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B. The Law of Marginal Utility
It is evident that things are valued as means in accordance with their ability to attain ends valued as more or less urgent. Each physical unit of a means (direct or indirect) that enters into human action is valued separately. Thus, the actor is interested in evaluating only those units of means that enter, or that he considers will enter, into his concrete action. Actors choose between, and evaluate, not “coal” or “butter” in general, but specific units of coal or butter. In choosing between acquiring cows or horses, the actor does not choose between the class of cows and the class of horses, but between specific units of them—e.g., two cows versus three horses. Each unit that enters into concrete action is graded and evaluated separately. Only when several units together enter into human action are all of them evaluated together.
The processes that enter into valuation of specific units of different goods may be illustrated in this example:21 An individual possessing two cows and three horses might have to choose between giving up one cow or one horse. He may decide in this case to keep the horse, indicating that in this state of his stock, a horse is more valuable to him than a cow. On the other hand, he might be presented with the choice of keeping either his entire stock of cows or his stock of horses. Thus, his stable and cowshed might catch fire, and he is presented with the choice of saving the inhabitants of one or of the other building. In this case, two cows might be more valuable to him than three horses, so that he will prefer to save the cows. When deciding between units of his stock, the actor may therefore prefer good X to good Y, while he may choose good Y if he must act upon his whole stock of each good.
This process of valuation according to the specific units involved provides the solution for the famous “value paradox” which puzzled writers for centuries. The question was: How can men value bread less than platinum, when “bread” is obviously more useful than “platinum”? The answer is that acting man does not evaluate the goods open to him by abstract classes, but in terms of the specific units available. He does not wonder whether “bread-in-general” is more or less valuable to him than “platinum-in-general,” but whether, given the present available stock of bread and platinum, a “loaf of bread” is more or less valuable to him than “an ounce of platinum.” That, in most cases, men prefer the latter is no longer surprising.22
As has been explained above, value, or utility, cannot be measured, and therefore cannot be added, subtracted, or multiplied. This holds for specific units of the same good in the same way as it holds for all other comparisons of value. Thus, if butter is an object serving human ends, we know that two pounds of butter will be valued more highly than one pound. This will be true until a point is reached when the butter is available in unlimited quantities to satisfy human wants and will then be transferred from the status of a means to that of a general condition of human welfare. However, we cannot say that two pounds of butter are “twice as useful or valuable” as one pound.
What has been involved in this key concept of “specific units of a good”? In these examples, the units of the good have been interchangeable from the point of view of the actor. Thus, any concrete pound of butter was evaluated in this case perfectly equally with any other pound of butter. Cow A and cow B were valued equally by the individual, and it made no difference to him which cow he was faced with the choice of saving. Similarly, horse A was valued equally with horse B and with horse C, and the actor was not concerned which particular horse he had to choose. When a commodity is in such a way available in specific homogeneous units equally capable of rendering the same service to the actor, this available stock is called a supply. A supply of a good is available in specific units each perfectly substitutable for every other. The individual above had an available supply of two cows and three horses, and a supply of pounds of butter.
What if one pound of butter was considered by the actor as of better quality than another pound of butter? In that case, the two “butters” are really different goods from the point of view of the actor and will be evaluated differently. The two pounds of butter are now two different goods and are no longer two units of a supply of one good. Similarly, the actor must have valued each horse or each cow identically. If he preferred one horse to each of the others, or one cow to the other, then they are no longer units of the supply of the same good. No longer are his horses interchangeable for one another. If he grades horse A above the others and regards horses B and C indifferently, then he has supplies of two different goods (omitting the cows): say, “Grade A horses—one unit”; and “Grade B horses—two units.” If a specific unit is differently evaluated from all other units, then the supply of that good is only one unit.
Here again, it is very important to recognize that what is significant for human action is not the physical property of a good, but the evaluation of the good by the actor. Thus, physically there may be no discernible difference between one pound of butter and another, or one cow and another. But if the actor chooses to evaluate them differently, they are no longer part of the supply of the same good.
The interchangeability of units in the supply of a good does not mean that the concrete units are actually valued equally. They may and will be valued differently whenever their position in the supply is different. Thus, suppose that the isolated individual successively finds one horse, then a second, then a third. Each horse may be identical and interchangeable with the others. The first horse will fulfill the most urgent wants that a horse can serve; this follows from the universal fact that action uses scarce means to satisfy the most urgent of the not yet satisfied wants. When the second horse is found, he will be put to work satisfying the most urgent of the wants remaining. These wants, however, must be ranked lower than the wants that the previous horse has satisfied. Similarly, the third horse acquired might be capable of performing the same service as the others, but he will be put to work fulfilling the highest of the remaining wants—which, however, will yet be lower in value than the others.
The important consideration is the relation between the unit to be acquired or given up and the quantity of supply (stock) already available to the actor. Thus, if no units of a good (whatever the good may be) are available, the first unit will satisfy the most urgent wants that such a good is capable of satisfying. If to this supply of one unit is added a second unit, the latter will fulfill the most urgent wants remaining, but these will be less urgent than the ones the first fulfilled. Therefore, the value of the second unit to the actor will be less than the value of the first unit. Similarly, the value of the third unit of the supply (added to a stock of two units) will be less than the value of the second unit. It may not matter to the individual which horse is chosen first and which second, or which pounds of butter he consumes, but those units which he does use first will be the ones that he values more highly. Thus, for all human actions, as the quantity of the supply (stock) of a good increases, the utility (value) of each additional unit decreases.
Let us now consider a supply from the point of view of a possible decrease, rather than an increase. Assume that a man has a supply of six (interchangeable) horses. They are engaged in fulfilling his wants. Suppose that he is now faced with the necessity of giving up one horse. It now follows that this smaller stock of means is not capable of rendering as much service to him as the larger supply. This stems from the very existence of the good as a means.23 Therefore, the utility of X units of a good is always greater than the utility of X – 1 units. Because of the impossibility of measurement, it is impossible to determine by how much greater one value is than the other. Now, the question arises: Which utility, which end, does the actor give up because he is deprived of one unit? Obviously, he gives up the least urgent of the wants which the larger stock would have satisfied. Thus, if the individual was using one horse for pleasure riding, and he considers this the least important of his wants that were fulfilled by the six horses, the loss of a horse will cause him to give up pleasure riding.
The principles involved in the utility of a supply may be illustrated in the following value-scale diagram (Figure 3). We are considering any given means, which is divisible into homogeneous units of a supply, each interchangeable and capable of giving service equal to that of the other units. The supply must be scarce in relation to the ends that it is capable of fulfilling; otherwise it would not be a good, but a condition of human welfare. We assume for simplicity that there are 10 ends which the means could fulfill, and that each unit of means is capable of serving one of the ends.
If the supply of the good is 6 units, then the first six ends, ranked in order of importance by the valuing individual, are the ones that are being satisfied. Ends ranked 7–10 remain unsatisfied. If we assume that the stock arrived in successive units, then the first unit went to satisfy end 1, the second unit was used to serve end 2, etc. The sixth unit was used to serve end 6. The dots indicate how the units were used for the different ends, and the arrow indicates the direction the process took, i.e., that the most important ends were served first; the next, second, etc. The diagram illustrates the aforementioned laws that the utility (value) of more units is greater than the utility of fewer units and that the utility of each successive unit is less as the quantity of the supply increases.
Now, suppose the actor is faced with the necessity of giving up one unit of his stock. His total will be 5 instead of 6 units. Obviously, he gives up satisfying the end ranked sixth, and continues to satisfy the more important ends 1–5. As a result of the interchangeability of units, it does not matter to him which of the six units he must lose; the point is that he will give up serving this sixth end. Since action considers only the present and the future not the past, it does not matter to him which units he acquired first in the past. He deals only with his presently available stock. In other words, suppose that the sixth horse that he had previously acquired (named “Seabiscuit”) he had placed in the service of pleasure riding. Suppose that he now must lose another horse (“Man o’ War”) which had arrived earlier, and which was engaged in the more important duty (to him) of leading a wagon. He will still give up end 6 by simply transferring Seabiscuit from this function to the wagon-leading end. This consequence follows from the defined interchangeability of units and from disregard of past events which are of no consequence for the present and the future.
Thus, the actor gives up the lowest-ranking want that the original stock (in this case, six units) was capable of satisfying. This one unit that he must consider giving up is called the marginal unit. It is the unit “at the margin.” This least important end fulfilled by the stock is known as the satisfaction provided by the marginal unit, or the utility of the marginal unit—in short: the marginal satisfaction, or marginal utility. If the marginal unit is one unit, then the marginal utility of the supply is the end that must be given up as the result of a loss of the unit. In Figure 3, the marginal utility is ranked sixth among the ends. If the supply consisted of four units, and the actor were faced with the necessity of giving up one unit, then the value of the marginal unit, or the marginal utility, would have a rank of four. If the stock consisted of one unit, and this had to be given up, the value of the marginal unit would be one—the value of the highest-ranked end.
We are now in a position to complete an important law indicated above, but with different phraseology: The greater the supply of a good, the lower the marginal utility; the smaller the supply, the higher the marginal utility. This fundamental law of economics has been derived from the fundamental axiom of human action; it is the law of marginal utility, sometimes known as the law of diminishing marginal utility. Here again, it must be emphasized that “utility” is not a cardinal quantity subject to the processes of measurement, such as addition, multiplication, etc. It is a ranked number expressible only in terms of higher or lower order in the preferences of men.
This law of marginal utility holds for all goods, regardless of the size of the unit considered. The size of the unit will be the one that enters into concrete human action, but whatever it is, the same principle applies. Thus, if in certain situations, the actor must consider only pairs of horses as the units to add or subtract from his stock, instead of the individual horses, he will construct a new and shorter scale of ends with fewer units of supply to consider. He will then go through a similar process of assigning means to serve ends and will give up the least valued end should he lose a unit of supply. The ends will simply be ranked in terms of the alternative uses of pairs of horses, instead of single horses.
What if a good cannot be divided into homogeneous units for purposes of action? There are cases where the good must be treated as a whole in human action. Does the law of marginal utility apply in such a case? The law does apply, since we then treat the supply as consisting of one unit. In this case, the marginal unit is equal in size to the total supply possessed or desired by the actor. The value of the marginal unit is equal to the first rank of the ends which the total good could serve. Thus, if an individual must dispose of his whole stock of six horses, or acquire a stock of six horses together, the six horses are treated as one unit. The marginal utility of his supply would then be equal to the first-ranking end that the unit of six horses could supply.
If, as above, we consider the case of additions instead of decreases to stock, we recall that the law derived for this situation was that as the quantity of supply increases, the utility of each additional unit decreases. Yet this additional unit is precisely the marginal unit. Thus, if instead of decreasing the supply from six to five horses, we increase it from five to six, the value of the additional horse is equal to the value of the sixth-ranking end—say, pleasure riding. This is the same marginal unit, with the same utility, as in the case of decreasing the stock from six to five. Thus, the law derived previously was simply another form of the law of marginal utility. The greater the supply of a good, the lower the marginal utility; the smaller the supply, the higher the marginal utility. This is true whether or not the marginal unit is the unit of decrease of stock or the unit of addition to stock, when these are considered by the actor. If a man's supply of a good equals X units, and he is considering the addition of one unit, this is the marginal unit. If his supply is X + 1 units, and he is considering the loss of one unit, this too is his marginal unit, and its value is identical with the former (provided that his ends and their ranking are the same in both cases).
We have dealt with the laws of utility as they apply to each good treated in human action. Now we must indicate the relationship among various goods. It is obvious that more than one good exists in human action. This has already been definitely proven, since it was demonstrated that more than one factor of production, hence more than one good, must exist. Figure 4 below demonstrates the relationship between the various goods in human action. Here the value scales of two goods are considered—X and Y. For each good, the law of marginal utility holds, and the relation between supply and value is revealed in the diagram for each good. For simplicity, let us assume that X is horses and Y cows, and that the value scales representing those held by the individual are as follows (horizontal lines are drawn through each end to demonstrate the relationship in the ranking of the ends of the two goods): End Y-1 is ranked highest (say, cow one); then ends X-1, X-2, and X-3 (horses one, two, and three); Y-2; Y-3; X-4; Y-4; X-5; Y-5; X-6; X-7; Y-6; Y-7.
Now, the man's value scales will reveal his choices involving alternatives of action in regard to these two goods. Suppose that his stock is: 3Y (cows) and 4X (horses).
He is faced with the alternative of giving up either one cow or one horse. He will choose the alternative that will deprive him of the least valued end possible. Since the marginal utility of each good is equal to the value of the least important end of which he would be deprived, he compares the marginal utility of X with the marginal utility of Y. In this case, the marginal unit of X has a rank of X-4, and the marginal unit of Y has a rank of Y-3. But the end Y-3 is ranked higher on his value scale than X-4. Hence, the marginal utility of Y is in this case higher than (or greater than) the marginal utility of X. Since he will give up the lowest possible utility, he will give up one unit of X. Thus, presented with a choice of units of goods to give up, he will give up the good with units of lowest marginal utility on his value scale. Suppose another example: that his stock is three horses and two cows. He has the alternative of giving up 1X or 1Y. In this case, the marginal utility of Y is ranked at Y-2, and that of X is ranked at X-3. But X-3 occupies a higher position on his value scale than Y-2, and therefore the marginal utility of Y is at this point lower than the marginal utility of X. He gives up a unit of Y.
The converse occurs if the man must choose between the alternative of increasing his stock by either one unit of X or one unit of Y. Thus, suppose that his stock is four units of X and four units of Y. He must choose between adding one horse or one cow. He then compares the marginal utility of increase, i.e., the value of the most important of the not yet satisfied wants. The marginal utility of X is then ranked at X-5; of Y at Y-5. But X-5 ranks higher than Y-5 on his value scale, and he will therefore choose the former. Thus, faced with the choice of adding units of goods, he will choose the unit of highest marginal utility on his value scale.
Another example: Previously, we saw that the man in a position of (4X, 3Y) would, if faced with the choice of giving up one unit of either X or Y, give up the unit of X, with a lower marginal utility. In other words, he would prefer a position of (3X, 3Y) to (4X, 2Y). Now suppose he is in a position of (3X, 3Y) and faced with the choice of adding one unit of X or one unit of Y. Since the marginal utility of the increased X is greater than that of Y, he will choose to add the unit of X and to arrive at a position of (4X, 3Y) rather than (3X, 4Y). The reader can work out the hypothetical choices for all the possible combinations of the actor's stock.
It is evident that in the act of choosing between giving up or adding units of either X or Y, the actor must have, in effect, placed both goods on a single, unitary value scale. Unless he could place X and Y on one value scale for comparison, he could not have determined that the marginal utility of the fourth unit of X was higher than that of the fourth unit of Y. The very fact of action in choosing between more than one good implies that the units of these goods must have been ranked for comparison on one value scale of the actor. The actor may not and cannot measure differences in utility, but he must be engaged in ranking all the goods considered on one value scale. Thus, we should actually consider the ends served by the two means as ranked on one value scale as follows:
1 — Y-1
2 — X-1
3 — X-2
4 — X-3
5 — Y-2
6 — Y-3
7 — X-4
8 — Y-4
9 — X-5
10 — Y-5
11 — X-6
12 — X-7
13 — Y-6
14 — Y-7
These principles permit of being extended from two to any number of goods. Regardless of the number of goods, any man will always have a certain combination of units of them in his stock. He may be faced with the choice of giving up one unit of any good that he might choose. By ranking the various goods and the ends served by the relevant units, the actor will give up the unit of that good of which the marginal utility to him is the lowest. Similarly, with any given combination of goods in his stock, and faced with the choice of adding one unit of any of the goods available, the actor will choose that good whose marginal utility of increase will be highest. In other words, all the goods are ranked on one value scale in accordance with the ends they serve.
If the actor has no units of some goods in his possession, this does not affect the principle. Thus, if he has no units of X or Y in his possession, and he must choose between adding a unit of X or one unit of Y, he will choose the marginal unit of greatest utility, in this case, Y. The principle is easily extended to the case of n goods.
It must be reiterated here that value scales do not exist in a void apart from the concrete choices of action. Thus, if the actor has a stock of (3X, 4Y, 2Z, etc.), his choices for adding and subtracting from stock take place in this region, and there is no need for him to formulate hypothetical value scales to determine what his choices would have been if his stock were (6X, 8Y, 5Z, etc.). No one can predict with certainty the course of his choices except that they will follow the law of marginal utility, which was deduced from the axiom of action.
The solution of the value paradox mentioned above is now fully clear. If a man prefers one ounce of platinum to five loaves of bread, he is choosing between units of the two goods based on the supply available. On the basis of the available supply of platinum and of bread, the marginal utility of a unit of platinum is greater than the marginal utility of a unit of bread.24
- 21. Cf. Ludwig von Mises, The Theory of Money and Credit (New Haven: Yale University Press, 1953), p. 46.
- 22. Also cf. T.N. Carver, The Distribution of Wealth (New York: Macmillan & Co., 1904), pp. 4–12. See below for a further discussion of the influences on man's valuation of specific units resulting from the size of the available stock.
- 23. This would not be true only if the “good” were not a means, but a general condition of human welfare, in which case one less unit of supply would make no difference for human action. But in that case it would not be a good, subject to the economizing of human action.
- 24. On the whole subject of marginal utility, see Eugen von Böhm-Bawerk, The Positive Theory of Capital (New York: G.E. Stechert, 1930), pp. 138–65, especially pp. 146–55.