TheInfoList

In
economics Economics () is a social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interact ...

,
utility As a topic of economics Economics () is a social science Social science is the Branches of science, branch of science devoted to the study of society, societies and the Social relation, relationships among individuals within thos ...

is the satisfaction or benefit derived by consuming a product; thus the marginal utility of a
good In most contexts, the concept of good denotes the conduct that should be preferred when posed with a choice between possible actions. Good is generally considered to be the opposite of evil Evil, in a general sense, is defined by what it ...
or
service Service may refer to: Activities :''(See the Religion section for religious activities)'' * Administrative service, a required part of the workload of university faculty * Civil service The civil service is a collective term for a sector of g ...
describes how much pleasure or satisfaction is gained from an increase in
consumption Consumption may refer to: *Resource consumption *Tuberculosis, an infectious disease, historically in biology: * Consumption (ecology), receipt of energy by consuming other organisms in social sciences: * Consumption (economics), the purchasing of ...
. It may be positive, negative, or zero. For example, purchasing more than one needs brings little satisfaction as the purchaser feels it is wasted money, hence zero marginal utility. If one is actually harmed by extra consumption then it is negative, and if some satisfaction is gained by extra consumption then it is positive. In other words, a negative marginal utility suggests that each additional unit of a good consumed provides more harm than benefits and leads to a lower level of overall utility, whereas a positive marginal utility suggests each additional unit consumed provides more benefit and leads to a higher level of overall utility. In the context of
cardinal utility In economics Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods an ...
, economists postulate a
law of diminishing marginal utility In economics Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods a ...
, which describes how the first
unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatrical presentation Music * Unit (album), ...
of consumption of a particular 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. This concept is used by economists to determine how much of a good a consumer is willing to purchase.

# Marginality

The term marginal refers to a small change, starting from some baseline level.
Philip Wicksteed Philip Henry Wicksteed (25 October 1844 – 18 March 1927) is known primarily as an economist. He was also a Georgist, Christian Unitarianism, Unitarian theologian, classicist, medievalist, and literary critic. Family background He was the son ...

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.
Frequently the marginal change is assumed to start from the endowment, meaning the total resources available for consumption (see
Budget constraint In economics Economics () is a social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behavi ...

). 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 conceptsIn conomics marginal concepts are associated with a ''specific change'' in the quantity used of a Good (economics), good or Service (economics), service, as opposed to some notion of the over-all significance of that class of good or service, or ...
, including marginal utility, may be expressed in terms of
differential calculus In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...
. 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.

# Utility

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. 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. Another conception is Benthamite philosophy, which equated usefulness with the production of pleasure and avoidance of pain, assumed subject to arithmetic operation. British economists, under the influence of this philosophy (especially by way of
John Stuart Mill John Stuart Mill (20 May 1806 – 7 May 1873), also cited as J. S. Mill, was an English philosopher, Political economy, political economist, Member of Parliament (United Kingdom), Member of Parliament (MP) and civil servant. One of the most i ...
), viewed utility as "the feelings of pleasure and pain" and further as a "''quantity'' of feeling" (emphasis added). Though generally pursued outside of the mainstream methods, there are conceptions of utility that do not rely on quantification. For example, the
Austrian school The Austrian School is a heterodox In religion, heterodoxy (from Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It ...
generally attributes value to ''the satisfaction of wants'', Georgescu-Roegen, Nicholas; ''Utility'', ''International Encyclopedia of the Social Sciences'' (1968). and sometimes rejects even the ''possibility'' of quantification.; ''Theorie des Geldes und der Umlaufsmittel'' (1912). It has been argued that the Austrian framework makes it possible to consider rational preferences that would otherwise be excluded.Mc Culloch, James Huston
"The Austrian Theory of the Marginal Use and of Ordinal Marginal Utility"
''Zeitschrift für Nationalökonomie'' 37 (1977) #3&4 (September).
In any standard framework, the same object may have different marginal utilities for different people, reflecting different preferences or individual circumstances.

# Law of Diminishing marginal utility

The British economist Alfred Marshall believed that the more something you have, the less of it you want. This phenomenon is referred to as diminishing marginal utility by economists. Diminishing marginal utility refers to the phenomenon that each additional unit of gain leads to an ever-smaller increase in subjective value. For example, three bites of candy are better than two bites, but the twentieth bite does not add much to the experience beyond the nineteenth (and could even make it worse). This effect is so well established that it is referred to as the "law of diminishing marginal utility" in economics (Gossen, 1854/1983), and is reflected in the convex shape of most subjective utility functions. 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 In economics, time preference (or time discounting, delay discounting, temporal discounting, long-term orientation) is the current relative valuation placed on receiving a good In most contexts, the concept of good denotes the conduct that ...
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." In modern economics, choice under conditions of certainty at a single point in time is modelled via
ordinal utilityIn economics Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and ...
, 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 the ordinal utility, a person's preferences have no unique marginal utility, and thus whether or not the marginal utility is diminishing is not meaningful. In contrast, the concept of diminishing marginal utility is meaningful in the context of
cardinal utility In economics Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods an ...
, which in modern economics is used in analyzing
intertemporal choiceIntertemporal choice is the process by which people make decisions about what and how much to do at various points in time, when choices at one time influence the possibilities available at other points in time. These choices are influenced by the r ...

, choice under uncertainty, and
social welfare Welfare (or commonly, social welfare) is a type of government support intended to ensure that members of a society can meet basic human needs Maslow's hierarchy of needs is an idea in psychology Psychology is the science of mind and ...
. The law of diminishing marginal utility is that subjective value changes most dynamically near the zero points and quickly levels off as gains (or losses) accumulate. And it is reflected in the concave shape of most subjective utility functions. Given a concave relationship between objective gains (x-axis) and subjective value (y-axis), each one-unit gain produces a smaller increase in subjective value than the previous gain of an equal unit. The marginal utility, or the change in subjective value above the existing level, diminishes as gains increase. As the rate of commodity acquisition increases, the ''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 the consumption of commodities causes the 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. 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, dosages of antibiotics, where having too few pills would leave bacteria with greater resistance, but a full supply could effect a cure. As suggested elsewhere in this article, occasionally, one may come across a situation where marginal utility increases even at a macroeconomic level. For example, providing a service may only be viable if it is accessible to most or all of the population. 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 huge 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 Marginalism is a theory of economics Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (economic ...
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. 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 Money is any item or verifiable record that is generally accepted as payment for goods and services and repayment of debts, such as taxes, in a particular country or socio-economic context. The main functions of money are distinguished as: a ...

, 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 In microeconomics Microeconomics is a branch of that studies the behavior of individuals and in making decisions regarding the allocation of and the interactions among these individuals and firms. Microeconomics focuses on the study ...

, as well as essential aspects of models of
imperfect competition In economics, imperfect competition refers to a situation where the characteristics of an economic market do not fulfil all the necessary conditions of a perfectly competitive market, resulting in market failure In neoclassical economics, market ...
.

### Paradox of water and diamonds

The "paradox of water and diamonds" is most commonly associated with
Adam Smith Adam Smith ( 1723 – 17 July 1790) was a Scottish economist, philosopher as well as a moral philosopher Ethics or moral philosophy is a branch of philosophy that "involves systematizing, defending, and recommending concepts of right and ...

, though it was recognized by earlier thinkers. The apparent contradiction lies in the fact that water possesses a lower economic value than diamonds, even though water is far more vital to human existence. Smith suggested that there was an irrational divide between the 'use value' of something and the 'exchange value'. The things which have the greatest value in use frequently have little or no value in exchange; and likewise, things 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 scarcely anything. A diamond has hardly any practical value in use, but a great quantity of other goods may be had in exchange for it. Price is determined by both marginal utility and marginal cost, and here is the key to the paradox. The marginal cost of water is lower than the marginal cost 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 or 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 logic Logic is an interdisciplinary field which studies truth and reasoning. Informal logic seeks to characterize Validity (logic), valid arguments informally, for instance by listing varieties of fallacies. Formal logic represents statem ...
in which usefulness can be quantified, the change in utility of moving from state $S_1$ to state $S_2$ is :$\Delta U=U\left(S_2\right)-U\left(S_1\right)\,$ Moreover, if $S_1$ and $S_2$ are distinguishable by values of just one variable $g\,$ which is itself quantified, then it becomes possible to speak of the ratio of the marginal utility of the change in $g\,$ to the size of that change: :$\left.\frac\_$ (where " c.p." indicates that the ''only''
independent variable Dependent and Independent variables are variables in mathematical modeling A mathematical model is a description of a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules ...
to change is $g\,$). Mainstream neoclassical economics will typically assume that the limit :$\lim_ \left.\frac\_$ exists, and use "marginal utility" to refer to the
partial derivative In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...

:$\frac=\lim_\left.\frac\_$. Accordingly, diminishing marginal utility corresponds to the condition :$\frac<0$.

# History

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 Austrian may refer to: * Austrians, someone from Austria or of Austrian descent ** Someone who is considered an Austrian citizen, see Austrian nationality law * Something associated with the country Austria, for example: ** Austria-Hungary ** Austr ...
economist
Friedrich von Wieser Friedrich Freiherr von Wieser (; 10 July 1851 – 22 July 1926) was an early (so-called "first generation") economist An economist is a professional and practitioner in the social science Social science is the branch A branch ( o ...
by
Alfred Marshall Alfred Marshall (26 July 1842 – 13 July 1924) was an English economist, who was one of the most influential economists of his time. His book, '' Principles of Economics'' (1890), was the dominant economic textbook in England for many years. ...

, was a translation of Wieser's term "Grenznutzen" (''border-use'').von Wieser, Friedrich; ''Über den Ursprung und die Hauptgesetze des wirtschaftlichen Wertes'' /nowiki>''The Nature and Essence of Theoretical Economics''/nowiki> (1884), p. 128.Wieser, Friedrich von; ''Der natürliche Werth'' /nowiki>''Natural Value''/nowiki> (1889), Bk I Ch V "Marginal Utility"
HTML
.

## Proto-marginalist approaches

Perhaps the essence of a notion of diminishing marginal utility can be found in
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questio ...

's ''Politics'', wherein he writes There has been marked disagreement about the development and role of marginal considerations in Aristotle's value theory.Schumpeter, Joseph Alois; ''History of Economic Analysis'' (1954) Part II Chapter 1 §3. 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 . Eighteenth-century Italian
mercantilists Mercantilism is an economic policy that is designed to maximize the exports and minimize the imports for an economy. It promotes imperialism, colonialism, tariffs and subsidies on traded goods to achieve that goal. The policy aims to reduce a ...

, such as
Antonio Genovesi Antonio Genovesi (1 November 171322 September 1769) was an Italian writer on philosophy and political economy. Biography Son of Salvatore Genovese, a shoemaker, and Adriana Alfinito of San Mango, Antonio Genovesi was born in Castiglione, near S ...

, Giammaria Ortes,
Pietro Verri Il conte Pietro Verri (12 December 1728 – 28 June 1797) was an economist, historian, philosopher and writer. Among the most important personalities of the 18th-century Italian culture, he is considered among the fathers of the Lombard reformist ...

, 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.Pribram, Karl; ''A History of Economic Reasoning'' (1983), Chapter 5 "Refined Mercantilism", "Italian Mercantilists". In ''Della moneta'' (1751), Abbé
Ferdinando Galiani Ferdinando Galiani (2 December 1728, Chieti, Kingdom of Naples – 30 October 1787, Naples, Kingdom of Naples) was an Italy, Italian economist, a leading Italian figure of the Age of Enlightenment, Enlightenment. Friedrich Nietzsche referred to him ...
, 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 Anne Robert Jacques Turgot, Baron de l'Aulne ( ; ; 10 May 172718 March 1781), commonly known as Turgot, was a French economist and statesman. Originally considered a physiocrat, he is today best remembered as an early advocate for economic liber ...

, 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 Richard Whately (1 February 1787 – 8 October 1863) was an English academic, rhetorician, logician, philosopher, economist, and theologian who also served as a reforming Church of Ireland Archbishop of Dublin. He was a leading Broad Churchman, ...

, who in ''Introductory Lectures on Political Economy'' (1832) wrote (Whatley's student
Senior Senior (shortened as Sr.) means "the elder" in Latin and is often used as a suffix As, AS, A/S or similar may refer to: Art, entertainment, and media * As (song), "As" (song), a song by Stevie Wonder * , a Spanish sports newspaper * , academic m ...

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 Daniel Bernoulli FRS FRS may also refer to: Government and politics * Facility Registry System, a centrally managed Environmental Protection Agency database that identifies places of environmental interest in the United States * Family Resour ...
, in "Specimen theoriae novae de mensura sortis". This paper appeared in 1738, but a draft had been written in 1731 or in 1732. In 1728,
Gabriel Cramer Gabriel Cramer (; 31 July 1704 – 4 January 1752) was a Genevan mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmet ...

had produced fundamentally the same theory in a private letter. 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 The natural logarithm of a number is its logarithm In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained ( ...
(Bernoulli) or
square root In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities ...

(Cramer) thereof. However, the more general implications of this hypothesis were not explicated, and the work fell into obscurity. I
"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 William Forster Lloyd FRS (1794 – 2 June 1852) was a British writer on economics. He is best known today for one of his 1833 lectures on population control which have influenced writers in modern economic theory. Life Born in 1794 at Bradenha ...
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. In ''An Outline of the Science of Political Economy'' (1836),
Nassau William Senior Nassau William Senior (; 26 September 1790 – 4 June 1864), was an English lawyer known as an economist An economist is a professional and practitioner in the social science Social science is the branch A branch ( or , ) or t ...

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. In "De la mesure de l'utilité des travaux publics" (1844),
Jules Dupuit Arsène Jules Étienne Juvenel Dupuit (18 May 1804 – 5 September 1866) was an Italian-born French civil engineer A civil engineer is a person who practices civil engineering Civil engineering is a Regulation and licensure in engineering, p ...
applied a conception of marginal utility to the problem of determining bridge tolls. In 1854,
Hermann Heinrich Gossen Hermann Heinrich Gossen (7 September 1810 – 13 February 1858) was a Prussia Prussia, , Old Prussian: ''Prūsa'' or ''Prūsija'' was a historically prominent Germans, German state that originated in 1525 with Duchy of Prussia, a duchy centered ...
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, in England, Menger in Austria, and Walras in Switzerland.
William Stanley Jevons William Stanley Jevons (; 1 September 183513 August 1882) was an English economist An economist is a professional and practitioner in the social science Social science is the branch A branch ( or , ) or tree branch (sometimes ...

first proposed the theory i
"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 Utilitarianism is a family of normative Normative generally means relating to an evaluative standard. Normativity is the phenomenon in human societies of designating some actions or outcomes as good or desirable or permissible and others as ba ...
Jeremy Bentham Jeremy Bentham (; 15 February 1748 Old_Style_and_New_Style_dates">O.S._4_February_1747.html" ;"title="Old_Style_and_New_Style_dates.html" ;"title="nowiki/>Old Style and New Style dates">O.S. 4 February 1747">Old_Style_and_New_Style_dates.htm ...

and of
John Stuart Mill John Stuart Mill (20 May 1806 – 7 May 1873), also cited as J. S. Mill, was an English philosopher, Political economy, political economist, Member of Parliament (United Kingdom), Member of Parliament (MP) and civil servant. One of the most i ...
, but he differed from his
classical Classical may refer to: European antiquity *Classical antiquity, a period of history from roughly the 7th or 8th century B.C.E. to the 5th century C.E. centered on the Mediterranean Sea *Classical architecture, architecture derived from Greek and ...
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." 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.
Carl Menger Carl Menger (; ; 28 February 1840 – 26 February 1921) was an Austrian economist and the founder of the Austrian School of economics. Menger contributed to the development of the theory of marginalism (marginal utility), which rejected the co ...
presented the theory i
''Grundsätze der Volkswirtschaftslehre''
(translated a
''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 The Austrian School is a heterodox In religion, heterodoxy (from Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It ...
" or as "the Vienna School".) Second, while his illustrative examples present utility as quantified, his essential assumptions do not. (Menger in fact crossed-out the numerical tables in his own copy of the published ''Grundsätze''.) Menger also developed the
law of diminishing marginal utility In economics Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods a ...
.Polleit, Thorsten (2011-02-11
What Can the Law of Diminishing Marginal Utility Teach Us?
''
Mises Institute The Ludwig von Mises Institute for Austrian Economics, or Mises Institute, is a libertarian Libertarianism (from french: libertaire, "libertarian"; from la, libertas, "freedom") is a political philosophy Political philosophy or politi ...

''
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 and Barone. An American,
John Bates Clark John Bates Clark (January 26, 1847 – March 21, 1938) was an American neoclassical Neoclassical or neo-classical may refer to: * Neoclassicism or New Classicism, any of a number of movements in the fine arts, literature, theatre, music, languag ...

, 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 , by William Smart, and by
Alfred Marshall Alfred Marshall (26 July 1842 – 13 July 1924) was an English economist, who was one of the most influential economists of his time. His book, '' Principles of Economics'' (1890), was the dominant economic textbook in England for many years. ...

; in Austria by
Eugen von Böhm-Bawerk Eugen Ritter von Böhm-Bawerk (; born Eugen Böhm, 12 February 185127 August 1914) was an Austrian Empire, Austrian economist who made important contributions to the development of the Austrian School, Austrian School of Economics and neoclassical e ...
and by
Friedrich von Wieser Friedrich Freiherr von Wieser (; 10 July 1851 – 22 July 1926) was an early (so-called "first generation") economist An economist is a professional and practitioner in the social science Social science is the branch A branch ( o ...
; in Switzerland by
Vilfredo Pareto Vilfredo Federico Damaso Pareto ( , , , ; born Wilfried Fritz Pareto; 15 July 1848 – 19 August 1923) was an Italian civil engineer A civil engineer is a person who practices civil engineering Civil engineering is a professional enginee ...

; 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.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). Böhm-Bawerk was perhaps the most able expositor of Menger's conception. 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 product In economics Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods an ...
ivity of time and with
time preference In economics, time preference (or time discounting, delay discounting, temporal discounting, long-term orientation) is the current relative valuation placed on receiving a good In most contexts, the concept of good denotes the conduct that ...
. This theory was adopted in full and then further developed by
Knut Wicksell Johan Gustaf Knut Wicksell (December 20, 1851 – May 3, 1926) was a leading Swedish Swedish or ' may refer to: * Anything from or related to Sweden, a country in Northern Europe * Swedish language, a North Germanic language spoken primarily i ...

and with modifications including formal disregard for time-preference by Wicksell's American rival
Irving Fisher Irving Fisher (February 27, 1867 – April 29, 1947) was an American economist An economist is a professional and practitioner in the social science Social science is the branch The branches and leaves of a tree. A branch ( or , ...

. 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 Classical may refer to: European antiquity *Classical antiquity, a period of history from roughly the 7th or 8th century B.C.E. to the 5th century C.E. centered on the Mediterranean Sea *Classical architecture, architecture derived from Greek and ...
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.Schumpeter, Joseph Alois; ''History of Economic Analysis'' (1954) Pt IV Ch 6 §4.

### Marginal Revolution and Marxism

Karl Marx Karl Heinrich Marx (; 5 May 1818 – 14 March 1883) was a German philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, M ...

acknowledged that "nothing can have value, without being an object of utility", but in his analysis "use-value as such lies outside the sphere of investigation of political economy", 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 Marxian economics, or the Marxian school of economics, is a Heterodox economics, heterodox school of political economic thought. Its foundations can be traced back to Karl Marx, Karl Marx's Critique of political economy#Marx's critique of politic ...
. However the first volume of ''
Das Kapital ''Das Kapital'', also known as ''Capital: A Critique of Political Economy'' or sometimes simply ''Capital'' (german: Das Kapital. Kritik der politischen Ökonomie, ; 1867–1883), is a foundational theoretical text in materialist philosophy, ...

'' 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 Friedrich August von Hayek ( , ; 8 May 189923 March 1992), often referred to by his initials F. A. Hayek, was an Austrian-British economist, and philosopher who is best known for his defence of classical liberalism. Hayek shared the 1974 Nob ...
and W. W. Bartley III have suggested that Marx, voraciously reading at the
British Museum The British Museum, in the Bloomsbury Bloomsbury is a district in the West End of London The West End of London (commonly referred to as the West End) is a district of Central London Central London is the innermost part of Lond ...

, 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. 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), but the first was Wicksteed's "The Marxian Theory of Value. ''Das Kapital'': a criticism" (1884, followed by "The Jevonian criticism of Marx: a rejoinder" in 1885). Initially there were only a few Marxist responses to marginalism, of which the most famous were
Rudolf Hilferding Rudolf Hilferding (10 August 1877 – 11 February 1941) was an Austrian-born Marxist Marxism is a method of socioeconomic Socioeconomics (also known as social economics) is the social science that studies how economic activity affects a ...
's ''Böhm-Bawerks Marx-Kritik'' (1904) and ''Politicheskoy ekonomii rante'' (1914) by
Nikolai Bukharin Nikolai Ivanovich Bukharin (russian: Никола́й Ива́нович Буха́рин) ( – 15 March 1938) was a Bolsheviks, Bolshevik Russian Revolution, revolutionary, Soviet Union, Soviet politician, Marxist philosopher and economist ...
. 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 Piero Sraffa (5 August 1898 – 3 September 1983) was an influential Italian economist An economist is a professional and practitioner in the social science Social science is the branch A branch ( or , ) or tree branch (sometime ...
providing an important critique of marginalism. It might also be noted that some followers of
Henry George Henry George (September 2, 1839 – October 29, 1897) was an American political economist Political economy is the study of Production (economics), production and trade and their relations with law, Custom (law), custom and government; and ...

similarly consider marginalism and neoclassical economics a reaction to ''
Progress and Poverty ''Progress and Poverty: An Inquiry into the Cause of Industrial Depressions and of Increase of Want with Increase of Wealth: The Remedy'' is an 1879 book by social theorist and economist Henry George Henry George (September 2, 1839 – October ...
'' which was published in 1879. In the 1980s
John Roemer John E. Roemer (; born February 1, 1945 in Washington, D.C., to Ruth Roemer and Milton Roemer, namesake of Roemer's law) is an American economist and political scientist. He is currently the Elizabeth S. and A. Varick Stout Professor of Political S ...
and other have worked to rebuild Marxian theses on a marginalist foundation.

## Reformulation

In his 1881 wor
''Mathematical Psychics''
Francis Ysidro Edgeworth Francis Ysidro Edgeworth (8 February 1845 – 13 February 1926) was an Anglo-Irish Anglo-Irish () is a term which was more commonly used in the 19th and early 20th centuries to identify an ethnic group An ethnic group or ethnicity i ...
presented the
indifference curve In economics Economics () is a social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behavi ...

, 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 Evgeny "Eugen" Evgenievich Slutsky (russian: Евге́ний Евге́ньевич Слу́цкий; – 10 March 1948) was a Russian and Soviet mathematical statistician A statistician is a person who works with Theory, theoretical or applie ...
derived a theory of consumer choice solely from properties of indifference curves. Because of , the
Bolshevik Revolution The October Revolution,. officially known as the Great October Socialist Revolution. under the Soviet Union The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a Federalism, federal socialist state in ...

, and his own subsequent loss of interest, Slutsky's work drew almost no notice, but similar work in 1934 by
John Richard Hicks Sir John Hicks (8 April 1904 – 20 May 1989) was a British economist. He is considered one of the most important and influential economists of the twentieth century. The most familiar of his many contributions in the field of economics were his ...

and R. G. D. Allen derived largely 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, 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") about decreasing marginal rates of substitutionHicks, Sir John Richard; ''Value and Capital'', Chapter I. "Utility and Preference" §7–8. 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.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).

## Revival

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 paradox of value (also known as the diamond–water paradox) is the contradiction that, although water Water (chemical formula H2O) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly col ...
. The marginalists of the revolution, however, had been formally concerned with problems in which there was neither
risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty Uncertainty refers to Epistemology, epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to ...

nor
uncertainty Uncertainty refers to epistemic Epistemology (; ) is the branch of philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, ...

. So too with the indifference curve analysis of Slutsky, Hicks, and Allen. The
expected utility hypothesis The expected utility hypothesis is a popular concept in economics Economics () is a social science Social science is the branch A branch ( or , ) or tree branch (sometimes referred to in botany Botany, also called , p ...
of Bernoulli and others was revived by various 20th century thinkers, with early contributions by
Ramsey Ramsey may refer to: Geography British Isles * Ramsey, Cambridgeshire Ramsey is a market town and civil parish In England, a civil parish is a type of administrative parish used for local government. It is a territorial designation whic ...
(1926),
von Neumann Von Neumann may refer to: * John von Neumann (1903–1957), a Hungarian American mathematician * Von Neumann family * Von Neumann (surname), a German surname * Von Neumann (crater), a lunar impact crater See also

* Von Neumann algebra * Von Ne ...

and Morgenstern (1944), and Savage (1954). 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. Quantified utility models simplify the analysis of risky decisions because, under quantified utility, diminishing marginal utility implies
risk aversion In economics Economics () is a social science Social science is the Branches of science, branch of science devoted to the study of society, societies and the Social relation, relationships among individuals within those societies ...

. In fact, many contemporary analyses of saving and portfolio choice require stronger assumptions than diminishing marginal utility, such as the assumption of
prudence Prudence ( la, prudentia, contracted from meaning "seeing ahead, sagacity") is the ability to govern and discipline oneself by the use of reason Reason is the capacity of consciously applying logic Logic is an interdisciplinary field ...
, which means
convex Convex means curving outwards like a sphere, and is the opposite of concave. Convex or convexity may refer to: Science and technology * Convex lens A lens is a transmissive optics, optical device which focuses or disperses a light beam by me ...

marginal utility.Kimball, Miles (1990), "Precautionary Saving in the Small and in the Large", ''
Econometrica ''Econometrica'' is a Peer review, peer-reviewed academic journal of economics, publishing article (publishing), articles in many areas of economics, especially econometrics. It is published by Wiley-Blackwell on behalf of the Econometric Society. ...
'', 58 (1) pp. 53–73.
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.

*
Diminishing returns In economics Economics () is a social science Social science is the branch A branch ( or , ) or tree branch (sometimes referred to in botany Botany, also called , plant biology or phytology, is the science of plant ...

*
Economic subjectivism The subjective theory of value is an economic theory Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consump ...
*
Marginalism Marginalism is a theory of economics Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (economic ...
*
Microeconomics Microeconomics is a branch of mainstream economics Mainstream economics is the body of knowledge, theories, and models of economics, as taught by universities worldwide, that are generally accepted by economists as a basis for discussion. Als ...
*
Paradox of value The paradox of value (also known as the diamond–water paradox) is the contradiction that, although water Water (chemical formula H2O) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly col ...
*
Rivalry (economics) In economics Economics () is a social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behavi ...
*
Shadow price A shadow price is a monetary value assigned to currently unknowable or difficult-to-calculate costs in the absence of correct market prices. It is based on the Willingness to pay, willingness to pay principle – the most accurate measure of the ...
*
Theory of value (economics) A theory of value is any economic theory Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (econom ...
*
Utility As a topic of economics Economics () is a social science Social science is the Branches of science, branch of science devoted to the study of society, societies and the Social relation, relationships among individuals within thos ...