Chapter 28 65
Chapter 28
Oligopoly
This chapter is a serious attempt to convey some of the standard models
of strategic interaction to intermediate microeconomics students. This is an
ambitious goal, but with some motivation it can be done. I have pursued a
middle ground in this chapter between the traditional approach to oligopoly and
the more modern game theoretic approach.
I’ve departed from the standard order of discussing things here since I think
that it is much clearer the way I do it.
I start with a little classification scheme: firms can choose prices or quantities,
and they can move simultaneously or sequentially. This gives us four cases
to analyse. You might discuss other strategic variables at this point: product
differentiation, investment decisions, entry, etc.
I proceed to analyse the case of quantity leadership—the Stackelberg model.
Here you should emphasize the importance of thinking strategically: putting
yourself in the shoes of the other guy and thinking about how he will react to
your choices. Once that insight is there, it is fairly straightforward to do the
analysis.
The next case to look at is the case of price leadership. The logic is just the
same, and the calculations are even easier.
Then we move to simultaneous quantity setting—the Cournot/Nash model.
I have been careful to phrase the concept of a Cournot equilibrium as an
equilibrium in beliefs as well as actions—each firm is maximizing given its beliefs
about the other firm’s choices, and each firm finds that its beliefs are confirmed
in equilibrium. I find that it is very useful to calculate out an equilibrium
example, so that students can see the richness of the idea involved. The graphical
treatment is also very helpful.
Section 28.7, on adjustment to equilibrium, is a little bit of a cheat. This is
not really consistent with a thoroughgoing game theoretic analysis, but I put it
in anyway since the students seem to like it. It shows in a graphic way how an
apparently sensible adjustment process can lead to the Cournot equilibrium.
Section 28.8, on many firms, is a very nice illustration of what the idea of a
“demand curve facing a firm” looks like. The idea that a Cournot equilibrium
approaches the competitive equilibrium as market shares go to zero is a useful
one, and the calculations in this section motivate this idea quite powerfully.
66 Chapter Highlights
Next, I treat simultaneous price setting—the Bertrand model. I like the
interpretation of “bidding” for the consumers. There are a number of real-world
examples where forcing firms to make sealed bids results in much lower prices.
The logic behind this is essentially that of Bertrand competition. In Ann Arbor,
the local coursepack providers quote you a 5-cents-a-page price for copying, but
the sealed bids usually end up under 2.5 cents.
Section 28.10 on collusion is also very important. I usually motivate this
using OPEC as an example. Each firm negotiates to set a quota that maximizes
overall cartel profits … and then each firm goes home and tries to cheat on the
cartel. It is worth pointing out that equation 28.6 implies that the smaller firm
1’s output is, relative to firm 2, the more incentive firm 2 has to cheat on the
cartel agreement. This is true since
Δπ1
Δy1
=−Δp
ΔYy∗
2.
If the output of firm 2 is large, then Δπ1/Δy1will be large.
In Figure 28.5 it is useful to point out that the reason that we get a whole
range of outputs that maximize industry profits is that we have assumed that
marginal costs are identical—in fact, we have assumed that they are zero for both
firms. If the marginal costs were different, we would most likely get a unique
cartel solution.
Oligopoly
A. Oligopoly is the study of the interaction of a small number of firms
1. duopoly is simplest case
B. Classification of theories
1. non-collusive
a) sequential moves
2. collusive
C. Stackelberg behavior
1. asymmetry — one firm, quantity leader, gets to set quantity first
2. maximize profits, given the reaction behavior of the other firm
6. firm 1
7. graphical solution in Figure 26.4.
Chapter 28 67
D. Price-setting behavior
1. leader sets price, follower takes it as given
2. given p1, firm 2 supplies S2(p1)
E. Cournot equilibrium — simultaneous quantity setting
1. each firm makes a choice of output, given its forecast of the other firm’s
output
2. let y1be the output choice of firm 1 and ye
2be firm 1’s beliefs about firm
2’s output choice
6. this gives firm 1’s reaction curve — how it chooses output given its beliefs
about firm 2’s output
7. see Figure 26.1.
F. Example of Cournot
1. assume zero costs
2. linear demand function p(Y)=a−bY
3. profit function: [a−b(y1+y2)]y1=ay1−by2
1−by1y2
4. derive reaction curve
5. look for intersection of reaction curves
G. Bertrand – simultaneous price setting
1. consider case with constant identical marginal cost
H. Collusion
1. firms get together to maximize joint profits
2. marginal impact on joint profits from selling output of either firm must be
the same