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Ends and Values and the Law of Marginal Utility

Tags History of the Austrian School of EconomicsValue and Exchange

02/08/2019Murray N. Rothbard

All action involves the employment of scarce means to attain the most valued ends. Man has the choice of using the scarce means for various alternative ends, and the ends that he chooses are the ones he values most highly. The less urgent wants are those that remain unsatisfied. Actors can be interpreted as ranking their ends along a scale of values, or scale of preferences. These scales differ for each person, both in their content and in their orders of preference. Furthermore, they differ for the same individual at different times.


1. Going for a drive


2. Going to a concert


3. Playing bridge


4. Continuing to watch a baseball game

The choice of which ends to include in the actor's value scale and the assignment of rank to the various ends constitute the process of value judgment. Each time the actor ranks and chooses between various ends, he is making a judgment of their value to him.

It is highly useful to assign a name to this value scale held by all human actors. We are not at all concerned with the specific content of men's ends, but only with the fact that various ends are ranked in the order of their importance. These scales of preference may be called happiness or welfare or utility or satisfaction or contentment. Which name we choose for value scales is not important. At any rate, it permits us to say, whenever an actor has attained a certain end, that he has increased his state of satisfaction, or his contentment, happiness, etc. Conversely, when someone considers himself worse off, and fewer of his ends are being attained, his satisfaction, happiness, welfare, etc., have decreased.

It is important to realize that there is never any possibility of measuring increases or decreases in happiness or satisfaction. Not only is it impossible to measure or compare changes in the satisfaction of different people; it is not possible to measure changes in the happiness of any given person. In order for any measurement to be possible, there must be an eternally fixed and objectively given unit with which other units may be compared. There is no such objective unit in the field of human valuation.

The individual must determine subjectively for himself whether he is better or worse off as a result of any change. His preference can only be expressed in terms of simple choice, or rank. Thus, he can say, "I am better off" or "I am happier" because he went to a concert instead of playing bridge (or "I will be better off" for going to the concert), but it would be completely meaningless for him to try to assign units to his preference and say, "I am two and a half times happier because of this choice than I would have been playing bridge." Two and a half times what? There is no possible unit of happiness that can be used for purposes of comparison and, hence, of addition or multiplication. Thus, values cannot be measured; values or utilities cannot be added, subtracted, or multiplied. They can only be ranked as better or worse. A man may know that he is or will be happier or less happy, but not by "how much," not by a measurable quantity.

All action is an attempt to exchange a less satisfactory state of affairs for a more satisfactory one. The actor finds himself (or expects to find himself) in a nonperfect state, and, by attempting to attain his most urgently desired ends, expects to be in a better state. He cannot measure the gain in satisfaction, but he does know which of his wants are more urgent than others, and he does know when his condition has improved.

Therefore, all action involves exchange — an exchange of one state of affairs, X, for Y, which the actor anticipates will be a more satisfactory one (and therefore higher on his value scale). If his expectation turns out to be correct, the value of Y on his preference scale will be higher than the value of X, and he has made a net gain in his state of satisfaction or utility. If he has been in error, and the value of the state that he has given up — X — is higher than the value of Y, he has suffered a net loss. This psychic gain (or profit) and loss cannot be measured in terms of units, but the actor always knows whether he has experienced psychic profit or psychic loss as a result of an action-exchange.

Human actors value means strictly in accordance with their valuation of the ends that they believe the means can serve. Obviously, consumers' goods are graded in value in accordance with the ends that men expect them to satisfy. Thus, the value placed on the enjoyment contributed by a ham sandwich or a house will determine the value a man will place on the ham sandwich or the house themselves. Similarly, producers' goods are valued in accordance with their expected contribution in producing consumers' goods.

Higher-order producers' goods are valued in accordance with their anticipated service in forming lower-order producers' goods. Hence, those consumers' goods serving to attain more highly valued ends will be valued more highly than those serving less highly valued ends, and those producers' goods serving to produce more highly valued consumers' goods will themselves be valued more highly than other producers' goods. Thus, the process of imputing values to goods takes place in the opposite direction to that of the process of production. Value proceeds from the ends to the consumers' good to the various first-order producers' goods, to the second-order producers' goods, etc. The original source of value is the ranking of ends by human actors, who then impute value to consumers' goods, and so on to the orders of producers' goods, in accordance with their expected ability to contribute toward serving the various ends.

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: 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.

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. 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 1). We are considering any given means that 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.

Figure 1: Value-Scale Diagram

Figure 1: Value-Scale Diagram

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 1, 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.



Murray N. Rothbard

Murray N. Rothbard made major contributions to economics, history, political philosophy, and legal theory. He combined Austrian economics with a fervent commitment to individual liberty.