180 • Chapter 5 • Competitors and Competition
TABLE 5.4
Profits and Number of Firms Under Monopolistic Competition
|
Before Entry |
After Entry |
Number of firms |
10 |
20 |
Fixed costs per firm |
$120 |
$120 |
Marginal cost |
$10 |
$10 |
Price |
$20 |
$20 |
Market demand |
240 units |
240 units |
Sales per firm |
24 units |
12 units |
Profit per firm |
$120 |
0 |
|
|
|
This example shows that when product differentiation enables sellers to set prices well above marginal costs, new entrants will steal market share from incumbents and drive down incumbents’ profits, even if price remains unchanged. If entry intensifies price competition, profits would fall even faster and there would ultimately be fewer than 20 firms in the market.
In Chamberlin’s classic model of competition in differentiated goods markets, the amount of entry is thought to be excessive because it drives up fixed costs. But this simple analysis is misleading, for it fails to consider that entrants increase the variety of products and services in the market by staking out new locations, flavors, product styles, and so on. If consumers place a high value on variety, then entry in monopolistically competitive markets will not be excessive. To continue our earlier example, if Subway were to open a shop in the center of Lineville, many consumers would enjoy lower travel costs.
We now turn our attention to what is perhaps the most complex of market structures, oligopoly.
OLIGOPOLY
In perfectly competitive and monopolistically competitive markets, sellers do not believe that their price or output will affect rivals’ prices or output. This is a good description of markets with many sellers. In a market with only a few sellers, however, it is more reasonable to expect that the pricing and output choices of any one firm will affect rivals’ pricing and output and, as a result, will have a tangible impact on the overall market price and output. A market in which the actions of individual firms materially affect the overall market is called an oligopoly.
Economists have produced many models of oligopolistic markets. A central element of these models is the careful consideration of how firms respond to each other’s choices. This is illustrated by considering two of the oldest and most important oligopoly models—Cournot quantity competition and Bertrand price competition.
Cournot Quantity Competition
One of the first models of oligopoly markets was developed by Augustin Cournot in 1835.12 Cournot initially considered a market in which there were only two firms, firm 1 and firm 2. These might be two producers of DRAM chips, such as Hynix (firm 1) and Micron (firm 2). These firms produce identical goods, so that they are forced to charge
Oligopoly • 181
EXAMPLE 5.4 CAPACITY COMPETITION IN THE U.S. BEEF PROCESSING INDUSTRY13
The year 2007 was a difficult one for the American cattle slaughter industry. The four industry leaders—Tyson, Cargill, National Beef, and JBS Swift—faced the twin problems of falling demand and rising costs. In the early 2000s, the industry slaughtered 800,000 head annually; today that figure has fallen below 700,000. At the same time, feed prices have increased due to rising demand for corn-based ethanol. By mid2007, Tyson et al. were losing $10 on every head of cattle. That was before competitive forces stepped in to make things worse.
In May 2007, Latin America’s largest beef processor, JBS SA, purchased Swift & Co. to form JBS Swift, the world’s largest beef processor. Swift has been a fixture in the U.S. meat industry ever since Gustavus Swift hired Andrew Chase in 1878 to design a ventilated railway car. JBS was a relative newcomer, starting operations in Brazil in 1953. JBS became an industry leader in the 1970s, when it launched an aggressive program to acquire existing slaughterhouses in Brazil and Argentina. JBS’s acquisition binge never slowed down. In January 2007, it acquired a slaughterhouse operated by Swift in Buenos Aires. But the acquisition of the entire Swift & Co. was altogether of another magnitude. In explaining its motives for acquiring Swift’s North American operations, JBS invoked the usual economies of scale mantra, though the two companies had no geographic overlap and little opportunity to exploit synergies.
It did not take long for JBS to make its presence felt in the U.S. market. In early September 2007, JBS added a second shift to its Greeley, Colorado, processing plant, increasing capacity by 2000 head per day. With the industry now flush with excess capacity, beef packer margins fell to minus $70 per head. Market analysts lowered their forecasts for profits and share prices tumbled. Unless capacity was withdrawn from the industry, the outlook would remain bleak.
Tyson was the first to blink. Having seen its share price cut in half in just less than a year, in January 2008 Tyson closed its Emporia, Kansas, plant, pulling 4000 head of capacity from the market. The Emporia plant seemed like a good candidate for closure, as its location hundreds of miles from major ranches made for some costly logistics. The move was hailed by industry analysts. One of these analysts, from Credit Suisse, observed, “Tyson is demonstrating leadership by doing the right thing for its business and for the industry” but also noted, “Perhaps the biggest winner here is JBSSwift.” Indeed, within a year JBS Swift acquired National Beef Packing and Smithfield, the fourth and fifth largest U.S. beef packers, respectively. In just one year, JBS had become the market share leader and had established a reputation for growth, even if it meant that other beef packers would have to cut back to maintain industry prices.
the same prices. In Cournot’s model, the sole strategic choice of each firm is the amount they choose to produce, Q1 and Q2. Once the firms are committed to production, they set whatever price is necessary to “clear the market.”This is the price at which consumers are willing to buy the total production, Q1 1 Q2. The intuition behind this assumption is that because both firms are committed to production, their incremental costs are zero. Thus, if either one is unable to sell all its output, it will lower price until it is able to do so. The market price is that which enables both firms to sell all their output.
We will analyze the output decisions of Hynix and Micron facing specific demand and cost functions. Suppose that both Hynix and Micron have the following total costs of production:
TC1 5 10Q1
TC2 5 10Q2
182 • Chapter 5 • Competitors and Competition
In other words, both firms have constant marginal costs of $10 per unit, just as in the case of monopoly discussed earlier. Thus, if Q1 5 Q2 5 10, then TC1 5 TC2 5 100. As in our monopoly example, let market demand be given by P 5 100 2 Q, where Q is the market quantity and equals Q1 1 Q2. With this demand curve, the market price falls if either firm tries to increase the amount that it sells. For example, if Hynix and Micron both produce 10 units (i.e., Q1 5 Q2 5 10), then P 5 $80. If they both produce 20 units (i.e., Q1 5 Q2 5 20), then P 5 $60.
How much will each firm produce? Each firm cares about the market price when it selects its production level. Because market price depends on the total production of both firms, the amount that Hynix desires to produce depends on how much it expects Micron to produce (and vice versa). Cournot investigated production under a simple set of expectations. Each firm “guesses” how much the other firm will produce and believes that its rival will stick to this level of output.14 Each firm’s optimal level of production is the best response to the level it expects its rival to choose.
A Cournot equilibrium is a pair of outputs Q* and Q* and a market price P* that
1 2
satisfy three conditions:
(C1) P* is the price that clears the market given the firms’ production levels; that is,
P* 5 100 2 Q* 2 Q*.
1 2
(C2) Q* is Hynix’s profit-maximizing output given that it guesses Micron will
1
choose Q*.
2
(C3) Q* is Micron’s profit-maximizing output given that it guesses Hynix will
2
choose Q*.
1
Conditions C2 and C3 imply that each firm correctly guesses its rival’s production level. This may seem like a strong assumption, and we will return to it shortly.
To find the market equilibrium choices of Q1 and Q2, consider first Hynix’s choice of Q1. According to condition C2, Hynix’s equilibrium choice of Q1 must maximize its profits, given Micron’s choice of Q2. Suppose that Hynix thinks that Micron is going to produce output Q2g, where the subscript g reminds us that this is a guess rather than the actual value. Then Hynix calculates that if it produces Q1 units of output, its profits, denoted by P1, will be
ß1 5 Revenue 2 Total cost 5 P1Q1 2 TC1 5 (100 2 Q1 2 Q2g)Q1 2 10Q1
Hynix needs to solve for the value of Q1 that maximizes its profits. We can use calculus to determine that the profit-maximizing value of Q1 satisfies:15
Profit-maximizing value of Q1 5 45 2 .5Q2g
Some managers who see the Cournot model for the first time believe that it is all rather abstract and bears little resemblance to how they actually make decisions. Managers may claim that they are more likely to determine the profitmaximizing output through spreadsheet analyses. (The same would apply to computing the optimal price in the Bertrand model that is discussed in the next section.) Yet in this case Hynix would reach the same conclusion if it prepared a spreadsheet as follows:
•Create columns for Hynix’s quantity, Micron’s quantity, the market price, and Hynix’s profits.
•Make a (hopefully) informed guess about Q2.
Oligopoly • 183
•Use the formula P 5 100 2 (Q1 1 Q2) to determine how price will vary with different levels of Q1. Even if Hynix does not have an exact demand formula, it can estimate how market price is likely to change as total output changes.
•Given the values of P computed above, compute profits for different levels of Q1. This will indicate the profit maximizing value of Q1 for any estimate of Q2.
The profit-maximizing value of Q1 is called Hynix’s best response to Micron. According to this equation, Hynix’s best response is a decreasing function of Q2g. This implies that if Hynix expects Micron to increase output, it will reduce its own output. This makes sense. If Micron increases output, then condition (C1) states that the market price must decrease. Facing a lower price, Hynix prefers to produce less itself. The line labeled R1 in Figure 5.2 depicts Hynix’s choice of Q1 as a function of its conjecture about Q2. Economists call this line Hynix’s reaction function.
Similarly, we can use condition (C3) to solve for Micron’s best response to Hynix’s choice of Q1:
Profit-maximizing value of Q2 5 45 2 .5Q1g
Micron’s choice of Q2 as a function of Hynix’s choice of Q1 is shown as reaction function R2 in Figure 5.2.
Thus far, the Cournot calculations are extremely intuitive. Firms are likely to reach conclusions such as these whether they perform the formal math, rely on spreadsheets, or even just use gut instinct. The remaining Cournot calculations rely on our assumption about equilibrium behavior. Recall that in the Cournot equilibrium, each firm chooses output simultaneously and each correctly guesses its rival’s output. In other words, each firm has made the simultaneous best response to the other’s output choice. In Chapter 7 we explore other possible equilibria involving sequential choices. A key managerial skill is to understand and even influence how firms are interacting. For now, we will compute the equilibrium choices in the Cournot world.
It turns out that only one pair of outputs is simultaneously the best response to
each other. These outputs, which we denote by Q* and Q*, are found by solving both
1 2
FIGURE 5.2
Cournot Reaction Functions
The curve R1 is firm 1’s reaction function. It shows firm 1’s profit-maximizing output for any level of output Q2 produced by firm 2. The curve R2 is firm 2’s reaction function. It shows firm 2’s profitmaximizing output for any level of output Q1 produced by firm 1. The Cournot equilibrium outputs,
denoted by Q* and Q*, occur at the point where
1 2
the two reaction functions cross. In this case, the equilibrium output of each firm is 30. At the Cournot equilibrium, each firm is choosing its profitmaximizing output, given the output produced by the other firm.
|
Q2 |
|
|
|
R1 |
|
|
|
45 |
|
|
Q2* |
= 30 |
|
|
|
|
|
R2 |
|
Q1* = 30 |
45 |
Q1 |