Science is not predestined for perpetual progress. In the history of every science, there have been periods of progress, often triggered by a "Copernican revolution" that suddenly reorients the science into a forward march. But there have also been periods of retrogression, often triggered by a "Keynesian revolution" that sends the science headlong into the woods.

Periods following the most recent "revolution" and continuing to the present are often called the "modern" era of the science. In Human Action, Mises frequently used the term "modern economics." Although he was writing after the Keynesian revolution, he was not referring to post-Keynesian economics. He thought Keynes's only contribution to economics was to dress up long-refuted inflationist fallacies in sophisticated jargon.[1]

By "modern economics," Mises meant the science following the elucidation, in the second half of the 19th century, of what he called the "modern theory of value and prices." And by this he meant the rise in economics of subjective, marginal theories of value — the event known in mainstream economics as the "marginal revolution." It was called a revolution because it dethroned the previously dominant objective, holistic theories of value that were propounded by classical economists such as Adam Smith, David Ricardo, and John Stuart Mill. This event was so epochal that it even occasioned a name change for the science. The discipline formally known as "political economy" was reborn as "economics."

The Paradox of Value

Mises wrote of the limitations of classical political economy,

The classical economists met in the pursuit of their investigations an obstacle which they failed to remove, the apparent antinomy of value. Their theory of value was defective.[2]

This "apparent antinomy of value" is what is commonly known as the "paradox of value." Economists stumped by this supposed paradox could not accept the notion that the exchange value (price) of a good was derived from its use value (utility). This notion, which common sense would seem to demand, appeared to be empirically falsified by many instances in which use value apparently did not determine exchange value.

The best-known such instance is known as the "diamond-water paradox," which was most famously discussed by Adam Smith (although he did not call it a "paradox" or even characterize it as a problem that needed to be solved).

What are the rules which men naturally observe in exchanging them [goods] for money or for one another, I shall now proceed to examine. These rules determine what may be called the relative or exchangeable value of goods.
The word VALUE, it is to be observed, has two different meanings, and sometimes expresses the utility of some particular object, and sometimes the power of purchasing other goods which the possession of that object conveys. The one may be called "value in use;" the other, "value in exchange." The things which have the greatest value in use have frequently little or no value in exchange; on the contrary, those which have the greatest value in exchange have frequently little or no value in use. Nothing is more useful than water: but it will purchase scarce anything; scarce anything can be had in exchange for it. A diamond, on the contrary, has scarce any use-value; but a very great quantity of other goods may frequently be had in exchange for it.[3]

The "apparent antinomy of value" diverted economists from working to formulate a value theory based on subjective utility, and led them to posit other ultimate sources of value. Before the marginal revolution, most British economists adhered to the labor theory of value. The definitive formulation of the labor theory of value was that of David Ricardo, who wrote,

The value of a commodity … depends on the relative quantity of labour which is necessary for its production.[4]

However, many economists (especially on the European continent) refused to accept the labor theory of value. Frederic Bastiat used "Crusoe Economics"[5] to point out the absurdity of such a theory.

Wealth does not consist in the amount of effort required for each satisfaction obtained, but that the exact opposite is true. We should understand that value does not consist in the want or the obstacle or the effort, but in the satisfaction; and we should readily admit that although Robinson Crusoe is both producer and consumer, in order to gauge his progress, we must look, not at his labor, but at its results.[6]

Although such reasoning as this was sufficient to reject the labor theory as obviously false, it was not enough to completely solve the "diamond-water paradox" or to explain exactly how exchange value is derived from use value.

Such a complete vindication of subjective value theory was finally accomplished by the "marginal-utility" approach to value theory, which was formulated independently by William Stanley Jevons (1863), Carl Menger (1871), and Leon Walras (1874).

The Concept of Marginal Utility

The principle of marginal utility (as well as the emptiness of the "value paradox") can be understood via the following thought experiment.

First let us rigorously define the term "utility" by adopting Mises's definition. Mises defined "utility" as the "importance attached to a thing on account of the belief that it can remove uneasiness."[7]

Let us say Adam Smith is offered a five-carat diamond for 100 gallons of spring water. Let us also say that Smith owns a spring that produces sufficient water for him to use up 1,000 gallons every month, but that he has no diamonds and no diamond mine.

Under these conditions, would he make the exchange? Most likely. But then if someone were to ask him which good is more useful, he would most likely say that water is. He then might proclaim, "See, the 'value in use' of water is higher than that of diamonds, yet the 'value in exchange' of water is lower than that of diamonds. Therefore, 'value in exchange' cannot be derived from 'value in use.'"

Now, it is easy to expect someone to say that water is more useful than diamonds. But what do they really mean by that? In common language, such a statement seems to involve a comparison between doing without water for the rest of one's life, versus doing without diamonds for the rest of one's life.

Thinking about it that way, Smith would obviously assign more importance to water than to diamonds. But that is not the choice that is before him. As Mises wrote:

The judgment of value refers only to the supply with which the concrete act of choice is concerned.[8]

The concrete act of choice Smith is concerned with has to do with exactly one diamond of a certain quality and exactly 100 gallons of water of a certain quality.

Furthermore Smith is making this decision under the following conditions regarding the abundance or scarcity of each good:

He has a spring that produces 1,000 gallons of water per month.
He has no diamonds and no diamond mine.

So the real question is: Under those conditions, is one diamond or 100 gallons of water more useful?

With the question understood that way, Smith may still answer that in some fundamental way, 100 gallons of water is more useful, and that a diamond is frippery in comparison.

But let us consider what is really involved in such an answer. Let us ask Smith himself, assuming he did not make the exchange, how would he otherwise allocate his water, if he were to use up 1,000 gallons of water per month?

Let us say he answers as follows:

"Well, laddie, in order of importance, I suppose I would use

100 gallons for minimal drinking water for my family and guests,
500 gallons for minimal bathing and cleaning,
300 gallons for minimal watering of the plants on my estate,
And 100 gallons for enjoying that marvelous American pastime Slip 'n Slide!"

Above we now have a scale of values[9] for Smith, ranking his allocations according to relative importance.

Now utility (use value), again, is the "importance attached to a thing on account of the belief that it can remove uneasiness." And another term for "uneasiness removal" is "want-satisfaction." So when we are talking about the utility of 100 gallons of water, we are really talking about the want-satisfaction Smith would have to give up were he to do without 100 gallons of water.

If the supply decreased by the loss of one unit, acting man must decide anew how to use the various units of the remaining stock. It is obvious that the smaller stock cannot render all the services the greater stock could.[10]

So, if Smith did make the exchange, and thus was 100 gallons of water poorer, would he give up the most important want-satisfaction, the least important want-satisfaction, or a want-satisfaction in between?

He would give up the least important want-satisfaction, because that is implied in the very meaning of "least important."

That employment of the various units which under this new disposition is no longer provided for, was in the eyes of acting man the least urgent employment among all those for which he had previously assigned the various units of the greater stock.[11]

The least important satisfaction is also called the "marginal satisfaction." According to his scale of values, the "marginal satisfaction" provided by 100 gallons of water is the satisfaction provided by a month of Slip 'n Slide.

The satisfaction which he derived from the use of one unit for this employment was the smallest among the satisfactions which the units of the greater stock had rendered to him. It is only the value of this marginal satisfaction on which he must decide if the question of renouncing one unit of the total stock comes up.[12]

Therefore, the marginal utility of 100 gallons of water is the importance associated with the want-satisfaction provided by a month of Slip 'n Slide use.

When faced with the problem of the value to be attached to one unit of a homogeneous supply, man decides on the basis of the value of the least important use he makes of the units of the whole supply; he decides on the basis of marginal utility.[13]

Adam Smith was very close to his mother, so let us suppose that if he had the diamond, he would use it to have a ring made for her. Thus, the utility of a five-carat diamond is really the importance associated with the want-satisfaction provided by his giving the diamond as a gift to his mother.

So the choice before Smith is not "water versus diamond." It is not even, at bottom, "100 gallons of water versus one diamond." It is really "a month of Slip 'n Slide" versus "a ring on his mother's finger for the rest of her life"! So by insisting that 100 gallons of water is more useful than a five-carat diamond, Smith is really saying that splashing around in his backyard for 30 days is more important than making his mother happy!

Faced with this marginal analysis (plus some Freudian foul play thrown in for good measure), even Smith would admit, "Of course I would choose Mother over Slip 'n Slide! Compared to her gladness, it is the marginal usefulness of 100 gallons of water that is frippery!"

If a man is faced with the alternative of giving up either one unit of his supply of a or one unit of his supply of b, he does not compare the total value of his total stock of a with the total value of his stock of b. He compares the marginal values both of a and of b. Although he may value the total supply of a higher than the total supply of b, the marginal value of b may be higher than the marginal value of a.[14]

With the appropriate marginal formulation, subjective-utility value theory makes perfect sense. The diamond-water paradox is revealed to be a mirage.

The Source of the "Paradox"

Mises laid bare the methodological "trick of the light" that caused this mirage:

The apparent paradox [of value] was the outcome of a vicious formulation of the problem involved.[15]

The common-sense notion of value stemming from utility can only result in paradox if one thinks in terms of "total value" and "total utility." This is a "vicious formulation," because acts of choice do not deal with class totalities but only with singular units.

Mises thought this "vicious formulation" stemmed from the philosophies of "universalism" and "conceptual realism," which ascribe importance to class concepts (universals) even in situations in which they are completely irrelevant. He also referred to the "propensity to hypostatize, i.e., to ascribe substance or real existence to mental constructs or concepts" as "the worst enemy of clear thinking."[16]

The philosophy of universalism has from time immemorial blocked access to a satisfactory grasp of praxeological problems, and contemporary universalists are utterly incapable of finding an approach to them. Universalism, collectivism, and conceptual realism see only wholes and universals. They speculate about mankind, nations, states, classes, about virtue and vice, right and wrong, about entire classes of wants and of commodities. They ask, for instance: Why is the value of "gold" higher than that of "iron"? Thus they never find solutions, but antinomies and paradoxes only. The best-known instance is the value-paradox which frustrated even the work of the classical economists.[17]

Mises contrasted universalism with the "methodological singularism" of praxeology and sound economics, according to which analysis is based on the limited aims and consequences of individual actions.[18]

The Law of Marginal Utility

Let us see the concept of marginal utility applied to changes in the supply of a good.

We've already established that, for Smith, the marginal utility of a five-carat diamond is greater than that of 100 gallons of water.

But let's ask Smith a question that will be familiar to readers who watched TV commercials in the 1980s: "What would you do-oo-oo for a Klondike Bar?"

"A Klondike bar?" Smith asks in befuddlement.

"Yes, it's a chocolate-covered ice-cream snack," we inform him.

"Well that does sound like an intriguing confection!" Smith replies.

"Would you give up 100 gallons of water for one?"

"That would mean no Slip 'n Slide, so no I would not."

"So for you, the marginal utility of 100 gallons of water is greater than the marginal utility of a Klondike bar," we conclude.

"But," we continue, "let's say an earthquake changes the underground flow of water, and your spring now produces sufficient water for you to use up 1,100 gallons every month instead of 1,000. What would you allocate your additional 100 gallons to?"

Smith immediately replies, "Oh, definitely water balloons. I've always fancied ambushing Jean-Jacques Rousseau with a barrage of water balloons!"

We say, "Alright then, so let's extend the value scale by putting water balloons at the bottom.

100 gallons for minimal drinking water for my family and guests
500 gallons for minimal bathing and cleaning
300 gallons for minimal watering of the plants on my estate
100 gallons for Slip 'n Slide
100 gallons for water balloons

Now that you have 1,100 gallons of water instead of 1,000 would you trade 100 gallons for a Klondike bar?"

Smith ponders this question. "Well, now that I have 1,100 gallons, giving up 100 gallons wouldn't mean giving up Slip 'n Slide anymore. Now it would mean giving up my water-balloon assault on Rousseau, which is less important. And truth be told I'd rather try the Klondike bar!"

Remember that when Smith had 1,000 gallons of water, the marginal utility of 100 gallons was greater than the marginal utility of a Klondike bar. But now that he has 1,100 gallons of water, the marginal utility provided by 100 gallons is less to him than the marginal utility of a Klondike bar.

As Murray N. Rothbard wrote:

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.[19]

What follows necessarily from this reasoning is that the greater is the number of units in the supply of a good, the less important is the want-satisfaction that depends on any given portion of those units, and therefore the lower is the good's marginal utility. So as the number of units goes up, marginal utility goes down. This is known as the "law of diminishing marginal utility."

But the above principle is actually only half of a more general law, as will be shown below.

We say to Smith, "Now let's say another earthquake strikes, but this one chokes the flow, making it so your spring now produces sufficient water for you to use up only 100 gallons every month."

"Only 100 gallons!?" Smith exclaims.

We say, "Now forget Klondike bars. We're talking real poverty now. In that situation, would you trade 100 gallons of water even for a diamond?"

Smith answers forcefully, "Well of course not! If I did, I wouldn't be giving up water balloons or games. I'd be giving up me family's very lives!"

Thus we see the flipside of the law introduced before. The smaller the number of units in the supply of a good, the more important is the want-satisfaction that depends on any given portion of those units, and therefore the higher is the good's marginal utility. So as supply goes down, marginal utility goes up.

Combining this principle with the previously mentioned law of diminishing marginal utility, we have a more general law of marginal utility, which states that there is an inverse relationship between the number of units of a good and the good's marginal utility.

What Marginal Utility Is Not

After explaining the law of marginal utility to Mises Academy students in this manner, one student responded, "This is a lot different from how diminishing marginal utility was explained in my introductory economics course." And indeed, there are fundamental differences between the Austrian formulation of the principle and what you might find in mainstream introductory presentations.

Here are two examples of how diminishing marginal utility is presented in mainstream introductory texts.

The first example is from the textbook Microeconomics by David Besanko and Ronald R. Braeutigam:

To understand the principle of diminishing marginal utility, think about the additional satisfaction you get from consuming another hamburger. Suppose you have already eaten one hamburger this week. If you eat a second hamburger, your utility will go up by some amount. This is the marginal utility of the second hamburger. If you have already consumed five hamburgers this week and are about to eat a sixth hamburger, the increase in your utility will be the marginal utility of the sixth hamburger. If you are like most people, the marginal utility of your sixth hamburger will be less than the marginal utility of the second hamburger. In that case, your marginal utility of hamburgers is diminishing.[20]

The second is from EZ-101 Microeconomics by J. Bruce Lindeman:

Suppose a hungry person enters a restaurant and eats some hamburgers.
The utility received from the first burger (its MU) is quite high; it is very satisfying because the consumer is very hungry.
If the consumer eats a second one, the utility received from it is less than the utility received from the first one. This MU of the second burger is lower, because the consumer already has had one and isn't so hungry as before.
By the same reasoning, a third burger may provide some more utility but not as much as the second. MU is diminishing with each successive burger.
This analogy can apply to nearly all goods and services.
Economists note that for some goods diminishing marginal utility may not be absolutely true, especially for MU at very low levels of consumption.[21]

Notice the difference between the above presentations of marginal utility and Mises's presentation of the concept. Mises treats of utility in a formal, praxeological sense: "Importance attached to a thing on account of the belief that it can remove uneasiness." In contrast, the passages above give a sensuous, psychological connotation: they treat of the satiation of hunger, or the sensuous enjoyment of taste.

Also, diminishing marginal utility is presented as an empirically discovered regularity that is the result of certain empirically discovered facts of human physiology and behavior. The diminishing marginal utility of hamburgers is due to the physiological/psychological facts that people get full and that people grow weary of tastes. And this regularity is sometimes present, sometimes not (which is probably why it is called a "principle" in the first excerpt and not a "law").

For example, the "if you are like most people" proviso in the first excerpt might not hold. The hamburger eater in question might be a hamburger glutton like "Wimpy" from the old Popeye cartoons. For someone like Wimpy, the first hamburger might only whet his appetite for the second one, and he would therefore get more enjoyment out of the second hamburger than the first one. Conceivably, our Wimpy could even be a superhuman Nozickian "utility monster," and eat hamburgers with ever-increasing marginal utility until he has eaten all the hamburgers on the planet! In such cases, the principle of diminishing marginal utility, according to its mainstream introductory formulation, would be definitely shown not to be a law. The principle would simply be too wimpy to apply to Wimpy.

That kind of "economic principle" is fundamentally different from the praxeological theorems of Misesian economics. It is true that people get full and that people get tired of the same taste. But these facts are data for economic history, not theoretical building blocks for economics proper.[22]

Mises stressed the difference between the approach exemplified by the two examples above and his own much stronger and more categorical formulation of the principle:

In treating marginal utility we deal neither with sensuous enjoyment nor with saturation and satiety. We do not transcend the sphere of praxeological reasoning in establishing the following definition: We call that employment of a unit of a homogeneous supply which a man makes if his supply is n units, but would not make if, other things being equal, his supply were only n-1 units, the least urgent employment or the marginal employment, and the utility derived from it marginal utility. In order to attain this knowledge we do not need any physiological or psychological experience, knowledge, or reasoning. It follows necessarily from our assumptions that people act (choose) and that in the first case acting man has n units of a homogeneous supply and in the second case n-1 units. Under these conditions no other result is thinkable. Our statement is formal and aprioristic and does not depend on any experience.[23]

Mises's formal and aprioristic formulation of the law of marginal utility was important milestone in the history of economic thought. In fact it was an important milestone in Mises's own thought. In his younger days, Mises himself seemed to identify the law with the psychological "first law of Gossen."[24] Yet this was before he formulated the formal praxeological foundations of economics in the early 1930s.[25] By the time he wrote his magnum opus Human Action, Mises was careful to point out, using the reasoning in the above quote, that "The law of marginal utility and decreasing marginal value is independent of Gossen's law of the saturation of wants (first law of Gossen)."[26]

Does the law of marginal utility, as a formal and aprioristic theorem, hold out against Wimpy the hamburger glutton?

Let us say Wimpy is in an analogous situation to Smith, except that instead of a spring, he has a magic hamburger-producing machine that automatically produces a dozen hamburgers per day. Let us say that for him the marginal utility of one out of his 12 daily hamburgers is less than that of a diamond. So he would exchange a hamburger for a diamond.

Now let's say that he somehow figures out how to make the machine instead produce a baker's dozen (13 hamburgers) per day. Furthermore, let us say that Wimpy's physiology is such that by eating 13 hamburgers in a single day he can achieve a state called "Hamburger Nirvana" which is indescribably more enjoyable than eating 12. So, in that case he would not exchange a hamburger for a diamond, because he would rather achieve Hamburger Nirvana. "Aha!" says the critic of praxeology, "that proves that it's conceivable to have increasing utility as supply increases. Therefore, 'diminishing utility' is not an apodictic 'law'!"

First of all, what is the relevant unit for Wimpy achieving Hamburger Nirvana? One hamburger? No, because the 13th hamburger can only help him achieve Hamburger Nirvana in combination with the other 12. The relevant unit is the full baker's dozen (13 hamburgers). What is important about him potentially giving up one hamburger is not the bare fact that he would be giving up one hamburger. What is important is the fact that in doing so, he would be going from having one complete baker's dozen to having zero complete baker's dozens.

Again, the law of marginal utility states that there is an inverse relationship between the number of units of a good and the good's marginal utility. The situation concerning Hamburger Nirvana involves a unit (the baker's dozen) that was not even under consideration in the other situation. So the two situations do not present a comparison between differing amounts of the same unit (which is the only kind of comparison the law deals with); they involve different units. The comparison does not disprove the law of marginal utility, because it is not a comparison that the law even tries to describe.[27]

The law of marginal utility is not some sneaky arch-rationalistic attempt to derive empirical data from pure reason. Like all praxeological theorems, it applies only to the conditions that it describes. And its cognition is simply the result of thinking clearly about what we mean when we use the terms "utility," "unit," "satisfaction," "increase," "decrease," etc. Any economist who values thinking clearly should not balk at the notion of praxeological theorems.

Conclusion

The "modern value theory" based on marginal-utility analysis turned out to be the "open sesame" of economics.

Mises explained how modern value theory shattered the analytical limitations that severely hampered the classical economists, and how it paved the way for praxeology, "the general theory of human choice."

Until the late nineteenth century political economy remained a science of the "economic" aspects of human action, a theory of wealth and selfishness. It dealt with human action only to the extent that it is actuated by what was — very unsatisfactorily — described as the profit motive, and it asserted that there is in addition other human action whose treatment is the task of other disciplines. The transformation of thought which the classical economists had initiated was brought to its consummation only by modern subjectivist economics, which converted the theory of market prices into a general theory of human choice.[28]

With modern value theory, the consumer was brought back into the economic picture, and so Homo economicus (the fictional being who cares not for his own consumption, but only for maximizing monetary profit) could finally be banished from economic analysis.

With modern value theory, Menger and his student Eugen von Böhm-Bawerk were able to revolutionize, systematize, and rigorize price theory.

With modern value theory, Mises demonstrated the impossibility of measuring utility.[29] And by integrating his theory of indirect exchange with modern value theory, Mises completed the victory of the marginal revolution by extending its conquest into the monetary realm. That in turn enabled Mises and his student F.A. Hayek to formulate macroeconomics on a sound microeconomic foundation.

All this was essential for finally explaining the market process in full, as Mises and his student Murray Rothbard did.

Fractured in divers and sundry pieces for over 200 years, economics (in its Austrian formulation) has finally been made whole, thanks to the subjectivist, marginal revolution and the handful of economists with the clarity of thought to take it to its logical conclusions.