## Gustav Cassel – The Mathematical School

Gustav Cassel – The Mathematical School

From Leon Walras, we jump ahead to Gustav Cassel, the Swedish engineer turned economist, who has de­veloped Walras' theory, and applied it more broadly to distribu­tion and money. It is true that Cassel aims to eliminate the old theories of value, and rejects the theory of marginal utility as a solution of the problem of value. But he really puts nothing in their place, his thought being so to limit the scope of economics as to avoid the problems of causation. If he were to go into the matter, he would doubtless be driven to some similar form of subjective marginism. He adopts an abstract mathematical procedure, assumes the existence of value and prices, and con­structs demand and supply schedules consisting of quantities which depend upon price. His theory is at bottom essentially the same as that of Walras or Jevons. He resorts to an idea of scarcity similar to Walras' rarete.

In fact, Cassel's rejection of marginal utility seems to be a frank attempt to limit economics to an empirical dealing with exchange ratios among objective quantities, merely taking util­ity and subjective value for granted. He seeks to explain eco­nomic phenomena by the single principle of "scarcity." In doing this, he assumes and takes for granted (1) limited supply and unlimited wants, (2) the necessity of exchange, and (3) the function of price in balancing supply and demand. He accepts observed movements in price in lieu of a theory of value causa­tion.

In developing his theory, Cassel adopts the device of first assuming "simple" cases, and then introducing the complica­tions. (1) He begins by assuming that supply is a fixed and known quantity of goods, and argues that, when the prices of all goods are fixed (by using a set of simultaneous equations), the demands of consumers can be known. Demand is made a function of price or prices, and is expressed in quantities of goods. (2) He next assumes that supply consists, not in a quan­tity of goods, but in a fixed quantity of the factors of production. The prices of the factors of production are then supposed to equal the prices of the goods into which they enter through production. (3) He then introduces money. The purchasing power of consumers is said to be derived from their participation in the processes of production; their incomes representing the total of prices paid for the use of the factors of production. (4) He then introduces a sort of quantitative dynamics by as­suming that fixed and constant percentages of change occur in production activity, and the equations are again set up on that basis.

Finally, Cassel states that his procedure gives us the relation among all prices, but not any single absolute price. If one such were known, all others could be absolutely determined. He proceeds, therefore, to expound the determination of the value of money, and more particularly the price of gold — presumably in an attempt to supply the missing absolute quantum.

His general theory of prices is more clearly worked out than Walras'. He develops a theory of money, and an analysis of monetary phenomena, which had much influence in the second and third decades of this century. But his system is too deficient in fundamental basis to endure. His thought is too abstract, and his logic too circular. It would be impossible to get all the data required for working out his equations; if we had the data, we could add nothing to our knowledge by solving them.

Such theory is viciously abstract in that it omits, not only institutional and social-control facts, but also the differences which exist in individual attitudes — differences between neces­sity and choice, or between impulsive and reflective action.

Like Walras, from whom he borrows, Cassel begs the whole question of economic life, value. By assuming value to start with, and thus evading the problem of its cause, he is estopped from dealing with its determination. The result is a system of business mathematics, not a social science.

Summary

In brief summary of the character and im­portance of the thought of Gossen, Jevons, and L. Walras, it may be stated that all emphasized the subjective element in \ralue causation, that all pursued a deductive, mathematical method, and that all arrived at a concept of the margin, where a final or most intense want is satisfied. Their philosophy is utilitarian and hedonistic. (With the exception of the emphasis of marginal utility, these observations apply also to Cassel.)

The mathematical approach is essential, especially in the thought of Cournot, Walras, and Cassel. (Much of Jevons' and most of Gossen's thought would stand up without mathematics. Without the equations, L. Walras does not seem to go beyond A. Walras, and Cassel not beyond L. Walras, in so far as any positive additions to value theory are concerned.) The mere mathematician needs measurable quantitative data, which are homogeneous, and are either fixed or vary in relation to one another. In dealing with values, this leads him to extremes of abstraction, and limits him to quantities exchanged. He more or less takes for granted and assumes the quality of value, and sets up "equations" which, if true, are truisms. In assuming the causation of value, he provides no basis for prediction, law, science.

Another notable point of likeness is that each of the three chief earlier economists discussed formulates more or less pre­cisely some law concerning the attainment of maximum satis­faction. Walras puts it thus: "Taking two commodities on a single market, the maximum satisfaction of wants or the maxi­mum of effective utility exists when and where the ratio of the intensities of the last wants satisfied, or the ratio of the raretes, is equal to price."

One great difference between Jevons and Walras deserves attention, and that is the fact that Jevons has a better apprecia­tion of the causation of values, and consequently goes more deeply than Walras into the real problem of determination. Walras, for example, frequently starts out by assuming his price, and his supply and his demand are price-determined quantities. Jevons seeks to build up to his price by proceeding from causal forces to determination. This difference undoubtedly proceeds from the fact that Jevons was more affected by the Classical English economics, which at bottom has a sort of social point of view, however much it may be shoved into the background. Walras is more mathematical and more inclined both to assume the existence of value and to think of it as a quality of goods, both material and immaterial; Jevons is more psychological'— though not more subjective — and endeavors carefully to guard against treating value as lying in goods.

As to Cassel, in his extreme individualistic and mathematical technique he goes beyond Walras and even spurns causal analy­sis. His subjectivism, therefore, has to be assumed — just as he assumes the existence of the value quality.

As will appear from a reading of the next chapter, the analysis of subjective elements made by these men lacks the refinement to which it has been carried by the Austrian School. And, ex­cepting Gossen, their emphasis on changes in quantity of goods and on exchange in markets tends toward the idea of value as a relation between commodities, which in the last analysis is hardly consistent with strict subjectivism.