Antoine Augustin Cournot(1801-1877) - 經濟

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作者: fizeau (.) 看板: Math
標題: [名人] Antoine Augustin Cournot(1801-1877)
時間: Tue Apr 29 21:14:04 2008

http://cepa.newschool.edu/het/profiles/cournot.htm

French philosopher, mathematician and economist, Augustin Cournot has been
rightly hailed as one of the greatest of the Proto-Marginalists. The unique
insights of his major economics work, Researches into the Mathematical
Principles of Wealth (1838) were without parallel. Although neglected in his
time, the impact of Cournot work on modern economics can hardly be
overstated.

Augustin Cournot was born in the small town of Gray (Haute-Saône). He was
educated in the schools of Gray until he was fifteen. Subsequently, for the
next four years, he worked haphazardly as a clerk in a lawyer's office.
Cournot directed his own studies throughout this time, mostly centered
around philosophy and law. Inspired by the work of Laplace, Cournot realized
that he had to learn mathematics if he was to pursue his philosophical
aspirations. So, at the relatively ripe age of nineteen, he enrolled in a
mathematical preparatory course at a school in Besançon. He subsequently
won entry into the École Normale Supérieure in Paris in 1821.

For political reasons, the ENS was closed down in 1822 and so Cournot
transferred to the Sorbonne, obtaining a lecentiate in mathematics in 1823.
He threw himself wholeheartedly into the stimulating intellectual and
scientific atmosphere of Paris, attending the seminars at the Academie des
Sciences and the salon of the economist Joseph Droz. Among his main
intellectual influences were Laplace, Lagrange and Hachette, a former
disciple of Condorcet, who imbibed in him the principles of mathematique
sociale, i.e. the idea that the social sciences, like the natural, could be
dealt with mathematically. Cournot counted the young mathematician Lejeune
Dirichlet as a close friend.

From 1823, Cournot was employed as a literary advisor to Marshal Gouvoin
Saint Cyr and a tutor to his son. For the next ten years, Cournot would
remain in Paris in this leisurely capacity, pursuing his studies and research
in his own way. In 1829, Cournot acquired a doctorate in sciences, focusing
on mechanics and astronomy. After Saint Cyr's death in 1830, Cournot took it
upon himself to edit and publish the remaining volumes of his late employer's
memoirs.

Cournot's thesis and a few of his articles brought him to the attention of
the mathematician Siméon-Denis Poisson who urged him to return to academia.
Cournot refused at first but, after his engagement with the Saint Cyr family
ended in 1833, he took up a temporary appointment at the Academy in Paris.
It was during this time that he translated John Herschel's Astronomy (1834)
and Dionysus Lardner's Mechanics (1835).

In 1834, through the good offices of Poisson, Cournot found a permanent
appointment as professor of analysis and mechanics at Lyons. A year later,
Poisson secured him a rectorship at the Academy of Grenoble. Although his
duties were mostly administrative, Cournot excelled at them. In 1838,
(again, at the instigation of the loyal Poisson), Cournot was called to Paris
as Inspecteur Général des Études. In that same year, he was made a Knight
of the Légion d'honneur (he was elevated to an Officer in 1845).

It was in this year that Cournot published his economics masterpiece, the
Recherches (1838). Cournot begins with some preliminary remarks on the role
of mathematics applied to the social sciences. His announces that his
purpose in using mathematics is merely to guide his reasoning and illustrate
his argument rather than lead to any numerical calculations. He acknowledges
(and disparages) N.F. Canard as his only predecessor.

In his first three chapters, he runs through the definition of wealth,
absolute vs. relative prices and the law of one price. Then, in Chapter 4,
he unveils his demand function. He writes it in general form as D = F(p). He
assumes that F(.) is continuous and takes it as an empirical proposition that
the demand function is downward-sloping (the loi de débit, "law of demand")
and proceeds to draw it in price-quantity space (Fig. 1). He also introduces
the idea of "elasticity", but does not write it down in a mathematical
formula.

It is important to note that Cournot's "demand function" is not a demand
schedule in the modern sense. His curve, D = F(p) merely summarizes the
empirical relationship between price and quantity sold, rather than the
conceptual relationship between price and the quantity sought by buyers.
Cournot refuses to derive demand from any "utility"-based theories of
individual behavior. As he notes, the "accessory ideas of utility, scarcity,
and suitability to the needs and enjoyments of mankind...are variable and by
nature indeterminate, and consequently ill suited for the foundation of a
scientific theory" (Cournot, 1838: p.10). He satisfies himself with merely
acknowledging that the functional form of F(.) depends on "the utility of the
article, the nature of the services it can render or the enjoyments it can
procure, on the habits and customs of the people, on the average wealth, and
on the scale on which wealth is distributed." (1838: p.47).

In Chapter 5, Cournot jumps immediately into an analysis of monopoly. Here,
the concept of a profit-maximizing producer is introduced. Cournot
introduces the cost function f(D) and discusses decreasing, constant and
increasing costs to scale. He shows mathematically how a producer will
choose to produce at a quantity where marginal revenue is equal to marginal
cost (he re-expresses marginal cost as a function of price in its own right,
f'(D(p)) = y(p)). In Chapter 6, he examines the impact of various forms of
taxes and bounties on price and quantity produced, as well as their impact on
the income of producers and consumers.

In Chapter 7, Cournot presents his famous "duopoly" model. He sets up a
mathematical model with two rival producers of a homogeneous product. Each
producer is conscious that his rival's quantity decision will also impact the
price he faces and thus his profits. Consequently, each producer chooses a
quantity that maximizes his profits subject to the quantity reactions of his
rival. Cournot mathematically derives a deterministic solution as the
quantities chosen by the rival producers are in accordance with each other's
anticipated reactions. Cournot showed how this equilibrium can be drawn as
the intersection of two "reaction curves". He depicts a stable and an
unstable equilibrium in Figures 2 and 3 respectively.

Comparing solutions, Cournot notes that under duopoly, the price is lower and
the total quantity produced greater than under monopoly. He runs with this
insight, showing that as the number of producers increases, the quantity
becomes greater and the price lower. In Chapter 8, he introduces the case
of unlimited competition, i.e. where the quantity of producers is so great
that the entry or departure of a individual producer has a negligible effect
on the total quantity produced. He goes on to derive the prices and
quantities in this "perfectly competitive" situation, in particular showing
that, at the solution, price is equal to marginal cost.

In the remainder of his book, Cournot takes up what he calls the
"communication of markets", or trade of a single good between regions. In
Ch. 10, he analyzes two isolated countries and one homogeneous product. He
shows that the impact of opening trade between the two countries leads to the
equalization of prices, with the lower cost producer exporting to the higher
cost country. Cournot tries to prove that there are conditions where the
opening of trade will lead to a decline in the quantity of the good and lower
revenue. He then proceeds to discuss the impact of import and export taxes
and subsidies (and algebraic error here was spotted later by Edgeworth
(1894)) . On account of this, Cournot raises doubts in Chapter 12 about the
"gains from trade" and defends the profitability of import duties.

Finally, Cournot also acknowledges that the solutions obtained via his
"partial equilibrium" method are incomplete. He recognizes the need to take
multiple markets into account and trying to solve for the general
equilibrium, but "this would surpass the powers of mathematical analysis"
(Cournot, 1838: p.127).

Cournot's 1838 work received hardly any response when it came out. The
denizens of the French Liberal School, who dominated the economics profession
in France at the time, took no notice of it, leaving Cournot crushed and
bitter. In 1839, plagued by ill-health, Poisson asked Cournot to represent
him at the concours d'agrégation de mathématiques at the Conseil Royal.
After Poisson died in 1840, Cournot continued on at the Conseil as a deputy
to Poisson's successor, the mathematician Louis Poinsot.

In 1841, Cournot published his lecture notes on analysis from Lyons,
dedicating the resulting Traité to Possion. In 1843, he made his first stab
at probability theory in his Exposition. He differentiated between three
types of probabilities: objective, subjective and philosophical. The former
two follow their standard ontological and epistemological definitions. The
third category refers to probabilities "which depend mainly on the idea that
we have of the simplicity of the laws of nature." (1843: p.440).

After the 1848 Revolution, Cournot was appointed to the Commission des Hautes
Études. It was during this time that he wrote his first treatise on the
philosophy of science (1851). In 1854, he became rector of the Academy at
Dijon. However, Cournot's lifelong eye-sight problem began getting worse.
Cournot retired from teaching in 1862 and moved back to Paris.

In 1859, Cournot wrote his Souvenirs, a haunting autobiographical memoir
(published posthumously in 1913). Despite the dark pessimism about the
decline of his creative powers, he wasn't quite yet finished. He published
two more philosophical treatises in 1861 and 1872 which sealed his fame in
the French philosophy community, but did nothing to advance his economics.
He took another stab at economics with his Principes (1863), which, on the
whole, was merely a restatement of the 1838 Recherches without the math and
in more popular prose. Once again, it was completely neglected. A Journal
des économistes review churlishly claimed that Cournot had "not gone beyond
Ricardo", etc. Cournot's bitterness increased accordingly.

However, by this time the Marginalist Revolution had already started. Léon
Walras (1874), who had read Cournot's work early on, argued that his own
theory was but a multi-market generalization of Cournot's partial equilibrium
model (indeed, the notation is almost identical). W. Stanley Jevons, who had
not read him, nonetheless hailed him as a predecessor in later editions of
his Theory (1871). Francis Ysidro Edgeworth (1881) went to Cournot to pick up
his theory of perfect competition. Alfred Marshall claimed to have read him
as far back as 1868, and extensively acknowledged Cournot's influence in his
1890 textbook, particularly in his discussion of the theory of the firm.

Cournot lived long enough to greet the works of Walras and Jevons with a warm
sense of vindication. This is evident in Cournot's Revue sommaire (1877), a
long, non-mathematical statement of his earlier work. He seemed particularly
grateful that Walras had bravely climbed the steps of the Institute de France
and accused the academicians of injustice towards Cournot. He died that same
year.

Walras, Jevons and the other young blades complained loudly that Cournot had
been unjustly neglected by his contemporaries. So, in 1883, the French
mathematician Joseph Bertrand took it upon himself to finally provide the
first review of the Cournot's Recherches (jointly with a Walras book) in the
Journal des savants. It was not a kind review. Bertrand argued that Cournot
had reached the wrong conclusion on practically everything, and reworked
Cournot's duopoly model with prices, rather than quantities, as the strategic
variables -- and obtained the competitive solution immediately. Edgeworth
(1897) revisited the model and assailed both Cournot and Bertrand for
obtaining deterministic solutions, arguing that the equilibrium solution in
the case of a small number of producers should always be indeterminate.

The development of monopolistic competition in the 1930s drew much
inspiration from Cournot's work. As the theory of games advanced in the
1950s, Mayberry, Nash and Shubik (1953) restated Cournot's duopoly theory as
a non-cooperative game with quantities as strategic variables. They showed
that Cournot's solution was nothing other than its "Nash equilibrium" (Nash,
1951). Cournot's influence on modern theory continues unabated, having been
given a particular boost in the attempt to develop non-cooperative
foundations for Walrasian general equilibrium theory (e.g. Novshek and
Sonnenschein (1978) and the 1980 JET Symposium).


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