**Antoine Augustin Cournot Model**

Cournot Competition Theory, Cournot Price

Cournot's ideas on the proper method in political economy are of great importance in assessing his role in theory development. In defense of the use of mathematics as a shorthand for expressing complex ideas, Cournot evaluated the earlier efforts of Smith, Say, and Ricardo:

There are authors, like Smith and Say, who, in writing on Political Economy, have preserved all the beauties of a purely literary style; but there are others, like Ricardo. who, when treating the most abstract questions, or when seeking great accuracy, have not been able to avoid algebra, and have only disguised it under arithmetical calculations of tiresome length. Any one who understands algebraic notation, reads at a glance in an equation results reached arithmetically only with great labor and pains (Mathematical Principles, p. 4).

In a brilliant defense of mathematical investigation, moreover, Cournot's chief criticism of past writers was "They imagined that the use of symbols and formulas would have no other end than that of leading to numerical calculations" and they did not see that the object of mathematical analysis was to "find relations between magnitudes which cannot be estimated numerically and between functions whose law is not capable of being expressed by algebraic symbols." This view of method persists in his later works also. "Science," Cournot wrote in 1863, "is not obliged to await empirical laws ... in order to draw certain and useful consequences from general characteristics which they can supply, or certain relationships which can exist between them and upon which reason, alone, sheds light." Thus Cournot championed the use of mathematics, specifically differential and integral calculus, in expressing arbitrary functions, with the restriction that certain conditions be met. An example, familiar to all students of economics, may make Cournot's method clearer.

One of Cournot's great achievements was to have discovered the law of demand (loi de debit). As most students know, the law of demand states that quantity demanded is a function of price, or D = F (P). Quantity demanded is, of course, related to a number of other variables (income, wealth, and the like), but these are assumed constant when drawing up an individual demand schedule. When one of the non-price determinants changes, the whole demand curve shifts, which connotes a change in demand. A change in quantity demanded occurs when price changes, all other determinants remaining constant. Cournot understood perfectly the value of analysis of the ceteris paribus assumption, or "other things equal." This is evident in his Principles de la theorie des richesses, where he noted that the law of demand

. .. rests essentially on population, on the distribution of wealth, on general well-being, on tastes, on the habits of the consuming population, on the multiplication of markets, on the extension of the market resulting from transport improvements. All these conditions relative to demand remain the same; if we suppose that production conditions change (i.e., that costs rise or fall, that monopolies are restricted or suppressed, that taxes are increased or lightened, that foreign competition is prohibited or allowed) prices will vary and the corresponding variations in demand, provided that prices are actually raised, will serve for the construction of our empirical tables. If, to the contrary, prices change because the law of demand has itself changed, due to a change in causes which no longer influence production but consumption, the construction of our tables will be made impossible, since they must show how demand changes by virtue of a change in price and not by virtue of other causes.'

It is clear that Cournot identified the law of demand with the modern conception of a demand function; likewise, his change in "demand" corresponds to the modern usage of a change in "quantity demanded." This method of analysis is so common today that the modern theorist would not think of expressing complex ideas in verbal form alone, but Cournot pioneered mathematical and graphical approaches when verbal expression was the only tack of the theorist.

A further and legitimate question might be raised: What kind of theory did Cournot seek to develop with mathematical tools? Was the theory he contemplated chimerical or out of touch with reality, as so many argue of economic theory today? The answer to these questions reveals the brilliantly dual nature of Cournot's approach to method. Cournot conceived of an economic analysis to be grounded in empirical observation and in facts. The point may be illustrated by returning to Cournot's pioneering concept of the law of demand.

Having rejected utility as a foundation for his demand function, Cournot presented what was basically an empirical approach to demand. The title of the chapter on demand in the original Recherches, "De la loi du debit, " or "The Law of Sales," hints at this empirical approach, and Cournot quite explicitly gave his demand function an empirical definition. He noted: "Sales or demand (for to us these two words are synonymous and we do not see for what account theory need take into consideration a demand which is not followed by a sale) . . . increase when price decreases." He acknowledged that prices and the law of demand could fluctuate in the period of a year, and he defined his curve to relate average annual price P with F (P)the quantity sold annually in the country or in the market under consideration." Hence, D = F (P) is a curve connecting time-series data on sales and the prices at which these sales are realized.

Thus Cournot's theoretical specification of demand (negatively sloped, continuous) resulted from his own observation and from simplifications and observations of the relations between price and quantity. Theory may then be lifted from these facts and manipulated in order to arrive at deductions based on certain assumptions. But theory was to be derived and specified in the first instance from actual observed facts and not from caprice. The tools, so derived, possess a usefulness and a generality that far transcend the empirical facts from which they were born. It was part of Cournot's genius to have been able to recognize and explain these methods of theory and model construction.