IN THE last three decades of the nineteenth century Political Economy underwent an important change, which has a different and a deeper significance than is customarily realised. Simultaneously and independently the so-called Austrian School, on the one hand, with Menger, Boehm-Bawerk and Wieser as its giants, and Jevons in England, were building the new frame-work within which Economics (to use Jevons’s new term) has moved ever since. Closely on their heels followed Marshall in this country and Walras and Pareto, of the so-called Lausanne School, on the Continent.

At first sight the change seems mainly a formal one. The new school of thought has frequently been referred to as the school of Marginal Utility to describe the two most important features of the new theories. The first noticeable difference between the old economists and the new consisted in an important shift of emphasis from supply and cost to consumer’ demand and utility as the determinants of exchange-value. Value was no longer regarded as determined by labour, or even by labour plus abstinence, but by the capacity of a commodity to afford satisfaction to consumers (i.e., its utility). This represented a psychological and Hedonist approach to the problem from the standpoint of consumers’ desires. The second feature of the new theories was their emphasis on the effect of changes at the margin – for instance, the loss or gain of utility resulting from “a little less” or “a little more” of a certain commodity (say, cloth or corn or tea); and it was the utility of “a little less” or “a little more” (the marginal utility) which was regarded as important in the determination of value. This emphasis on the margin was the result of an attempt to construct economic science in a mathematical framework. Jevons (1835-1882), for instance, was at considerable pains to prove that economics must be a mathematical science inform, whether the economist actually spoke in words or in algebraic symbols. He accordingly employed the mathematical conceptions of the differential calculus and of functional equations as a convenient analytical technique; and since the differential calculus deals in terms of small increments and decrements (of “a little more” or “a little less” of something or other), economists tended to frame their theories in terms of marginal changes of this kind.

But the change went ·deeper than this: it was a change of conceptual approach, and a change in the type of question that was being answered. The new economists were not concerned primarily with conceptions of “real cost” and “surplus” they were not concerned with a principle of intrinsic value as a key to the problem of equivalence. They were concerned with a more empirical enquiry – the causes of changes in market values. This enquiry founded their horizon so far as the theoretical core of economics was concerned; and all the major economic problems could be reduced to these terms. It was natural that, in pursuit of such an enquiry, the analogy of a theory of equilibrium should be suggested from mechanics. “Value” represented a certain “position” or “level” which, in equilibrium, a commodity occupied relatively to the remainder of commodities. In this sense “value “was always a “relative” value; and the concept of “absolute value” as a sort of “fixed star” in the economic universe was meaningless. The purpose of economic theory was to postulate the series of equilibria which would result under various possible sets of conditions; just as a theory of mechanics enables one to calculate that, given a collection of forces at work in a certain arrangement, things will come to rest in a certain equilibrium position. But, as everyone knows who has ever played with a collection of pulleys or thought about the structure of a suspension bridge, it may not always be possible to calculate a “stable equilibrium” where opposing strains and stresses balance one another; while in certain very complicated situations one may not know enough of the facts to be able to calculate what the new equilibrium will be if one starts a movement by displacing one of the forces at work. To be able to calculate an equilibrium, therefore, the situation one is dealing with and one’s knowledge about it must fulfil certain conditions. Whether these conditions are fulfilled or not is the criterion by which one judges whether a theory of equilibrium in economics, as in mechanics, is adequate or not.

The attempt to calculate an equilibrium in a given situation is comparable to the familiar attempt in algebra to “solve” a system of simultaneous equations. In these equations there are a number of “unknown variables” (usually written as x, y, z, etc.) and a number of “constants” (usually written as a, b, c, etc.). About the former, it is assumed, one knows initially nothing at all. The latter are part of the given data of the problem: some particular value, or number, is, or can be, assigned to them; and the actual arithmetical “solution” of the equations will differ according to the value assignable to these “constants.” The “solution” consists in “determining” (or finding the value of) the unknowns (the x, y, z , etc.). A simple rule exists as to whether a system of equations is capable of being solved: it has a solution if the number of equations (or known relationships) is equal to the number of unknown variables which have to be determined. And this is the criterion of whether a theory of equilibrium is “adequate” or not.

Economic theory has employed the conception of “functional equations” (one quantity is expressed as a “function” of another if the one varies, or moves, with the other in some particular way). Moreover, it has employed functional equations of an “arbitrary” or general type, which merely postulate some functional relationship between quantities, and not any one particular relationship. By this means it has made its conclusions of a more general character – a given theory is made to cover a wider range of possible cases. For instance, economic theory may assume that consumers’ demand for “a little more” of x will decrease with the quantity of it that is offered for sale, but without specifying the precise nature of that variation of demand; and in this way x can be taken to represent a wider range of particular cases (e.g., com or cloth or tea or gramophones or labour).

In the new economics, therefore, it was no longer a question of searching for a single “cause” of value, a primary constituent or principle to which all questions of exchange and distribution could be related. There was no longer a need (at any rate for the theory of value as now conceived) to analyse everything into terms of what was virtually a single factor of production – a common term of real cost in relation to which qualitative differences could be resolved. It was a question of grouping together certain functional relationships, all of which, in combination and “simultaneously,” determined value. It was a matter of pure convenience how many factors of production there were, provided only one could make sufficient assumptions about the supply of them. All that was necessary was to be able to postulate a sufficient number of conditions and to find the right number of independent variables for a determinate equilibrium to be established. In the search for these independent factors Jevons and the Austrians transferred their attention from conditions of production to consumption, from supply to demand, and sought the important determining factor in what, underlay consumers’ demand. And here Hedonism gave them an important clue. Consumers’ demand was a reflection of consumers’ desire; and desire, in turn, (at least in rational men) was rooted in the pleasure which the object of desire afforded. This capacity of affording plea· sure Jevons termed Utility. The earlier economists had indicated that value could not be a function of utility, since some commodities, like water, had a high utility but little or no value, and others, like diamonds, had small utility but high value; and Marx had pointed out that utility was not a quantity and could not therefore bear a relation to a quantity value. The discovery which Jevons and the Austrians claimed to enunciate was that price was a function, not of aggregate utility (which it obviously could not be), but of the increment of utility – of the additional utility afforded to the consumer by the marginal unit of a given supply.

For instance, of a given supply of fish offered for sale on a market on a particular day the marginal utility of the supply of fish would be the utility to some consumer or other of the nth or final lot of fish sold. (By nth is meant, that, there are 100 fish, it is the hundredth, if 1,000 fish, the thousandth, and so on.) Price could not be greater than this (if the fish is marketed at a single price), otherwise the final lot of fish would not find a purchaser who thought it worth while (as measured by its utility) to buy more fish at this price; while on the other hand the seller of fish, desiring to get the highest price he could, would presumably not part with his fish at a price appreciably below this. Whether utility itself was a quantity or not, this marginal increment of it was capable of being expressed in quantitative form. Jevons said: “Repeated reflection and enquiry has led me to the somewhat novel opinion that value depends entirely upon utility... Labour is found often to determine value, but only in an indirect manner by varying the degree of utility of the commodity through an increase or limitation of the supply."[1]

The starting-point of the new theory was an empirical observation about the nature of desires, which has been variously described as the Law of Diminishing Utility or the Law of Satiety of Wants. The utility of a thing would generally increase with the amount of it possessed and enjoyed, but generally at a diminishing rate, the increment of utility afforded by an increment of supply tending towards zero at some near or distant point-the point of satiety. It was this increment of utility at any one point – “the final degree of utility,” as Jevons called it, or “marginal utility,” as Marshall termed it – which determined value, since this fixed the worth of a little more, or a little less, of the thing to the person in question, and so determined the rate at which he was willing to exchange it against something else – against money or other commodities. For instance, suppose two persons A and B exchanging corn against cloth. One could express the utility of corn and of cloth to each of the parties as some function of the respective quantities of corn and cloth possessed. The seller of corn will find it in his interest to continue to give com in exchange for cloth up to the point where the utility of the bushel of com he is parting with is equal to that of the quantity of cloth he obtains in return; and similarly for the other party. Hence the position of equilibrium – the point where exchange between them will stop – will be that rate of exchange where the marginal utility of corn and cloth is equal for each of the two parties. Hence, given this condition and the form of the utility function for the two parties, a determinate equilibrium – the amount of com and cloth exchanged – can be calculated. Expressed symbolically in terms of two commodities a and b, we have the following conditions of equilibrium:

[Φ1 (x1) / Ψ1 (y1) ] = [ x/y] = [Φ2 (x2) / Ψ2 (y2) ]

where Φ1 (x1) and Ψ1 (y1) represent the utility-functions of a and b to A, and Φ2 (x2) and Ψ2 (y2) the utility-functions of a and b to B. In graphical form the relation between the .pair of utility-functions to A can be expressed as a curve, and similarly for B; and the equilibrium will be represented as the point of intersection of the curves.

In this problem there are two equations and two unknowns, so that the equation yield a determinate solution.[2] Some economists have been quick to point out, as a corollary of this reasoning, that this equilibrium-rate of exchange, which the conditions of a free market tend to establish, is that which gives the maximum common gain of utility to the persons concerned in the exchange – in other words, that which coincides with what is socially desirable from a Hedonist point of view. Any interference with a free market and the prices which it tends to establish will accordingly reduce, and not augment, this common gain.

Prices are viewed simply as the resultant of subjective valuations in the minds of the individuals concerned. Expressed in the simple form of two commodities being bartered against one another, the problem does not raise great difficulty; and in the manner of treatment of the simplest case the underlying unity of modern economics is typified. But when we depart from this abstract case and approach nearer to the conditions of the economic world, where exchange is generally not between owners of stocks of two commodities but between producers and consumers, and where the buyer is concerned not with one isolated transaction but with a multitude of related transactions, a number of complications arise; and it is in their different handling of these complications that the differences between schools of economists subsequent to Jevons mainly consisted. To a considerable extent, therefore, the differences between these schools is purely formal.


1.] W. S. Jevons: Theory of Political Economy (1871), pp. 1-2.

2. This was the view of Jevons. It has since been established that under direct barter the conditions do not suffice to give a single solution.