**Leon Walras, The Mathematical School**

Leon Walras (1834-1910) is another economist who was slow in gaining recognition, and whose fame has suffered from no fault of his work, but from causes exterior to it. His Elements d'economie politique pure (Elements of Pure Economics) was published in 1874, thus shortly following the works of Jevons and Menger.1 His thought was undoubtedly independent, however, and he himself recommends Jevons' book as complementary to his own. He constructed a more complete system based upon mathematical analysis than did Jevons. The establishment of the Mathematical School may be dated from Walras, for, though he was preceded by Cournot, his work was much more complete and systematic.

To some extent, like Senior, Gossen, and Jevons, Walras sought to make economics an abstract science, distinguishing pure economics from applied economics, on the one hand, and from social economics on the other. Truth, he held, rather than the useful or the good, should be the goal. In his opinion, economists had given too much attention to exceptional cases, such as old masters' pictures.

His great object was to expound a mathematical theory of exchange, and it is on the second part of his book, entitled "Mathematical Theory of Exchange" that interest is to be chiefly centered. To achieve his end, he assumes a perfect competition such as might obtain in the Bourse, and, like Say, makes the entrepreneur, receiving and distributing payments for "productive services," the center of the scheme. He neglects the action of impulses, and, after the fashion of the hedonist, employs the general hypothesis of exchanges between parties who seek in exchanging to secure the greatest possible satisfaction of their desires.

Social wealth, as defined by him, consists of all things, material and immaterial, which have utility and are limited in quantity. The amount of the value of external things is proportional to the amount of satisfactions they bring us. There is no direct or immediate relation between supply and price; but such a relation does exist between price and demand, and the demand curve depends upon this relation. The cause is intensity of utility. And where two commodities are concerned the demand curve depends upon the relation between the intensity of utility of the one commodity and that of the other. The price, then, where neither of the commodities entering the exchange is valueless, is such that the intensity of the last want satisfied is the same for each.

For Jevons' "final degree of utility" — and Gossen's Werth der lezten A tome — Walras uses the raretS, which he defines as "the intensity of the last want satisfied." 1 Exchange values are proportional to raretes. Two commodities being given, for instance, if the utility and the quantity of one of the two commodities in respect to one or more exchangers varies, so that the rarete varies, the value of that commodity in relation to the other, or its price, will likewise vary.

In some respects Walras' rarete appears to be a truer concept than the common notion of marginal utility; for, in defining it as depending on supply and utility,2 he gives clear recognition to the fact that supply limitations are included and expressed in it. It would not be difficult for both cost and utility theorists to approach some agreement with Walras' formula, according to which utility and supply, working in obedience to the theory of maximum satisfaction, determine the demand curve from which, positing the law of a single price for the market, comes price.

It is to be emphasized, however, that rarete is subjective. Like his fellows of the mathematical-utility school, Walras' theory is based upon the assumption of a direct relation between demand and price and the absence of such a relation between supply and price.

In contrast with Gossen, Walras treats with notable clearness the subject of market values; and he goes beyond Jevons in formulating his exchange equations for dealings in any number of commodities rather than two alone.

Nevertheless one puts down the "pure political economy" with the feeling that little if anything has been added to real knowledge. What boots it that "the effective demand or supply of one good in terms of another is equal to the effective supply or demand of the other multiplied by its price in terms of the first good"? Other economists had stated that demand equals supply!

Instead of seeking causes, he sets up a number of simultaneous equations equal to the number of the "unknown" (prices), and proceeds to turn the crank. Starting from the obvious and question-begging equation, "demand for a X value of a = supply of b X value of b," Walras draws curves whose axes are (1) quantity of a given good demanded at a given price, and (2) prices of the given good in terms of another good: his curve "gives the quantity of a effectively demanded, as functions of the price of a." Finally comes the italicized statement: "Two goods being given, in order that there be equilibrium, or a stationary price of one in terms of the other, it is necessary and sufficient that the effective demand of each of the two goods be equal to its effective supply {offre). When that equality does not exist, in order to reach an equilibrium price there is necessary a rise in the price of the good of which the effective demand is greater than the effective supply, and a fall in the price of the one whose effective supply is greater than the effective demand." He uses a formula which is practically identical with that shown on a preceding page in the discussion of Jevons.