apple is greater than the total satisfaction from seven plums but less than the total satisfaction from eight plums.3
This is the only interpretation that can be harmonized with the fundamental conception expounded by the marginal-utility theorists, and especially by Böhm-Bawerk himself, that the utility (and consequently the subjective use-value also) of units of a commodity decreases as the supply of them increases. But to accept this is to reject the whole idea of measuring the subjective use-value of commodities. Subjective use-value is not susceptible of any kind of measurement.
The American economist Irving Fisher has attempted to approach the problem of value measurement by way of mathematics.4 His success with this method has been no greater than that of his predecessors with other methods. Like them, he has not been able to surmount the difficulties arising from the fact that marginal utility diminishes as supply increases, and the only use of the mathematics in which he clothes his arguments, and which is widely regarded as a particularly becoming dress for investigations in economics, is to conceal a little the defects of their clever but artificial construction.
Fisher begins by assuming that the utility of a particular good or service, though dependent on the supply of that good or service, is independent of the supply of all others. He realizes that it will not be possible to achieve his aim of discovering a unit for the measurement of utility unless he can first show how to determine the proportion between two given marginal utilities. If, for example, an individual has 100 loaves of bread at his disposal during one year, the marginal utility of a loaf to him will be greater than if he had 150 loaves. The problem is, to determine the arithmetical proportion between the two marginal utilities. Fisher attempts to do this by comparing them with a third utility. He therefore supposes the individual to have B gallons of oil annually as well, and calls that increment of B whose utility is equal to that of the 100th loaf of bread. In the second case, when not 100 but 150 loaves are available, it is assumed that the supply of B remains unchanged. Then the utility of the 150th loaf may be equal, say, to the utility of b/2. Up to this point it is unnecessary to quarrel with Fisher’s argument; but now follows a jump that neatly avoids all the difficulties of the problem. That is to say, Fisher simply continues, as if he were stating something quite self-evident: “Then the utility of the 150th loaf is said to be half the utility of the 100th.” Without any further explanation he then calmly proceeds with his problem, the solution of which (if the above proposition is accepted as correct) involves no further difficulties, and so succeeds eventually in deducing a unit which he calls a “util.” It does not seem to have occurred to him that in the particular sentence just quoted he has argued in defiance of the whole of marginal-utility theory and set himself in opposition to all the fundamental doctrines of modern economics. For obviously this conclusion of his is legitimate only if the utility of b is equal to twice the utility of b/2. But if this were really so, the problem of determining the proportion between two marginal utilities could have been solved in a quicker way, and his long process of deduction would not have been necessary. Just as justifiably as he assumes that the utility of is equal to twice the utility of b/2, he might have assumed straightaway that the utility of the 150th loaf is two-thirds of that of the 100th.
Fisher imagines a supply of B gallons that is divisible into n small quantities b, or 2n small quantities b/2. He assumes that an individual who has this supply B at his disposal regards the value of commodity unit x as equal to that of b and the value of commodity unit y as equal to that of b/2. And he makes the further assumption that in both valuations, that is, both in equating the value of x with that of b and in equating the value of y with that of b/2, the individual has the same supply of B gallons at his disposal.
He evidently thinks it possible to conclude from this that the utility of b is twice as great as that of b/2. The error here is obvious. The individual is in the one case faced with the choice between x (the value of the 100th loaf) and b = 2b/2. He finds it impossible to decide between the two, i.e., he values both equally. In the second case he has to choose between y (the value of the 150th loaf) and b/2. Here again he finds that both alternatives are of equal value. Now the question arises, what is the proportion between the marginal utility of b and that of b/2? We can determine this only by asking ourselves what the proportion is between the marginal utility of the nth part of a given supply and that of the 2nth part of the same supply, between that of b/n and that of b/2n. For this purpose let us imagine the supply B split up into 2n portions of b/2n. Then the marginal utility of the (2n-1)th portion is greater than that of the 2nth portion. If we now imagine the same supply B divided into n portions, then it clearly follows that the marginal utility of the nth portion is equal to that of the (2n-1)th portion plus that of the 2nth portion in the previous case. It is not twice as great as that of the 2nth portion, but more than twice as great. In fact, even with an unchanged supply, the marginal utility of several units taken together is not equal to the marginal utility of one unit multiplied by the number of units, but necessarily greater than this product. The value of two units is greater than, but not twice as great as, the value of one unit.5
Perhaps Fisher thinks that this consideration may be disposed of by supposing b and b/2 to be such small quantities that their utility may be reckoned infinitesimal. If this is really his opinion, then it must first of all be objected that the peculiarly mathematical conception of infinitesimal quantities is inapplicable to economic problems. The utility afforded by a given amount of commodities, is either great enough for valuation, or so small that it remains imperceptible to the valuer and cannot therefore affect his judgment. But even if the applicability of the conception of infinitesimal quantities were granted, the argument would still be invalid, for it is obviously impossible to find the proportion between two finite marginal utilities by equating them with two infinitesimal marginal utilities.
Finally, a few words must be devoted to Schumpeter’s attempt to set up as a unit the satisfaction resulting from the consumption of a given quantity of commodities and to express other satisfactions as multiples of this unit. Value judgments on this principle would have to be expressed as follows: “The satisfaction that I could get from the consumption of a certain quantity of commodities is a thousand times as great as that which I get from the consumption of an apple a day,” or “For this quantity of goods I would give at the most a thousand times this apple.” 6 Is there really anybody on earth who is capable of adumbrating such mental images or pronouncing such judgments? Is there any sort of economic activity that is actually dependent on the making of such decisions? Obviously not.7 Schumpeter makes the same mistake of starting with the assumption that we need a measure of value in order to be able to compare one “quantity of value” with another. But valuation in no way consists in a comparison of two “quantities of value.” It consists solely in a comparison of the importance of different wants. The judgment “Commodity a is worth more to me than commodity b” no more presupposes a measure of economic value than the judgment ”A is dearer to me—more highly esteemed—than B” presupposes a measure of friendship.
If it is impossible to measure subjective use-value, it follows directly that it is impracticable to ascribe “quantity” to it. We may say, the value of this commodity is greater than the value of that; but it is not permissible for us to assert, this commodity is worth so much. Such a way of speaking necessarily implies a definite unit. It really amounts to stating how many times a given unit is contained in the quantity to be defined. But this kind of calculation is quite inapplicable to processes of valuation.
The consistent application of these principles implies a criticism also of Schumpeter’s views on the total value of a stock of goods. According to Wieser, the total value of a stock of goods is given by multiplying the number of items or portions constituting the stock by their marginal utility at any given moment. The untenability of this argument is shown by the fact that it would prove that the total stock of a free good must always be worth nothing. Schumpeter therefore suggests
