revenue". Total revenue for each quantity equals the quantity times the price at which that quantity is demanded. The monopoly firm's total revenue curve is given in Panel (b). Because a monopolist must cut the price of every unit in order to increase sales, total revenue does not always increase as output rises. In this case, total revenue reaches a maximum of $25 when 5 units are sold. Beyond 5 units, total revenue begins to decline.
Figure 10.3 Demand, Elasticity, and Total Revenue
Suppose a monopolist faces the downward-sloping demand curve shown in Panel (a). In order to increase the quantity sold, it must cut the price. Total revenue is found by multiplying the price and quantity sold at each price. Total revenue, plotted in
Panel (b), is maximized at $25, when the quantity sold is 5 units and the price is $5. At that point on the demand curve, the price elasticity of demand equals −1.
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.
Suppose the firm in Figure 10.3 "Demand, Elasticity, and Total Revenue" sells 2 units at 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. In the next chapter, we will look at cases in which firms charge different prices to different customers).
Marginal revenue is less than price for the monopoly firm. Figure 10.4 "Demand and Marginal Revenue" shows the relationship between demand and marginal revenue, based on the demand curve introduced in Figure 10.3 "Demand, Elasticity, and Total Revenue". As always, we follow the convention of plotting marginal values at the midpoints of the intervals.
Figure 10.4 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 marginal revenue is …||then demand is …|
|zero,||unit price elastic.|
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 10.5 "The Monopoly Solution" 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 10.5 The Monopoly Solution
The monopoly firm maximizes profit by producing an output Qm at point G, where the marginal revenue and marginal cost curves intersect. It sells this output at price Pm.
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 10.6 "Computing Monopoly Profit". The average total cost (ATC) at an output of Qm units is ATCm. The firm's profit per unit is thus Pm - ATCm. Total profit is found by multiplying the firm's output, Qm, by profit per unit, so total profit equals Qm(Pm - ATCm) - the area of the shaded rectangle in Figure 10.6 "Computing Monopoly Profit".
Figure 10.6 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 ATCmPmEF.
Dispelling Myths About Monopoly
Three common misconceptions about monopoly are:
As Figure 10.5 "The Monopoly Solution" 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 Qm units of output for more than Pm, 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 10.6 "Computing Monopoly Profit". 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.
The Troll Road Company is considering building a toll road. It estimates that its linear demand curve is as shown below. Assume that the fixed cost of the road is $0.5 million per year. Maintenance costs, which are the only other costs of the road, are
also given in the table.
|Tolls per trip||$1.00||0.90||0.80||0.70||0.60||0.50|
|Number of trips per year (in millions)||1||2||3||4||5||6|
|Maintenance cost per year (in millions)||$0.7