Chemistry Reference
In-Depth Information
Chapter 1
The Classical Cournot Model
In this chapter we will introduce the classical Cournot model, which is also known as
the single-product quantity setting oligopoly model without product differentiation.
In the first section of the chapter the Cournot model will be discussed as an N-firm
static game and the best responses of the firms and the equilibria will be determined
in a series of examples, many of which will be built upon in developing the ideas
in subsequent chapters. Section 1.2 introduces the dynamic adjustment processes
via which we shall assume that firms adjust output over time. We will in particu-
lar discuss expectation formation processes and adaptive adjustments and gradient
adjustments. The final section will illustrate by simple examples the complexity
of the dynamics that can arise in these models due to certain nonlinear features
to be described below. The fundamental techniques for the global analysis of the
dynamics of such models will be explained in Sect. 1.3.
1.1
Introduction
The basic model can be described as follows. Consider an industry of N firms pro-
ducing a homogeneous product. Let k
D
1;2;:::;N denote the firms and let x
k
be
the output quantity of firm k. We assume that the inverse demand (or price) function
depends on the total output level of the industry, so the market price may be writ-
ten p
D
f
P
kD1
x
k
. The particular form of the function f can be derived from
microeconomic principles (see for example, Vives (1999)), and several function
types are discussed in the literature.
An important example of an inverse demand function which is linear is obtained
by assuming that the utility function of a typical consumer is quadratic,
1
2
bq
2
;
U.q/
D
aq
.a;b >0/;
where q is the quantity of the good purchased by the consumer. If we denote the
market price of the good by p, then for a sufficiently large income the consumer
