TÉCNICAS ANALÍTICAS TERRESTRES MONOSCOPICAS

Duopoly is an intermediate market structure, between monopoly (maximum concen-tration of market shares) and perfect competition (minimum concenconcen-tration of market shares). One would expect equilibrium price and output under duopoly also to lie be-tween the extremes of monopoly and perfect competition.

This fact can be checked in figure 7.8, which is based on figure 7.7 with a few lines added. Recall that each firm’s reaction curve intercepts the axes at the values q^M and q^C. Therefore, a line with slope−1 intersecting the axes at the farther extremes of the reaction curves unites all points such that q₁+ q2= q^C(see figure 7.8). Likewise, a line with slope−1 intersecting the axes at the closer extremes of the reaction curves unites all points such that q1+ q2= q^M(see figure 7.8). We can see that the Cournot equilibrium point, N , lies between these two lines. This implies that total output under Cournot is greater than that under monopoly and lower than that under perfect competition.

To summarize, according to the Cournot model:

Duopoly output is greater than monopoly output and lower than perfect compe-tition output. Likewise, duopoly price is lower than monopoly price and greater than price under perfect competition.

In chapter 9, we present a generalization of this principle: In an oligopoly with n firms, equilibrium price is closer to perfect competition the greater n is.

Figure 7.8 Comparing the Cournot Equilibrium with Monopoly and Perfect Competition.

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7.4 BERTRAND VERSUS COURNOT

The two models of duopoly competition presented in the previous sections, though similar in assumptions, are in stark contrast when it comes to predicted behavior. The Cournot model predicts that price under duopoly is lower than monopoly price but greater than that under perfect competition. The Bertrand model, by contrast, predicts that duopoly competition is sufficient to drive prices down to marginal cost level, that is, two firms are enough to achieve the perfect competition price level.

This contrast suggests two questions: Which model is more realistic? Why should we consider more than one model instead of just choosing the “best” one? The answer to both questions is that industries differ. Some industries are more realistically described by the Cournot model, some by the Bertrand model.

Specifically, suppose that firms must make capacity (or output) decisions in ad-dition to pricing decisions. In this context the relative timing of each decision (out-put/capacity and pricing) is the crucial aspect that selects Cournot or Bertrand as the right model. As we saw in chapter4, games with two strategic decisions are best mod-eled as two-stage games, with the long-run decisions taken in the first stage and the short-run decisions in the second one. The idea is that the short-run decisions (second stage) are taken given the values of the long-run decisions (first stage).

Suppose that capacity or output is a long-run decision with respect to prices. In other words, suppose that it is more difficult to adjust capacity/output than it is to adjust prices. Then, the “right” model is one wherein firms first set capacity/output and then prices. From the analysis of the previous sections, we know this corresponds to the Cournot model.

Suppose, by contrast, that output is a short-run decision with respect to prices, that is, it is easier to adjust output levels than it is to adjust prices. Then, the “right”

model is one whereby firms set prices first and then output levels. Although we have not presented the Bertrand model as such, this is essentially what it corresponds to. In the Bertrand model, firms simultaneously set prices and receive demand based on those prices. Implicitly assumed in the model is that firms produce an output exactly equal to the quantity demanded, that is, output is perfectly adjusted to the quantity demanded at the prices (initially) set by firms.

To summarize:

If capacity and output can be easily adjusted, then the Bertrand model is a better approximation of duopoly competition. If, by contrast, output and capacity are difficult to adjust, then the Cournot model is a good approximation of duopoly competition.

Most real-world industries seem closer to the case when capacity is difficult to adjust. In other words, capacity or output decisions are normally the long-run variable, prices being set in the short run. Examples include wheat, cement, steel, cars, and computers. Consider, for instance, the video-game industry. In August 1999, Sony cut the price of its system from $129 to $99. One hour after Sony’s price-change notice, Nintendo sent out a news release announcing its price cut to match Sony’s.⁷⁷Aggressive pricing by Sony and Nintendo boosted demand for their products. In fact, Nintendo suffered severe shortages during the 1999 holiday season. These events suggest that, in the context of video-game systems, prices are easier to adjust than quantities. The Cournot model would then seem a better approximation to the behavior of the industry.

There are, however, situations where capacities—or at least output levels—are adjusted more rapidly than prices. Examples include software, insurance, and banking.

A software company, for example, can easily produce additional copies of its software almost on demand; sometimes, in fact, it will simply ship a copy electronically. In this sense, the Bertrand model would provide a better approximation than the Cournot model.^j A specific example is provided by encyclopedias.⁷⁸Encyclopedia Britannica

jThere are, however, other aspects to be taken into account in an industry like software: product differentiation (see chapter12) and network externalities (see chapter 17). The same qualification applies to the video-game industry.

has been, for more than two centuries, a standard reference work. Until recently, the thirty-two-volume hardback set sold for $1600. In the early 1990s, Microsoft entered the market with Encarta, which it sold on CD for less than $100. Britannica responded by issuing its own CD version as well. Recently, both Britannica and Encarta were selling for $89.99. Although this is still far from the Bertrand equilibrium (price equal to the cost of the CDs), it is certainly closer to Bertrand than the initial, monopoly-like price of

$1600.

7.5 THE MODELS AT WORK: COMPARATIVE STATICS

What is the use of solving models and deriving equilibria? Models are simplified de-scriptions of reality, a way of understanding a particular situation. Once we understand how a given market works, we can use the model to predict how the market will change as a function of changes in various exogenous conditions, for example, the price of an input or of a substitute product. This exercise is known in economics as comparative statics: The meaning of the expression is that we compare two equilibria, with two sets of exogenous conditions, and predict how a shift in one variable will influence the other variables. The word “statics” implies that we are not predicting the dynamic path that takes us from one equilibrium to the other, but rather answering the question, “Once all of the adjustments have taken place and we are back in equilibrium, what will things look like?” In this section, we look at some examples of how the Cournot and Bertrand models can be used to perform comparative statics.

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Figure 7.9 Optimal Solution after Increase in Marginal Cost: Two Extreme Cases.