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Marginal utility

From Wikipedia, the free encyclopedia

In economics, utility is the satisfaction or benefit derived by consuming a product; thus the marginal utility of a good or service is the change in the utility from an increase in the consumption of that good or service.

In the context of cardinal utility, economists sometimes speak of a law of diminishing marginal utility, meaning that the first unit of consumption of a good or service yields more utility than the second and subsequent units, with a continuing reduction for greater amounts. Therefore, the fall in marginal utility as consumption increases is known as diminishing marginal utility. Mathematically:


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What I want to do in this video is think about a concept that we've already thought about multiple times in the context of many, many videos. And this is the idea of utility-- utility, which is really just a way of saying how much benefit or satisfaction or value do you get out of getting a good or service. But the angle that we're going to take in this video is going to be slightly different. In the past, when we were measuring benefit or value, we either measured in terms of dollars, where we said, hey, the benefit of getting an incremental Honda Civic was $5,000. And we talk about the incremental-- we're talking about, and we've heard the word many times-- we were talking about the marginal benefit. Or early on, when we talked about the production possibilities frontier and we talked about the marginal benefit of another squirrel, we were talking about it in terms of berries. We were talking about it in terms of another good or service. What we're going to do in this video is just think about it in absolute terms. We're just going to think of some arbitrary way of measuring utility and then just assign values to. What's the value of getting one chocolate bar? And then what's the value that we give to the next chocolate bar and then the chocolate bar after that? And we're going to do the same things about fruit. And from that, we're going to see if we can build up some of the things that we already know about demand curves and how things relate to price and the price of other goods and things like that. And in particular, we're going to focus on marginal utility. So obviously, you could have total utility. If I have four chocolate bars, you could say the total utility I'm getting from all four of them. Or, you could think about marginal utility, the utility I'm getting from the next incremental chocolate bar or the next incremental pound of fruit. And before I move on, there's one thing-- and this was a point of confusion for me when I first learned this-- is OK, I'm using the word marginal utility now. In the past, I've used the word marginal benefit. They sound very similar. In fact, I even used the word benefit when I defined the word utility. How are these two things different? And the simple answer is, conceptually, they aren't. Conceptually, they are the exact same thing. The difference is how the words tend to be used in the context of a traditional microeconomics class. So when people talk about utility, they tend to measure it in terms of some type of absolute measure that they just came up with. You can view them as utility unit, some type of satisfaction units. While when they talk about marginal benefit, they tend to measure it either in dollars or in terms of some other goods. But I've seen either term used either way. So they really do mean the exact same thing. But in this video, we're going to use the term utility, and we're going to come up with a measuring scale, and it's a somewhat arbitrary one. And we're going to use that to come up with some conclusions about the basket of goods someone might purchase depending on different prices. So as you could imagine, I pre-wrote these two things. We're going to talk about chocolate bars, and we are going to talk about fruit. So right here in these little tables here, I've shown the marginal utility of each incremental. In the case of chocolate bars, each incremental bar, and in the case of fruit, each incremental pound of fruit. So this is saying that first chocolate bar-- obviously, if I have no chocolate bars I'm getting no utility from chocolate bars-- and this is saying that that first chocolate bar has a marginal utility. So the utility of that next incremental one is 100. I'm not saying $100. I'm not saying it's equivalent to 100 pounds of fruit. I'm not saying it's equivalent to 100 berries. I'm just arbitrarily saying it is 100. And what matters is not that this is 100 or 1,000 or a million. What matters is how this compares to other things. So for example, if I-- let's say this is 100, and if I know that I like fruit-- a pound of fruit-- 20% more than that first-- Or if I like an incremental-- my first pound of fruit-- 20% more, then I would have to say that the marginal utility of my first pound of fruit is 120. And this is what we said right over here. And if, another way to think about it is, if the marginal utility of the second chocolate bar I get-- because I've already enjoyed a little bit of chocolate bar, and I'm a little chocolated out-- is 20% less than that, then if this is 100, then this would have to be 80. I could have set this to be 1,000 and this to be 800 and this to be 1,200. I could have set this to be 10 and this to be 8 and this to be 12. What matters is, is that they really just have the same ratios between them that really do reflect my actual preferences. So let's just think about this a little bit. My first chocolate bar, I'm pretty excited. I just call it 100. The next chocolate bar, I'm a little bit less excited about it. I've already had some chocolate. My craving has been satiated to some degree, but I still like chocolate. So I'll call that an 80. We could call it 80 satisfaction units, whatever you want to call it. Then the next chocolate bar after this-- now I'm starting to get pretty stuffed, and I'm really chocolated out. And so I'm not getting as much benefit from it. And then finally if you give me another chocolate bar, it's even less. And if we were to list a fifth chocolate bar, I might not want it at all. My marginal utility might go to 0 maybe for that fifth chocolate bar. Maybe that sixth chocolate bar, I have to somehow get rid of it somehow, because I'm so tired of chocolate bars. Maybe it'll have a negative marginal utility. And we could think about the same thing with fruit. The first pound of fruit, I'm pretty excited about fruit. I have a fruit craving. I like that first pound of fruit even more than that first chocolate bar. I like it 20% more. So I get to 120, you could call it utility points or whatever arbitrary unit you want to call it. Then my next pound of fruit, once again I'm having diminishing utility, diminishing benefit as I get more and more incremental pounds of fruit. Now, it's very important to realize this is marginal utility, not total utility. This is a utility I'm getting from each incremental pound. It's positive, so I'm still enjoying that next incremental pound. I'm just enjoying it a little bit less than the pound before. And to realize what total utility is, if I were to have two pounds of fruit, I would have 120 of utility from that first pound. And then I would have 100 from the second pound. And so you would say I had a total utility of 220, you could call them utility units, from both pounds. Now with just the information that I've given here, there's a few things you could say. You could say, well look, my first pound of fruit I enjoy more, 20% more than my first chocolate bar. You could also say that my second pound of fruit, I enjoy it or I could derive about the same amount of value as my first chocolate bar. You could say that my second chocolate bar I enjoy less than my first chocolate bar. You could even say 20% less if these numbers are good. But this still doesn't give you a lot of information about how you would actually spend your money. You might say, well, obviously wouldn't you want to just buy fruit over chocolate bars, or at least that first pound of fruit over that first chocolate bar? Well, you might, but it depends on how much that fruit actually costs. Just looking at this alone, we can just make relative judgments about how much we prefer each incremental bar or each incremental pound or them relative to each other. But it really doesn't tell us how we would spend our actual money. So let's think about things. Let's put some prices on some of these goods and think about how we would actually allocate our dollar given these marginal utility numbers right over here. So let's say that the chocolate bars are $1 per bar. And let's say that the fruit is $2 per pound. So this is going to be per pound. This is going to be per bar. And what we're going to think about is we're going to think about marginal utility for that incremental chocolate bar per price of that incremental chocolate bar. And here the price is going to be at $1 per pound. So here, for that first bar, I'm going to be spending $1, and I'm getting 100 marginal utility points, whatever you want to call it. So I'm getting 100 marginal utility points for that dollar. So I'm getting 100 marginal utility points per dollar. Here, same logic. I'm getting 80 marginal utility points per dollar. This is pretty simple math. Here I'm getting 60 marginal utility points for the dollar. Here I'm getting 40. So that doesn't seem too interesting. It might be a little bit more interesting here. What is the marginal utility per incremental fruit that I'm getting per dollar, per price, or actually per price of the incremental fruit here? Well here, that first pound of fruit I'm getting 120 marginal utility points we could call them. But I paid $2 for it. So 120-- let me write it over here. So for that first incremental fruit, the marginal utility for that first fruit is 120. And the price of that first pound of fruit is equal to 2. So I'm getting 60 marginal utility points per dollar. I'm getting 60. Here, 100 marginal utility points, but I'm spending $2. So that's 50 points per dollar. This is 25 points per dollar. This is 10 points per dollar. Now this makes things a little bit more interesting. If I had $5 to spend, how would I want to spend my $5? What you really just want to think about, where are you getting the most satisfaction for each dollar? Where are you getting the most bang for your buck? So where am I going to spend my first dollar? So dollar one. So let's think about it a little bit. My first dollar, where am I going to get the most satisfaction per dollar? Well, I get the most satisfaction per dollar right over here. I get 100 satisfaction units for a dollar. Even though I like a pound of fruit, I'm getting less satisfaction per dollar. So I'm getting less bang for my buck. So my first dollar is going to go right over there. I'm going to buy one candy bar. Then where am I going to spend my second dollar? So once again, I just want to look at all of my options, and we're going to assume that I'm going to spend my $5 on either of these two just to limit our universe. Once again, I'm going to maximize my bang for buck. I get 80 satisfaction points or marginal utility points over here per dollar. I only get 60 over here. So I'm going to buy even a second chocolate bar. Let's keep going. Where am I going to spend my third dollar? Now, it gets a little bit interesting. I could spend my third dollar right over here and get 60 points per dollar, or I could spend it over here and get 60 points per dollar. I'd actually get the same amount. There are both 60 points per dollar. So I'm kind of neutral. I'm going to get the same bang for my buck whether I get another chocolate bar or whether I get another fruit. So just for simplicity, let's say I get another chocolate bar. I could have got the fruit too. It's really a toss up. I could flip a coin, and I choose to get another chocolate bar. So I first spent my first $3 on three chocolate bars. Now where am I going to spend my fourth dollar? Well, my fourth dollar, now my best bang for my buck isn't to get another chocolate bar. I'm only going to get 40 units per buck there. Now it is to spend it on fruit. So now the next dollar I could spend on half a pound of fruit, and I would get this. So my fourth dollar I could spend on this for half a pound of fruit because it's $2 per pound. And then I could spend my fifth dollar there too. So this is my fourth and my fifth dollar because it's $2. You could think of it that we're spending $2 for one pound of fruit. And we're getting 60 utility points per dollar. So we're getting the best bang for our buck right over there. But what was useful about this is it allowed us without thinking about money to say how much do we like these things irrespective of their actual price and then give it a certain price. It allowed us to think rationally about, well, how would we actually spend our money. In this case, when chocolate bars are $1 and fruit is $2 per pound, we decided to buy three chocolate bars and only one pound of fruit.



The term marginal refers to a small change, starting from some baseline level. Philip Wicksteed explained the term as follows:

Marginal considerations are considerations which concern a slight increase or diminution of the stock of anything which we possess or are considering.[1]

Frequently the marginal change is assumed to start from the endowment, meaning the total resources available for consumption (see Budget constraint). This endowment is determined by many things including physical laws (which constrain how forms of energy and matter may be transformed), accidents of nature (which determine the presence of natural resources), and the outcomes of past decisions made by the individual himself or herself and by others.

For reasons of tractability, it is often assumed in neoclassical analysis that goods and services are continuously divisible. Under this assumption, marginal concepts, including marginal utility, may be expressed in terms of differential calculus. Marginal utility can then be defined as the first derivative of total utility—the total satisfaction obtained from consumption of a good or service—with respect to the amount of consumption of that good or service.

In practice the smallest relevant division may be quite large. Sometimes economic analysis concerns the marginal values associated with a change of one unit of a discrete good or service, such as a motor vehicle or a haircut. For a motor vehicle, the total number of motor vehicles produced is large enough for a continuous assumption to be reasonable: this may not be true for, say, an aircraft carrier.


Depending on which theory of utility is used, the interpretation of marginal utility can be meaningful or not. Economists have commonly described utility as if it were quantifiable, that is, as if different levels of utility could be compared along a numerical scale.[2][3] This has affected the development and reception of theories of marginal utility. Quantitative concepts of utility allow familiar arithmetic operations, and further assumptions of continuity and differentiability greatly increase tractability.

Contemporary mainstream economic theory frequently defers metaphysical questions, and merely notes or assumes that preference structures conforming to certain rules can be usefully proxied by associating goods, services, or their uses with quantities, and defines "utility" as such a quantification.[4]

Another conception is Benthamite philosophy, which equated usefulness with the production of pleasure and avoidance of pain,[5] assumed subject to arithmetic operation.[6] British economists, under the influence of this philosophy (especially by way of John Stuart Mill), viewed utility as "the feelings of pleasure and pain"[7] and further as a "quantity of feeling" (emphasis added).[8]

Though generally pursued outside of the mainstream methods, there are conceptions of utility that do not rely on quantification. For example, the Austrian school generally attributes value to the satisfaction of wants,[9][10][11] and sometimes rejects even the possibility of quantification.[12] It has been argued that the Austrian framework makes it possible to consider rational preferences that would otherwise be excluded.[10]

In any standard framework, the same object may have different marginal utilities for different people, reflecting different preferences or individual circumstances.[13]

Diminishing marginal utility

The concept in cardinal utility theory that marginal utilities diminish across the ranges relevant to decision-making is called the "law of diminishing marginal utility" (and is also known as Gossen's First Law). This refers to the increase in utility an individual gains from increasing their consumption of a particular good. "The law of diminishing marginal utility is at the heart of the explanation of numerous economic phenomena, including time preference and the value of goods ... The law says, first, that the marginal utility of each homogenous unit decreases as the supply of units increases (and vice versa); second, that the marginal utility of a larger-sized unit is greater than the marginal utility of a smaller-sized unit (and vice versa). The first law denotes the law of diminishing marginal utility, the second law denotes the law of increasing total utility."[14]

In modern economics, choice under conditions of certainty at a single point in time is modeled via ordinal utility, in which the numbers assigned to the utility of a particular circumstance of the individual have no meaning by themselves, but which of two alternative circumstances has higher utility is meaningful. With ordinal utility, a person's preferences have no unique marginal utility, and thus whether or not marginal utility is diminishing is not meaningful. In contrast, the concept of diminishing marginal utility is meaningful in the context of cardinal utility, which in modern economics is used in analyzing intertemporal choice, choice under uncertainty, and social welfare.

The law of diminishing marginal utility is similar to the law of diminishing returns which states that as the amount of one factor of production increases as all other factors of production are held the same, the marginal return (extra output gained by adding an extra unit) decreases.

As the rate of commodity acquisition increases, marginal utility decreases. If commodity consumption continues to rise, marginal utility at some point may fall to zero, reaching maximum total utility. Further increase in consumption of units of commodities causes marginal utility to become negative; this signifies dissatisfaction. For example,

  • beyond some point, further doses of antibiotics would kill no pathogens at all, and might even become harmful to the body.
  • to satiate thirst a person drinks water but beyond a point, consumption of more water might make the person vomit, hence leading to negative marginal and thus diminished total utility
  • it takes a certain amount of food energy to sustain a population, yet beyond a point, more calories cannot be consumed and are simply discarded (or cause disease).

Diminishing marginal utility is traditionally a microeconomic concept and often holds for an individual, although the marginal utility of a good or service might be increasing as well. For example:

  • bed sheets, which up to some number may only provide warmth, but after that point may be useful to allow one to effect an escape by being tied together into a rope;
  • tickets, for travel or theatre, where a second ticket might allow one to take a date on an otherwise uninteresting outing;
  • dosages of antibiotics, where having too few pills would leave bacteria with greater resistance, but a full supply could effect a cure.
  • the third leg is more useful than the first two when building a chair.

As suggested elsewhere in this article, occasionally one may come across a situation in which marginal utility increases even at a macroeconomic level. For example, the provision of a service may only be viable if it is accessible to most or all of the population, and the marginal utility of a raw material required to provide such a service will increase at the "tipping point" at which this occurs. This is similar to the position with very large items such as aircraft carriers: the numbers of these items involved are so small that marginal utility is no longer a helpful concept, as there is merely a simple "yes" or "no" decision.

Marginalist theory

Marginalism explains choice with the hypothesis that people decide whether to effect any given change based on the marginal utility of that change, with rival alternatives being chosen based upon which has the greatest marginal utility.

Market price and diminishing marginal utility

If an individual possesses a good or service whose marginal utility to him is less than that of some other good or service for which he could trade it, then it is in his interest to effect that trade. Of course, as one thing is sold and another is bought, the respective marginal gains or losses from further trades will change. If the marginal utility of one thing is diminishing, and the other is not increasing, all else being equal, an individual will demand an increasing ratio of that which is acquired to that which is sacrificed. One important way in which all else might not be equal is when the use of the one good or service complements that of the other. In such cases, exchange ratios might be constant.[10] If any trader can better his position by offering a trade more favorable to complementary traders, then he will do so.

In an economy with money, the marginal utility of a quantity is simply that of the best good or service that it could purchase. In this way it is useful for explaining supply and demand, as well as essential aspects of models of imperfect competition.

Paradox of water and diamonds

The "paradox of water and diamonds", usually most commonly associated with Adam Smith,[15] though recognized by earlier thinkers,[16] is the apparent contradiction that water possesses a value far lower than diamonds, even though water is far more vital to a human being.

Price is determined by both marginal utility and marginal cost, and here the key to the "paradox" is that the marginal cost of water is far lower than that of diamonds.

That is not to say that the price of any good or service is simply a function of the marginal utility that it has for any one individual nor for some ostensibly typical individual. Rather, individuals are willing to trade based upon the respective marginal utilities of the goods that they have or desire (with these marginal utilities being distinct for each potential trader), and prices thus develop constrained by these marginal utilities.

Quantified marginal utility

Under the special case in which usefulness can be quantified, the change in utility of moving from state to state is

Moreover, if and are distinguishable by values of just one variable which is itself quantified, then it becomes possible to speak of the ratio of the marginal utility of the change in to the size of that change:

Diminishing marginal utility, given quantification
Diminishing marginal utility, given quantification

(where “c.p.” indicates that the only independent variable to change is ).

Mainstream neoclassical economics will typically assume that the limit

exists, and use “marginal utility” to refer to the partial derivative


Accordingly, diminishing marginal utility corresponds to the condition



The concept of marginal utility grew out of attempts by economists to explain the determination of price. The term “marginal utility”, credited to the Austrian economist Friedrich von Wieser by Alfred Marshall,[17] was a translation of Wieser's term “Grenznutzen” (border-use).[18][19]

Proto-marginalist approaches

Perhaps the essence of a notion of diminishing marginal utility can be found in Aristotle's Politics, wherein he writes

external goods have a limit, like any other instrument, and all things useful are of such a nature that where there is too much of them they must either do harm, or at any rate be of no use[20]

(There has been marked disagreement about the development and role of marginal considerations in Aristotle's value theory.[21][22][23][24][25])

A great variety of economists have concluded that there is some sort of interrelationship between utility and rarity that affects economic decisions, and in turn informs the determination of prices. Diamonds are priced higher than water because their marginal utility is higher than water .[26]

Eighteenth-century Italian mercantilists, such as Antonio Genovesi, Giammaria Ortes, Pietro Verri, Marchese Cesare di Beccaria, and Count Giovanni Rinaldo Carli, held that value was explained in terms of the general utility and of scarcity, though they did not typically work-out a theory of how these interacted.[27] In Della moneta (1751), Abbé Ferdinando Galiani, a pupil of Genovesi, attempted to explain value as a ratio of two ratios, utility and scarcity, with the latter component ratio being the ratio of quantity to use.

Anne Robert Jacques Turgot, in Réflexions sur la formation et la distribution de richesse (1769), held that value derived from the general utility of the class to which a good belonged, from comparison of present and future wants, and from anticipated difficulties in procurement.

Like the Italian mercantists, Étienne Bonnot, Abbé de Condillac, saw value as determined by utility associated with the class to which the good belong, and by estimated scarcity. In De commerce et le gouvernement (1776), Condillac emphasized that value is not based upon cost but that costs were paid because of value.

This last point was famously restated by the Nineteenth Century proto-marginalist, Richard Whately, who in Introductory Lectures on Political Economy (1832) wrote

It is not that pearls fetch a high price because men have dived for them; but on the contrary, men dive for them because they fetch a high price.[28]

(Whatley's student Senior is noted below as an early marginalist.)

Marginalists before the Revolution

The first unambiguous published statement of any sort of theory of marginal utility was by Daniel Bernoulli, in “Specimen theoriae novae de mensura sortis”.[29] This paper appeared in 1738, but a draft had been written in 1731 or in 1732.[30][31] In 1728, Gabriel Cramer had produced fundamentally the same theory in a private letter.[32] Each had sought to resolve the St. Petersburg paradox, and had concluded that the marginal desirability of money decreased as it was accumulated, more specifically such that the desirability of a sum were the natural logarithm (Bernoulli) or square root (Cramer) thereof. However, the more general implications of this hypothesis were not explicated, and the work fell into obscurity.

In “A Lecture on the Notion of Value as Distinguished Not Only from Utility, but also from Value in Exchange”, delivered in 1833 and included in Lectures on Population, Value, Poor Laws and Rent (1837), William Forster Lloyd explicitly offered a general marginal utility theory, but did not offer its derivation nor elaborate its implications. The importance of his statement seems to have been lost on everyone (including Lloyd) until the early 20th century, by which time others had independently developed and popularized the same insight.[33]

In An Outline of the Science of Political Economy (1836), Nassau William Senior asserted that marginal utilities were the ultimate determinant of demand, yet apparently did not pursue implications, though some interpret his work as indeed doing just that.[34]

In “De la mesure de l’utilité des travaux publics” (1844), Jules Dupuit applied a conception of marginal utility to the problem of determining bridge tolls.[35]

In 1854, Hermann Heinrich Gossen published Die Entwicklung der Gesetze des menschlichen Verkehrs und der daraus fließenden Regeln für menschliches Handeln, which presented a marginal utility theory and to a very large extent worked-out its implications for the behavior of a market economy. However, Gossen's work was not well received in the Germany of his time, most copies were destroyed unsold, and he was virtually forgotten until rediscovered after the so-called Marginal Revolution.

Marginal Revolution

Marginalism eventually found a foothold by way of the work of three economists, Jevons in England, Menger in Austria, and Walras in Switzerland.

William Stanley Jevons first proposed the theory in “A General Mathematical Theory of Political Economy” (PDF), a paper presented in 1862 and published in 1863, followed by a series of works culminating in his book The Theory of Political Economy in 1871 that established his reputation as a leading political economist and logician of the time. Jevons' conception of utility was in the utilitarian tradition of Jeremy Bentham and of John Stuart Mill, but he differed from his classical predecessors in emphasizing that "value depends entirely upon utility", in particular, on "final utility upon which the theory of Economics will be found to turn."[36] He later qualified this in deriving the result that in a model of exchange equilibrium, price ratios would be proportional not only to ratios of "final degrees of utility," but also to costs of production.[37][38]

Carl Menger presented the theory in Grundsätze der Volkswirtschaftslehre (translated as Principles of Economics) in 1871. Menger's presentation is peculiarly notable on two points. First, he took special pains to explain why individuals should be expected to rank possible uses and then to use marginal utility to decide amongst trade-offs. (For this reason, Menger and his followers are sometimes called “the Psychological School”, though they are more frequently known as “the Austrian School” or as “the Vienna School”.) Second, while his illustrative examples present utility as quantified, his essential assumptions do not.[11] (Menger in fact crossed-out the numerical tables in his own copy of the published Grundsätze.[39]) Menger also developed the law of diminishing marginal utility.[14] Menger's work found a significant and appreciative audience.

Marie-Esprit-Léon Walras introduced the theory in Éléments d'économie politique pure, the first part of which was published in 1874 in a relatively mathematical exposition. Walras's work found relatively few readers at the time but was recognized and incorporated two decades later in the work of Pareto and Barone.[40]

An American, John Bates Clark, is sometimes also mentioned. But, while Clark independently arrived at a marginal utility theory, he did little to advance it until it was clear that the followers of Jevons, Menger, and Walras were revolutionizing economics. Nonetheless, his contributions thereafter were profound.

Second generation

Although the Marginal Revolution flowed from the work of Jevons, Menger, and Walras, their work might have failed to enter the mainstream were it not for a second generation of economists. In England, the second generation were exemplified by Philip Henry Wicksteed, by William Smart, and by Alfred Marshall; in Austria by Eugen von Böhm-Bawerk and by Friedrich von Wieser; in Switzerland by Vilfredo Pareto; and in America by Herbert Joseph Davenport and by Frank A. Fetter.

There were significant, distinguishing features amongst the approaches of Jevons, Menger, and Walras, but the second generation did not maintain distinctions along national or linguistic lines. The work of von Wieser was heavily influenced by that of Walras. Wicksteed was heavily influenced by Menger. Fetter referred to himself and Davenport as part of “the American Psychological School”, named in imitation of the Austrian “Psychological School”. (And Clark's work from this period onward similarly shows heavy influence by Menger.) William Smart began as a conveyor of Austrian School theory to English-language readers, though he fell increasingly under the influence of Marshall.[41]

Böhm-Bawerk was perhaps the most able expositor of Menger's conception.[41][42] He was further noted for producing a theory of interest and of profit in equilibrium based upon the interaction of diminishing marginal utility with diminishing marginal productivity of time and with time preference.[43] This theory was adopted in full and then further developed by Knut Wicksell[44] and with modifications including formal disregard for time-preference by Wicksell's American rival Irving Fisher.[45]

Marshall was the second-generation marginalist whose work on marginal utility came most to inform the mainstream of neoclassical economics, especially by way of his Principles of Economics, the first volume of which was published in 1890. Marshall constructed the demand curve with the aid of assumptions that utility was quantified, and that the marginal utility of money was constant (or nearly so). Like Jevons, Marshall did not see an explanation for supply in the theory of marginal utility, so he synthesized an explanation of demand thus explained with supply explained in a more classical manner, determined by costs which were taken to be objectively determined. (Marshall later actively mischaracterized the criticism that these costs were themselves ultimately determined by marginal utilities.[46])

Marginal Revolution and Marxism

Karl Marx acknowledged that "nothing can have value, without being an object of utility",[47][48] but in his analysis "use-value as such lies outside the sphere of investigation of political economy",[49] with labor being the principal determinant of value under capitalism.

The doctrines of marginalism and the Marginal Revolution are often interpreted as somehow a response to Marxist economics. However the first volume of Das Kapital was not published until July 1867, after the works of Jevons, Menger, and Walras were written or well under way (Walras published Éléments d'économie politique pure in 1874 and Carl Menger published Principles of Economics in 1871); and Marx was still a relatively minor figure when these works were completed. It is unlikely that any of them knew anything of him. (On the other hand, Friedrich Hayek and W. W. Bartley III have suggested that Marx, voraciously reading at the British Museum, may have come across the works of one or more of these figures, and that his inability to formulate a viable critique may account for his failure to complete any further volumes of Kapital before his death.[50]

Nonetheless, it is not unreasonable to suggest that the generation who followed the preceptors of the Revolution succeeded partly because they could formulate straightforward responses to Marxist economic theory. The most famous of these was that of Böhm-Bawerk, Zum Abschluss des Marxschen Systems (1896),[51] but the first was Wicksteed's "The Marxian Theory of Value. Das Kapital: a criticism" (1884,[52] followed by "The Jevonian criticism of Marx: a rejoinder" in 1885).[53] Initially there were only a few Marxist responses to marginalism, of which the most famous were Rudolf Hilferding's Böhm-Bawerks Marx-Kritik (1904)[54] and Politicheskoy ekonomni rante (1914) by Nikolai Bukharin.[55] However, over the course of the 20th century a considerable literature developed on the conflict between marginalism and the labour theory of value, with the work of the neo-Ricardian economist Piero Sraffa providing an important critique of marginalism.

It might also be noted that some followers of Henry George similarly consider marginalism and neoclassical economics a reaction to Progress and Poverty which was published in 1879.[56]

In the 1980s John Roemer and other analytical Marxists have worked to rebuild Marxian theses on a marginalist foundation.


In his 1881 work Mathematical Psychics, Francis Ysidro Edgeworth presented the indifference curve, deriving its properties from marginalist theory which assumed utility to be a differentiable function of quantified goods and services. Later work attempted to generalize to the indifference curve formulations of utility and marginal utility in avoiding unobservable measures of utility.

In 1915, Eugen Slutsky derived a theory of consumer choice solely from properties of indifference curves.[57] Because of the World War, the Bolshevik Revolution, and his own subsequent loss of interest, Slutsky's work drew almost no notice, but similar work in 1934 by John Richard Hicks and R. G. D. Allen[58] derived much the same results and found a significant audience. (Allen subsequently drew attention to Slutsky's earlier accomplishment.)

Although some of the third generation of Austrian School economists had by 1911 rejected the quantification of utility while continuing to think in terms of marginal utility,[12] most economists presumed that utility must be a sort of quantity. Indifference curve analysis seemed to represent a way to dispense with presumptions of quantification, albeit that a seemingly arbitrary assumption (admitted by Hicks to be a "rabbit out of a hat"[59]) about decreasing marginal rates of substitution[60] would then have to be introduced to have convexity of indifference curves.

For those who accepted that indifference curve analysis superseded earlier marginal utility analysis, the latter became at best perhaps pedagogically useful, but "old fashioned" and observationally unnecessary.[60][61]


When Cramer and Bernoulli introduced the notion of diminishing marginal utility, it had been to address a paradox of gambling, rather than the paradox of value. The marginalists of the revolution, however, had been formally concerned with problems in which there was neither risk nor uncertainty. So too with the indifference curve analysis of Slutsky, Hicks, and Allen.

The expected utility hypothesis of Bernoulli and others was revived by various 20th century thinkers, with early contributions by Ramsey (1926),[62] von Neumann and Morgenstern (1944),[63] and Savage (1954).[64] Although this hypothesis remains controversial, it brings not only utility, but a quantified conception of utility (cardinal utility), back into the mainstream of economic thought.

A major reason why quantified models of utility are influential today is that risk and uncertainty have been recognized as central topics in contemporary economic theory.[65] Quantified utility models simplify the analysis of risky decisions because, under quantified utility, diminishing marginal utility implies risk aversion.[66] In fact, many contemporary analyses of saving and portfolio choice require stronger assumptions than diminishing marginal utility, such as the assumption of prudence, which means convex marginal utility.[67]

Meanwhile, the Austrian School continued to develop its ordinalist notions of marginal utility analysis, formally demonstrating that from them proceed the decreasing marginal rates of substitution of indifference curves.[10]

See also


  1. ^ Wicksteed, Philip Henry; The Common Sense of Political Economy (1910), Bk I Ch 2 and elsewhere.
  2. ^ Stigler, George Joseph; The Development of Utility Theory, I and II, Journal of Political Economy (1950), issues 3 and 4.
  3. ^ Stigler, George Joseph; The Adoption of Marginal Utility Theory, History of Political Economy (1972).
  4. ^ Kreps, David Marc; A Course in Microeconomic Theory, Chapter two: The theory of consumer choice and demand, Utility representations.
  5. ^ Bentham, Jeremy; Introduction to the Principles of Morals and Legislation, Chapter I §I–III.
  6. ^ Bentham, Jeremy; Introduction to the Principles of Morals and Legislation, Chapter IV.
  7. ^ Jevons, William Stanley; “Brief Account of a General Mathematical Theory of Political Economy”, Journal of the Royal Statistical Society v29 (June 1866) §2.
  8. ^ Jevons, William Stanley; Brief Account of a General Mathematical Theory of Political Economy, Journal of the Royal Statistical Society v29 (June 1866) §4.
  9. ^ Menger, Carl; Grundsätze der Volkswirtschaftslehre (Principles of Economics) Chapter 2 §2.
  10. ^ a b c d Mc Culloch, James Huston; “The Austrian Theory of the Marginal Use and of Ordinal Marginal Utility”, Zeitschrift für Nationalökonomie 37 (1977) #3&4 (September).
  11. ^ a b Georgescu-Roegen, Nicholas; Utility, International Encyclopedia of the Social Sciences (1968).
  12. ^ a b von Mises, Ludwig Heinrich; Theorie des Geldes und der Umlaufsmittel (1912).
  13. ^ Davenport, Herbert Joseph; The Economics of Enterprise (1913) Ch VII, pp. 86–87.
  14. ^ a b Polleit, Thorsten (2011-02-11) What Can the Law of Diminishing Marginal Utility Teach Us?, Mises Institute
  15. ^ Smith, Adam; An Inquiry into the Nature and Causes of the Wealth of Nations (1776) Chapter IV. "Of the Origin and Use of Money"
  16. ^ Gordon, Scott (1991). "The Scottish Enlightenment of the eighteenth century". History and Philosophy of Social Science: An Introduction. Routledge. ISBN 0-415-09670-7.
  17. ^ Marshall, Alfred; Principles of Economics, 3 Ch 3 Note.
  18. ^ von Wieser, Friedrich; Über den Ursprung und die Hauptgesetze des wirtschaftlichen Wertes [The Nature and Essence of Theoretical Economics] (1884), p. 128.
  19. ^ Wieser, Friedrich von; Der natürliche Werth [Natural Value] (1889), Bk I Ch V “Marginal Utility” (HTML).
  20. ^ Aristotle, Politics, Bk 7 Chapter 1.
  21. ^ Soudek, Josef (1952). "Aristotle's Theory of Exchange: An Inquiry into the Origin of Economic Analysis". Proceedings of the American Philosophical Society. 96 (1): 45–75. JSTOR 3143742.
  22. ^ Kauder, Emil (1953). "Genesis of the Marginal Utility Theory from Aristotle to the End of the Eighteenth Century". The Economic Journal. 63 (251): 638–50. doi:10.2307/2226451. JSTOR 2226451.
  23. ^ Gordon, Barry Lewis John (1964). "Aristotle and the Development of Value Theory". Quarterly Journal of Economics. 78 (1): 115–28. doi:10.2307/1880547. JSTOR 1880547.
  24. ^ Schumpeter, Joseph Alois; History of Economic Analysis (1954) Part II Chapter 1 §3.
  25. ^ Meikle, Scott; Aristoteles' Economic Thought (1995) Chapters 1, 2, & 6.
  26. ^ Přibram, Karl; A History of Economic Reasoning (1983).
  27. ^ Pribram, Karl; A History of Economic Reasoning (1983), Chapter 5 “Refined Mercantilism”, “Italian Mercantilists”.
  28. ^ Whately, Richard; Introductory Lectures on Political Economy, Being part of a course delivered in the Easter term (1832).
  29. ^ Bernoulli, Daniel; “Specimen theoriae novae de mensura sortis” in Commentarii Academiae Scientiarum Imperialis Petropolitanae 5 (1738); reprinted in translation as “Exposition of a new theory on the measurement of risk” in Econometrica 22 (1954).
  30. ^ Bernoulli, Daniel; letter of 4 July 1731 to Nicolas Bernoulli (excerpted in PDF Archived 2008-09-09 at the Wayback Machine).
  31. ^ Bernoulli, Nicolas; letter of 5 April 1732, acknowledging receipt of “Specimen theoriae novae metiendi sortem pecuniariam” (excerpted in PDF Archived 2008-09-09 at the Wayback Machine).
  32. ^ Cramer, Garbriel; letter of 21 May 1728 to Nicolaus Bernoulli (excerpted in PDF Archived 2008-09-09 at the Wayback Machine).
  33. ^ Seligman, E. R. A. (1903). "On Some Neglected British Economists". The Economic Journal. 13 (51): 335–63. doi:10.2307/2221519. JSTOR 2221519.
  34. ^ White, Michael V. (1992). "Diamonds Are Forever(?): Nassau Senior and Utility Theory". The Manchester School. 60 (1): 64–78. doi:10.1111/j.1467-9957.1992.tb00211.x.
  35. ^ Dupuit, Jules (1844). "De la mesure de l'utilité des travaux publics". Annales des ponts et chaussées. Second series. 8.
  36. ^ W. Stanley Jevons (1871), The Theory of Political Economy, p. 111.
  37. ^ W. Stanley Jevons (1879, 2nd ed.), The Theory of Political Economy, p. 208.
  38. ^ R.D. Collison Brown (1987), "Jevons, William Stanley," The New Palgrave: A Dictionary of Economics, v. 2, pp. 1008–09.
  39. ^ Kauder, Emil; A History of Marginal Utility Theory (1965), p. 76.
  40. ^ Donald A. Walker (1987), "Walras, Léon" The New Palgrave: A Dictionary of Economics, v. 4, p. 862.
  41. ^ a b Salerno, Joseph T. 1999; “The Place of Mises’s Human Action in the Development of Modern Economic Thought.” Quarterly Journal of Economic Thought v. 2 (1).
  42. ^ Böhm-Bawerk, Eugen Ritter von. “Grundzüge der Theorie des wirtschaftlichen Güterwerthes”, Jahrbüche für Nationalökonomie und Statistik v 13 (1886). Translated as Basic Principles of Economic Value.
  43. ^ Böhm-Bawerk, Eugen Ritter von; Kapital Und Kapitalizns. Zweite Abteilung: Positive Theorie des Kapitales (1889). Translated as Capital and Interest. II: Positive Theory of Capital with appendices rendered as Further Essays on Capital and Interest.
  44. ^ Wicksell, Johan Gustaf Knut; Über Wert, Kapital unde Rente (1893). Translated as Value, Capital and Rent.
  45. ^ Fisher, Irving; Theory of Interest (1930).
  46. ^ Schumpeter, Joseph Alois; History of Economic Analysis (1954) Pt IV Ch 6 §4.
  47. ^ Marx, Karl Heinrich; Capital V1 Ch 1 §1.
  48. ^ Marx, Karl Heinrich; Grundrisse (completed in 1857 though not published until much later)
  49. ^ Marx, Karl Heinrich: A Contribution to the Critique of Political Economy] (1859), p. 276
  50. ^ Hayek, Friedrich August von, with William Warren Bartley III; The Fatal Conceit: The Errors of Socialism (1988) p. 150.
  51. ^ Böhm-Bawerk, Eugen Ritter von: "Zum Abschluss des Marxschen Systems" ["On the Closure of the Marxist System"], Staatswiss. Arbeiten. Festgabe für K. Knies (1896).
  52. ^ Wicksteed, Philip Henry; "Das Kapital: A Criticism", To-day 2 (1884) pp. 388–409.
  53. ^ Wicksteed, Philip Henry; "The Jevonian criticism of Marx: a rejoinder", To-day 3 (1885) pp. 177–79.
  54. ^ Hilferding, Rudolf: Böhm-Bawerks Marx-Kritik (1904). Translated as Böhm-Bawerk's Criticism of Marx.
  55. ^ Буха́рин, Никола́й Ива́нович (Nikolai Ivanovich Bukharin); Политической экономии рантье (1914). Translated as The Economic Theory of the Leisure Class.
  56. ^ Gaffney, Mason, and Fred Harrison: The Corruption of Economics (1994).
  57. ^ Слуцкий, Евгений Евгениевич (Slutsky, Yevgyeniy Ye.); "Sulla teoria del bilancio del consumatore", Giornale degli Economisti 51 (1915).
  58. ^ Hicks, John Richard, and Roy George Douglas Allen; "A Reconsideration of the Theory of Value", Economica 54 (1934).
  59. ^ Hicks, Sir John Richard; Value and Capital, Chapter I. 2"Utility and Preference" §8, p. 23 in the 2nd edition.
  60. ^ a b Hicks, Sir John Richard; Value and Capital, Chapter I. "Utility and Preference" §7–8.
  61. ^ Samuelson, Paul Anthony; "Complementarity: An Essay on the 40th Anniversary of the Hicks-Allen Revolution in Demand Theory", Journal of Economic Literature vol 12 (1974).
  62. ^ Ramsey, Frank Plumpton; "Truth and Probability" (PDF Archived 2008-02-27 at the Wayback Machine), Chapter VII in The Foundations of Mathematics and other Logical Essays (1931).
  63. ^ von Neumann, John and Oskar Morgenstern; Theory of Games and Economic Behavior (1944).
  64. ^ Savage, Leonard Jimmie: Foundations of Statistics (1954).
  65. ^ Diamond, Peter, and Michael Rothschild, eds.: Uncertainty in Economics (1989). Academic Press.
  66. ^ Demange, Gabriel, and Guy Laroque: Finance and the Economics of Uncertainty (2006), Ch. 3, pp. 71–72. Blackwell Publishing.
  67. ^ Kimball, Miles (1990), "Precautionary Saving in the Small and in the Large", Econometrica, 58 (1) pp. 53–73.

Further reading

External links

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