The marginal desire (originally the least intense of the desires now gratified) now marks and expresses the actual value of each of the other units of the stock. This is the marginal valuation. The stock being made up of homogeneous units, equally fitted to gratify any one of the series of desires, no unit can be valued at the moment more than any other unit. The aspect of valuation here presented is called either the marginal principle (thinking of the least intense desire), or the principle of indifference (thinking of the equal fitness of the objective units), and may be expressed as follows: each unit of a person's stock of like goods which is actually at hand and equally convenient for use, is of equal value with every other unit, no matter to what use it is there applied. Of course this holds only as to the particular time and set of conditions, and desires may change in the next moment.

§ 10. Diagram of marginal valuation. This principle of valuation may be illustrated by the following diagram in which horizontal distance represents stocks of goods of various amounts, and perpendicular distance represents marginal valuation or value per unit. Let us assume that in the case of a stock of ten units the marginal valuation (value per unit) is 36. The value then ascribed to the whole stock will be 360 (represented on the diagram by the rectangle ab). If instead of a stock of ten we consider a stock of fifteen, then since fifteen units will gratify more desires than ten units, leaving fewer desires still unsatisfied, the marginal valuation will be lower - for example 30 instead of 36. In this case the value of the stock is 450 (rectangle ac). And similarly, for stocks of various amounts, we get marginal and total valuations as shown in the following table: FIG. 6. Marginal Valuation.

 Units of commodity Marginal valuation interms of anything else taken as a standard Valuation of whole amount 10 36 360 15 30 450 20 25 500 30 19 570 40 15 600 50 10 500 60 5 300

The first thing of significance in the diagram is that the marginal valuation, or value per unit, is large in the case of a small stock, and small in the case of a large stock. And this means simply that when we have a small supply of a commodity we set a high value (per unit) upon it; when we have a large supply its value per unit to us is small. This, of course, is a familiar fact of daily experience.2

§11. The paradox of value. One thing more may be pointed out by way of further study of the diagram. Corresponding with any given stock - for example a stock of ten units - there is a rectangle (Fig. 5, ab) which represents graphically the total value of the stock - that is, the product

2 It is evident that the various parts of a stock of goods can be valued on the marginal principle only when it is possible to choose among the various units and to apply them to various uses in such proportions as one will. If another person controls the whole stock and compels us to choose "all or none" we may be forced to value the whole stock according to our more intense desires. This is a fact of great importance in some practical problems, such as those of monopoly of the value per unit by the number of units. In the case of a very small stock this rectangle will be very small. On the other hand, in the case of a very large stock, since the value per unit is small and may even reach zero, the rectangle will also be very small, reaching zero, as we have already seen, in the case of free goods. Somewhere in between these two extremes, of course, there will be a maximum rectangle (Fig. 5, af), a stock the total value of which is greater than that of either a larger or a smaller stock. This fact (brought out also in the third column of the table) that after a certain point an increase of the total stock will result in a decrease of the total value, has been called the "paradox of value." Cases have been known of the partial destruction of a stock of goods by its owners as the result of their calculation that the remainder would actually sell on the market for more than could be secured for the whole original supply.

Note

The Weber-Fechner law. In part the effects of repeated stimuli are probably explained by a law of psychology. It is that geometric increase of the stimuli acting on any of the senses is required to produce an arithmetic increase of sensation. It holds "approximately and within a certain middle region of the intensive scale for intensities of noise and tone, of pressure, of various kinesthetic complexes (lifted weights, movements of the arms, movements of the eyes), and of smell." "There is some little evidence that affection on the intensive side obeys Weber's law." (Titchener, "A Textbook of Psychology," 1911, pp. 218, 259.)

The points on the curve R1 to R4 indicate the total stimuli (measured on the ordinate by scale shown at right) required to produce a given degree of sensation, shown by abscissas measured on line S0 to S4 . While the stimuli increase in geometric ratio (1, 2, 4, 8) the sensations increase in an arithmetic ratio (1, 2, 3, 4.) The relative quantity of sensation per unit of stimulus is represented by the height of a, b, c, d respectively above the base line. The second R produces sensation equal to the first, the third and fourth R (average) produce 1/2 as much sensation, the 5th to 8th R (average) produce 1/4 as much. The curve a-d corresponds with the observed trend of decreasing valuation in many cases. It is clear, however, that valuation does not always (perhaps not usually) rise and fall in curves exactly parallel with sensation; for example, a first and a second unit of R might (if there were no more) be neither pleasurable nor valuable; a third and fourth might raise the total sensation to a degree where it was desirable and valuable; and not until the fifth or some latter unit would an additional unit of R add a smaller proportional value. The correspondence between decreasing sensation and decreasing valuation is thus found only at certain middle regions of the scale. FIG. 6. The Wiber-Fkchneb Law.