Cournot Oligopoly: The technical requirements increase substantially in this section.  As usual, there are two, possibly three, alternative approaches to covering this material: graphical, algebraic, and using calculus.  In this instance it is advisable to use a mix of all three to give students as many different perspectives as possible.  The central concept is the idea of a best-response or reaction function and helping students gain an understanding of its meaning now will be helpful later in this chapter as well as in the following one.

 

It is very important to highlight that Cournot competition involves firms competing via their choice of quantity.  This means that price is not a strategic variable, but is determined by the combination of the production decisions of each of the firms.  Furthermore, because it is total, industry-wide production that matters, the price that one firm faces is determined, at least in part, by the choices of the other firms.  This strategic interdependency is at the heart of oligopoly markets and helping students see how this manifests itself in the model is of paramount importance.

 

To illustrate this interdependency, start by describing a generic profit function for a firm.  Point out that when we consider an inverse demand function, the price of the good depends on quantity.  More specifically, the quantity that matters in this model is the overall amount of the good produced by all firms.  This means that price, revenue, and eventually profit earned by one firm depends on that firm’s choice of output as well as on the choice of output made by its competitor(s).

 

The next step is to derive the best-response functions.  It is useful to point out to students that while the functional form of the profit function is different in this case (to accommodate the strategic nature of quantity choice), the mechanism for optimization is exactly the same.  The best-response function is simply the first order condition for profit maximization, or a simplified version of the MR=MC condition.

 

The final step in the derivation is the part that is most different from earlier models.  The best-response functions (one for each firm) describe the best choice of output given the choice of each firm’s competitor(s).  The equilibrium occurs where all firms are simultaneously making ‘best’ decisions.  Graphically this equilibrium is interpreted as the intersection of the best-response curves, while mathematically this means solving a set of simultaneous equations.

 

The section concludes by considering extensions to the basic model.  The number of firms, product differentiation, and cost differences are all considered.  Of these variations, the discussion of the number of firms (n) is probably the most relevant for the rest of the chapter.  It is a good idea to take time to explain that the Cournot model can include monopoly and perfect competition as special cases (where n=1 or n becomes very large, respectively).  The end result of this analysis is that as the number of firms increases, so does the degree of competition.  However, as the next section will show, increasing n is not a necessary condition for a market to exhibit competitive behavior.