## The Mathematical School (Gossen – Jevons)

Gossen, Jevons, Walras and The Mathematical School

The development of the marginal-utility analysis in value theory is commonly associated with the names of Jevons and of the members of the Austrian School. But, both in the con­cept of the margin and in the emphasis of utility and demand, these men were anticipated. As is usually the case, there were forerunners.

First Developments.

Not to dwell upon such sugges­tions as may be found in the writings of Galiani, Barbon, and others, the French writer, Condillac, must be especially men­tioned both because of his clear statement and his considerable influence. Condillac stated that value depends upon wants, being less in the thing itself than in the estimate we form of it. "A thing does not have value because of its cost, as some sup­pose; but it costs because it has a value." The true value of goods varies according to the intensity of wants and the supply of goods: assuming equal utility, it varies according to out estimates of rarete or abundance.

Jeremy Bentham, famous in English jurisprudence and political philosophy, suggested the idea when he wrote: "The greater the quantity of the matter of property a man is already in possession of, the less is the quantity of happiness he receives by the addition of another quantity of the matter of property, to a given amount."

Also noteworthy in this connection are the English writers Craig, Longfield, and Lloyd. John Craig in 1821 developed the significance of utility in value determination in an original way, analyzing the utility of a good into different strata which come into play as supply is increased.2 But Longfield (1833) had a clearer expression of the marginal idea as applied both to utility and cost: to him market price was "measured by that demand, which being of the least intensity yet leads to actual purchases." In the following year, W. F. Lloyd published a most remarkable Lecture on the Notion of Value. Value, he reasoned, may be defined as the esteem in which an object is held. Although human wants are varied and no limit can be assigned to their development, yet, for any specific object, an increase in supply will bring satiety and value will vanish (p. 10). Lloyd says: "In its ultimate sense, value undoubtedly signifies a feeling of mind which shows itself always at the margin of separation between satisfied and unsatisfied wants." The claim of this Englishman to the distinction of first clearly explaining value in terms of marginal utility seems strong.

At about the same time, a Frenchman, Auguste Walras, in studying the basis of property rights, reached the conclusion that value arises from the rarete (relative scarcity) of objects which have utility. He argued that value is the relation between the quantity of a good and the sum of the effective needs for it, in other words, its rarete. He failed, however, to develop the idea of degrees of utility and the marginal analysis. It is of interest to note that a countryman, Augustin Cournot, soon published a work which, while not developing the idea of marginal utility, did bring out clearly the relation between incremental variations in quantity of goods and those in prices. Cournot's work would thus tend to supplement that of A. Wal­ras, and in any event was pioneering in the field of mathematical economics and marginism.

The German, Thomas, has often been overlooked in this connection. In his Theorie des Verkehrs (1841), however, he very cleaily states the main idea of the modern subjective theories of value: Value depends on estimation, and for estima­tion there must be not only an object, but a subject who eval­uates. Value depends upon the strength of desire, and price upon a comparison of the estimations put by the parties to an exchange upon their goods. He expresses the idea of a scale with upper and lower limits (Grenzeri) Thomas, however, seems not to have thought it necessary to enter into the minute psychological analysis characteristic of the modern marginal-utility thinkers.

Similar ideas were soon advanced quite independently by a French engineer named Dupuit. He wrote that "goods have a utility not only for each consumer, but also for each want for the satisfaction of which they are employed"; and seems to have clearly grasped the concept of final or marginal utility.
Finally, Senior should also be mentioned as a forerunner; and Banfield and Jennings, to whom Jevons himself expressed in­debtedness, should not be forgotten.

The first writer, however, who developed the ideas now under consideration, and centered a more or less comprehensive sys­tem of economic theory in them, was Gossen.