The Economics Book

91

Cournot’s model uses

two reaction curves to

illustrate the output

decisions of two firms,

where each firm is aware

of the other’s existence

but does not know how

much the other intends

to produce.

See also: Cartels and collusion 70–73 ■ Monopolies 92–97 ■ The competitive market 126–29 ■ Game theory 234–41

no other firms can enter the industry
(because there are no other natural
springs), and each firm has to
decide, simultaneously, how many
bottles of water to supply.
The total output of the industry
is the sum of the two firms’ output
decisions. Each firm must choose
the output that maximizes its profit
based on what it thinks the other
firm’s output will be. If Firm A
thinks that Firm B will produce
nothing, Firm A will select the low
output of a monopolist to maximize
profits. On the other hand if Firm A
thinks that Firm B will produce a
high output, Firm A may choose to
produce nothing—because prices
would fall too far to make production
worthwhile. Cournot represented
the decisions of both firms on a
“reaction curve.” The equilibrium
of the market is where the two
reaction curves intersect. At this
point each firm is selling the most
profitable amount given what the
other firm is doing. This notion of
equilibrium became known as the
Nash equilibrium, and it is a
central plank of game theory, the
branch of modern economics that
analyzes strategic interaction
between firms and individuals.
Cournot used mathematics to
find this equilibrium and prove that
the duopolists would choose an
output that was higher than would
occur in monopoly, but lower than
with perfect competition. In other
words a few firms would be better
for society than a monopolist, but
worse than perfect competition.
From this starting point, Cournot
extended the model to show how,
if the number of firms increases,
the industry output reassuringly
moves closer to the level expected
for perfect competition. Cournot’s

INDUSTRIAL AND ECONOMIC REVOLUTIONS

model was developed by French

economist Joseph Bertrand, who

showed that if firms choose by their

desired price levels rather than

output, the equilibrium for

duopolists equals that of perfect

competition. This is because any

firm that sets a high price will be

undercut by another, who will then

steal all its buyers. In this way the

price will be driven to the most

competitive level. ■

0

5

10

15

20

25

30

FIRM B’S OUTPUT

FIRM A’S OUTPUT

051015202530

If Firm A thinks Firm B will

produce 30, Firm A will

produce zero (to avoid losses)

Firm A

Firm B

Cournot equilibrium

(the perfect production point)

If Firm A thinks Firm B will

produce zero, Firm A will produce 15

(to make a monopoly level of profit)

Antoine Cournot

An insatiable reader, Antoine

Augustin Cournot was born in

France in 1801. Although

relatively poor, he studied

mathematics at one of the best

schools in the country and

completed a PhD in engineering.

After spending some time as a

private tutor and as a secretary

for one of Napoleon’s generals,

he became a university lecturer

and then professor. Cournot was

plagued by eye problems but

managed to publish several

works that pioneered the use

of mathematics in economics,

before going blind. His work was

not well received in his lifetime

because of its reliance on novel

mathematical notation. Today he

is regarded as a profound thinker

who advanced prophetic ideas.

Key works

1838 Researches into the

Mathematical Principles of the

Theory of Wealth

1863 Principles of the Theory

of Wealth