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{{Short description|Benefit derived from consuming a product}}
{{use dmy dates|date=May 2024}}
In [[mainstream economics]], '''marginal utility''' describes the change in ''[[utility]]'' (pleasure or satisfaction resulting from the consumption) of one unit of a good or service.<ref>{{Cite web |title=Marginal Utility |url=https://www.britannica.com/topic/marginal-utility |website=Britannica Money}}</ref>
Marginal utility can be positive, negative, or zero. Negative marginal utility implies that every additional unit consumed of a commodity causes more harm than good, leading to a decrease in overall utility. In contrast, positive marginal utility indicates that every additional unit consumed increases overall utility.<ref>{{Cite web |date=January 2020 |title=Marginal Utility |url=https://www.intelligenteconomist.com/marginal-utility/ |website=Intelligent Economist |language=en}}</ref>

In the context of [[cardinal utility]], liberal economists postulate a '''law of diminishing marginal utility.''' This law states that the first units of consumption of a good or service yields more satisfaction or utility than the subsequent units, and there is a continuing reduction in satisfaction or utility for greater amounts. As consumption increases, the additional satisfaction or utility gained from each additional unit consumed falls,  a concept known as '''''diminishing marginal utility.''''' This idea is used by economics to determine the optimal quantity of a good or service that a consumer is willing to purchase.<ref>{{Cite web |title=Law of Diminishing Marginal Utility |url=https://corporatefinanceinstitute.com/resources/economics/law-of-diminishing-marginal-utility/ |website=Corporate Finance institute |language=en}}</ref>

== Marginality ==
In the study of economics, the term ''[[Marginalism|marginal]]'' refers to a small change, starting from some baseline level. [[Philip Wicksteed]] explained the term as follows:
<blockquote>Marginal considerations are considerations which concern a slight increase or diminution of the stock of anything which we possess or are considering.<ref>[[Philip Wicksteed|Wicksteed, Philip Henry]]; ''The Common Sense of Political Economy'' (1910), Bk I Ch 2 and elsewhere.</ref>

Another way to think of the term marginal is the cost or benefit of the next unit used or consumed, for example the benefit that you might get from consuming a piece of chocolate. The key to understanding marginality is through [[marginal analysis]]. Marginal analysis examines the additional benefits of an activity compared to additional costs sustained by that same activity. In practice, companies use marginal analysis to assist them in [[maximizing]] their potential profits and often used when making decisions about expanding or reducing production.{{citation needed|date=April 2023}}</blockquote>

== Utility ==
[[Utility]] is an economic concept that refers to the level of satisfaction or benefit that individuals derive from consuming a particular good or service, which is quantified using units known as '''utils''' (derived from the Spanish word for ''useful''). However, determining the exact level of utility that a consumer experiences can be a challenging and abstract task. To overcome this challenge, economists rely on the consent of '''revealed preferences,''' where they observe the choices made by consumers and use this information to rank consumption options from the least preferred to the most desirable.{{citation needed|date=April 2023}}

Initially, the term utility equated usefulness with the production of pleasure and avoidance of pain by moral philosophers, Jeremy Bentham and John Stuart Mill.<ref>[[Jeremy Bentham|Bentham, Jeremy]]. ''Introduction to the Principles of Morals and Legislation'', Chapter I §I–III.</ref> In line with this philosophy, the concept of utility was defined as "the feelings of pleasure and pain"<ref>Jevons, William Stanley; "Brief Account of a General Mathematical Theory of Political Economy", ''[[Journal of the Royal Statistical Society]]'' v29 (June 1866) §2.</ref> and further as a "''quantity'' of feeling".<ref>Jevons, William Stanley; ''Brief Account of a General Mathematical Theory of Political Economy'', ''Journal of the Royal Statistical Society'' v29 (June 1866) §4.</ref>

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.<ref>[[David M. Kreps|Kreps, David Marc]]; ''A Course in Microeconomic Theory'', Chapter two: ''The theory of consumer choice and demand'', ''Utility representations''.</ref>

In any standard framework, the same object may have different marginal utilities for different people, reflecting different preferences or individual circumstances.<ref>Davenport, Herbert Joseph; ''The Economics of Enterprise'' (1913) Ch VII, pp. 86–87.</ref>

==Law of diminishing marginal utility ==<!-- This section is linked from [[Law of diminishing marginal utility]], [[Diminishing-utility theory]], [[Diminishing utility]] -->
[[Alfred Marshall]], a British economist, observed that as you accumulate more of something, your desire for it decreases. Economists refer to this phenomenon as diminishing marginal utility.<ref>{{Cite journal|author= H.G. |url= https://mitpress.mit.edu/9780262070904/the-laws-of-human-relations-and-the-rules-of-human-action-derived-therefrom/ |title= The Laws of Human Relations and the Rules of Human Action Derived Therefrom|journal= Economist |year= 1983 }}</ref> The law states that as the amount consumed of a commodity increases, other things being equal, the utility derived by the consumer from the additional units, i.e., marginal utility, goes on decreasing.<ref>{{Cite book |last=Sethi |first=D.K |title=Frank ISC Economics |last2=Andrews |first2=U |publisher=Macmillan Education |isbn=9789386811684 |edition=18th |pages=34}}</ref> 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).<ref>{{Cite journal|author= G.J. |url= https://amp.economist.com/free-exchange/2013/08/07/the-utility-of-bad-art |title= The utility of bad art |journal= Economist |year= 2013 }}</ref> This principle is so well established that economists call it the '''"law of diminishing marginal utility"''' and it is reflected in the concave shape of most utility functions.<ref>{{Cite journal|author= D.K. & A.T. |url= https://www.jstor.org/stable/1914185|title= TProspect Theory: An Analysis of Decision under Risk
|journal= Econometrica |year= 1979 |volume= 47|issue= 2|pages= 263–291|doi= 10.2307/1914185|jstor= 1914185|citeseerx= 10.1.1.592.6674}}</ref> This concept is fundamental to understanding a variety of economic phenomena, such as [[time preference]] and the [[Value (economics)|value of goods]]. 

'''Assumptions''' -

# All the units of a commodity must be identical, i.e., some in all respects - in size, colour, design, quality, etc.
# The unit of the good must be standard, e.g., a bottle of cold drink, a pair of shoes, a full mango, etc. The units not be too small or too large.
# There should be no change in taste of the consumer during the process of consumption.
# The utility is measurable.
# The consumer is rational while taking consumption decisions.
# There must be a continuity in consumption and if a break in the continuity is necessary, the time interval between the consumption of two units must be short.
# There should be no change in the price of substitute goods.<ref>{{Cite book |last=Sethi |first=D.K |title=Frack ISC Economics |isbn=9789386811684 |edition=18th |pages=35}}</ref>

Modern economics employs [[ordinal utility]] to model decision-making under certainty at a specific point in time. In this approach, the number assignment to an individual's utility for a particular situation hold no significance on their own. Rather, the significance lies in the comparison between two different circumstances and which one holds a higher utility. With ordinal utility, a person's preferences do not have a unique marginal utility, making the concept of diminishing marginal utility irrelevant. On the other hand, diminishing marginal utility is a significant concept in [[cardinal utility]], which is used to analyse [[intertemporal choice]], [[expected utility hypothesis|choice under uncertainty]], and [[social welfare function|social welfare]] in modern economic theory.<ref>{{Cite web|title=Marginal Utility & its Diminishing Methods
|url=https://journals.indexcopernicus.com/api/file/viewByFileId/686333.pdf}}</ref>

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.<ref name=":1">{{Cite web |title=Marginal Utility & its Diminishing Methods |date=5 September 2023 |url=https://www.adda247.com/school/law-of-diminishing-marginal-utility/}}</ref>

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.<ref>{{Cite book | author = E.T. Berkman, L.E. Kahn, J.L. Livingston | title = Self-Regulation and Ego Control | location = United States | date = 2016 | chapter= Chapter 13 Valuation as a Mechanism of Self-Control and Ego Depletion | pages = 255–279 | isbn = 978-0-12-801850-7}}</ref>

As the rate of commodity acquisition increases, the ''marginal'' utility decreases. If commodity consumption continues to rise, the marginal utility will eventually reach zero, and the total utility will be at its maximum. Beyond that point, any further increase in commodity consumption leads to negative marginal utility, which represents 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 affect a cure.<ref name=":2">{{Cite web |title=Marginal utility theory (1870S) |date=29 April 2020 |url=https://sciencetheory.net/marginal-utility-theory-1870s/}}</ref>

As mentioned earlier in this article, there are instances where marginal utility can increase on a macroeconomic level. For instance, offering a service may only be feasible if it is accessible to the majority or all of the population. At the point where this becomes a reality, the marginal utility of the raw material required to provide the service will increase significantly. This is akin to situations involving massive objects like aircraft carriers, where the quantity of such items is so small that the concept of marginal utility becomes irrelevant, and the decision to acquire them is a simple binary choice between "yes" or "no".<ref name=":2" />

== Marginalist theory ==
[[Marginalism]] is an economic theory and method of analysis that suggests that individuals make economic decisions by weighing the benefits of consuming an additional unit of a good or service against the cost of acquiring it. In other words, value is determined by the additional utility of satisfaction provided by each extra unit consumed.{{citation needed|date=April 2023}}

=== Market price and diminishing marginal utility ===
If a person has a good or service that has less value to them compared to another good or service they could trade it for, it would be beneficial for them to make that trade. The marginal gains or losses from further trades will vary as items are exchanged. If the marginal utility of one item is decreasing while the other is not increasing, then the individual will demand a greater amount of the item they're acquiring in comparison to the one they're giving up. However, if the two items complement each other, then the exchange ratios might remain constant.<ref name="mc_culloch">Mc Culloch, James Huston; [https://www.mises.org/etexts/mcCulloch.pdf "The Austrian Theory of the Marginal Use and of Ordinal Marginal Utility"], ''Zeitschrift für Nationalökonomie'' 37 (1977) #3&amp;4 (September).</ref> In situations where traders can improve their position by offering trades that are more favorable to complementary traders, they are likely to do so.

In an economy that uses [[money]], the marginal utility of a given quantity of money is equivalent to the marginal utility of the best good or service that could be purchased with that money. This concept is helpful for explaining the principles of [[supply and demand]], and is essential aspects of models of [[imperfect competition]].

[[Image:AdamSmith.jpg|thumb|right|105px|[[Adam Smith]]]]

==== Paradox of water and diamonds ====
{{Main|Paradox of value}}

The "paradox of water and diamonds" is most commonly associated with [[Adam Smith]],<ref>Smith, Adam; ''An Inquiry into the Nature and Causes of the Wealth of Nations'' (1776) Chapter IV. "Of the Origin and Use of Money"</ref> though it was recognized by earlier thinkers.<ref>{{Cite book|first = Scott|last = Gordon|year = 1991|title = History and Philosophy of Social Science: An Introduction|chapter = The Scottish Enlightenment of the eighteenth century|publisher = [[Routledge]]|isbn = 0-415-09670-7}}</ref> 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.<ref>{{Cite web |url= https://ed.ted.com/lessons/the-paradox-of-value-akshita-agarwal |title= The paradox of value-Akshita Agarwal | author= Alex Gendler |language=English}}</ref>

Price is determined by both marginal utility and marginal cost, and here is the key to the apparent 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.<ref name=":1" />

=== Marginalism limitations ===
[[Marginalism]] has many limitations and economic theories. Some scholars, such as [[Warren J. Samuels]], have raised concerns that individuals may not always behave as portrayed in marginalist theories, highlighting complexities in human decision-making that go beyond simple optimizing behavior. Additionally, utility is difficult to quantify precisely, as it varies significantly from person to person and may not be stable over time.<ref name=":0" /> Another limitation lies in measuring the marginal change: while monetary values can be straightforward to track, gauging the utility derived from non-monetary goods like food is more challenging, as individual preferences and the wide range of alternatives complicate accuracy.<ref name=":0">{{Cite web |title=Marginalism {{!}} Encyclopedia.com |url=https://www.encyclopedia.com/social-sciences/applied-and-social-sciences-magazines/marginalism |access-date=2022-05-02 |website=www.encyclopedia.com}}</ref>

== Quantified marginal utility ==
Under the [[special case]] in which usefulness can be quantified, the change in utility of moving from state <math>S_1</math> to state <math>S_2</math> is
: <math>\Delta U = U(S_2) - U(S_1).</math>
Moreover, if <math>S_1</math> and <math>S_2</math> are distinguishable by values of just one variable <math>g,</math> which is itself quantified, then it becomes possible to speak of the ratio of the marginal utility of the change in <math>g</math> to the size of that change:
[[Image:UtilityQuantified.svg|thumb|right|400px|Diminishing marginal utility, given quantification]]
: <math>\left.\frac{\Delta U}{\Delta g}\right|_\text{c.p.},</math>
where "[[ceteris paribus|c.p.]]" indicates that the ''only'' [[Dependent and independent variables|independent variable]] to change is <math>g.</math>

Mainstream [[neoclassical economics]] will typically assume that the limit
: <math>\lim_{\Delta g\to 0} \left.\frac{\Delta U}{\Delta g}\right|_\text{c.p.}</math>
exists, and use "marginal utility" to refer to the [[partial derivative]]
: <math>\frac{\partial U}{\partial g} = \lim_{\Delta g\to 0}\left.\frac{\Delta U}{\Delta g}\right|_\text{c.p.}.</math>
Accordingly, diminishing marginal utility corresponds to the condition
: <math>\frac{\partial^2 U}{\partial g^2} < 0.</math>

== History ==
Economists sought to explain how prices are determined, and in this pursuit, they developed the concept of marginal utility. The term "marginal utility", credited to the [[Austrian School|Austrian]] economist [[Friedrich von Wieser]] by [[Alfred Marshall]],<ref>Marshall, Alfred; ''Principles of Economics'', Chapter 3, Note 3.</ref> was a translation of Wieser's term {{Lang|de|Grenznutzen}} ("border-use").<ref name="wieser_ein">von Wieser,  Friedrich; ''Über den Ursprung und die Hauptgesetze des wirtschaftlichen Wertes'' <nowiki>[</nowiki>''The Nature and Essence of Theoretical Economics''<nowiki>]</nowiki> (1884), p.  128.</ref><ref name="wieser_zwei">Wieser, Friedrich von; ''Der natürliche Werth''  [''Natural Value''] (1889), Book I, Chapter V, "Marginal Utility" ([http://praxeology.net/FW-NV-I-5.htm HTML]).</ref>

=== Proto-marginalist approaches ===
Perhaps the essence of a notion of diminishing marginal utility can be found in [[Aristotle]]'s [[Politics (Aristotle)|''Politics'']], wherein he writes {{Blockquote|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.<ref>[[Aristotle]], ''Politics'', Book 7 Chapter 1.</ref>}}

There has been marked disagreement about the development and role of marginal considerations in Aristotle's value theory.<ref>{{cite journal |last=Soudek |first=Josef |title=Aristotle's Theory of Exchange: An Inquiry into the Origin of Economic Analysis |journal=Proceedings of the American Philosophical Society |volume=96 |issue=1 |year=1952 |pages=45–75 |jstor=3143742 }}</ref><ref name="kauder">{{cite journal |last=Kauder |first=Emil |title=Genesis of the Marginal Utility Theory from Aristotle to the End of the Eighteenth Century |journal=[[The Economic Journal]] |volume=63 |issue=251 |year=1953 |pages=638–50 |jstor=2226451 |doi=10.2307/2226451}}</ref><ref>{{cite journal |last=Gordon |first=Barry Lewis John |title=Aristotle and the Development of Value Theory |journal=[[Quarterly Journal of Economics]] |volume=78 |issue=1 |pages=115–28 |year=1964 |jstor=1880547 |doi=10.2307/1880547}}</ref><ref name="schumArist">Schumpeter, Joseph Alois; ''History of Economic Analysis'' (1954) Part II, Chapter 1 §3.</ref><ref>Meikle, Scott; ''Aristoteles' Economic Thought'' (1995) Chapters 1, 2, & 6.</ref>

Numerous economists have established a connection between utility and rarity, which influences economic decisions and price determination. Diamonds are priced higher than water because their marginal utility is higher than water.<ref>[[Karl Přibram|Přibram, Karl]]; ''A History of Economic Reasoning'' (1983).</ref>

Eighteenth-century Italian [[Mercantilism|mercantilists]], such as [[Antonio Genovesi]], [[Giammaria Ortes]], [[Pietro Verri]], [[Cesare, Marquis of Beccaria|Marchese Cesare di Beccaria]], and [[Giovanni Rinaldo|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.<ref name="pribramItalMerc">Pribram, Karl; ''A History of Economic Reasoning'' (1983), Chapter 5 "Refined Mercantilism", "Italian Mercantilists".</ref> 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.
[[Image:Richard Whately.jpg|thumb|right|105px|[[Richard Whately]]]]
[[Anne Robert Jacques Turgot]], in ''{{Lang|fr|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 de Condillac|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 ''{{Lang|fr|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: {{Blockquote|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.<ref>Whately, Richard; ''Introductory Lectures on Political Economy, Being part of a course delivered in the Easter term'' (1832).</ref>}} (Whatley's student [[Nassau William Senior|Senior]] is noted below as an early marginalist.)

=== Marginalists before the Revolution ===
[[Image:Gabriel Cramer.jpg|thumb|105px|[[Gabriel Cramer]]]]

[[Daniel Bernoulli]], is credited with publishing the first clear statement on the theory of marginal utility in his paper "Specimen theoriae novae de mensura sortis",<ref>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).</ref> which was released in 1738, although he had drafted it in 1731 or 1732.<ref>Bernoulli, Daniel; letter of 4 July 1731 to Nicolas Bernoulli ([http://www.cs.xu.edu/math/Sources/Montmort/stpetersburg.pdf#search=%22Nicolas%20Bernoulli%22 Excerpted in PDF]. {{webarchive|url=https://web.archive.org/web/20080909221757/http://www.cs.xu.edu/math/Sources/Montmort/stpetersburg.pdf|date=2008-09-09}}).</ref><ref>Bernoulli, Nicolas; letter of 5 April 1732, acknowledging receipt of "Specimen theoriae novae metiendi sortem pecuniariam" ([http://www.cs.xu.edu/math/Sources/Montmort/stpetersburg.pdf#search=%22Nicolas%20Bernoulli%22 Excerpted in PDF]. {{webarchive|url=https://web.archive.org/web/20080909221757/http://www.cs.xu.edu/math/Sources/Montmort/stpetersburg.pdf|date=2008-09-09}}).</ref> [[Gabriel Cramer]] had developed a similar theory in a private letter in 1728, aimed at resolving the [[St. Petersburg paradox]].<ref>Cramer, Garbriel; letter of 21 May 1728 to [[Nicolaus I Bernoulli|Nicolaus Bernoulli]] ([http://www.cs.xu.edu/math/Sources/Montmort/stpetersburg.pdf#search=%22Nicolas%20Bernoulli%22 Excerpted in PDF]. {{webarchive|url=https://web.archive.org/web/20080909221757/http://www.cs.xu.edu/math/Sources/Montmort/stpetersburg.pdf|date=2008-09-09}}).</ref> Both Bernoulli and Cramer concluded that the desirability of money decreases as it accumulates, with the [[natural logarithm]] (Bernoulli) or [[square root]] (Cramer) serving as the measure of a sum's desirability. However, the broader implications of this hypothesis were not explored, and the work faded into obscurity.

In [http://socserv2.socsci.mcmaster.ca/~econ/ugcm/3ll3/lloyd/value "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.<ref>{{cite journal |author-link=Edwin Robert Anderson Seligman |last=Seligman |first=E. R. A. |title=On Some Neglected British Economists |journal=[[The Economic Journal]] |volume=13 |issue=51 |pages=335–63 |year=1903 |jstor=2221519 |doi=10.2307/2221519|hdl=2027/hvd.32044081864944 |hdl-access=free }}</ref>

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.<ref>{{cite journal |last=White |first=Michael V. |title=Diamonds Are Forever(?): Nassau Senior and Utility Theory |journal=[[The Manchester School (journal)|The Manchester School]] |volume=60 |year=1992 |issue=1 |pages=64–78 |doi=10.1111/j.1467-9957.1992.tb00211.x }}</ref>

In "''{{Lang|fr|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.<ref>{{cite journal |last=Dupuit |first=Jules |title=De la mesure de l'utilité des travaux publics |journal=Annales des ponts et chaussées |series=Second series |volume=8 |year=1844 }}</ref><ref>{{cite journal |last=Bonnafous |first=Alain |year=2017 |title=Consumer Surplus and Pricing of Transport Infrastructures: The Legacy of Jules Dupuit |journal=University of Lyon}}</ref>

In 1854, [[Hermann Heinrich Gossen]] published {{Lang|de|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.{{Citation needed|date=October 2021}}

=== Marginal Revolution ===
Marginalism eventually found a foothold by way of the work of three economists, [[William Stanley Jevons|Jevons]] in England, [[Carl Menger|Menger]] in Austria, and [[Léon Walras|Walras]] in Switzerland.
[[Image:Jevons.jpeg|thumb|105px|[[William Stanley Jevons]]]]
[[William Stanley Jevons]] first proposed the theory in "A General Mathematical Theory of Political Economy",<ref>{{Cite web |last=Jevons |first=William Stanley |date=1866 |title=Brief Account of a General Mathematical Theory of Political Economy |url=http://socserv2.socsci.mcmaster.ca/~econ/ugcm/3ll3/jevons/mathem.txt |url-status=dead |archive-url=https://web.archive.org/web/20061215140931/http://socserv2.socsci.mcmaster.ca/~econ/ugcm/3ll3/jevons/mathem.txt |archive-date=2006-12-15 |website=socserv2.socsci.mcmaster.ca}}</ref> 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 [[Utilitarianism|utilitarian]] tradition of [[Jeremy Bentham]] and of [[John Stuart Mill]], but he differed from his [[classical economics|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."<ref>Stanley Jevons (1871), ''The Theory of Political Economy'', p. 111.</ref> 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.<ref>W. Stanley Jevons (1879, 2nd ed.), [https://archive.org/details/theorypolitical00jevogoog <!-- quote=jevons "the theory of political economy". --> ''The Theory of Political Economy''], p. 208.</ref><ref>R. D. Collison Brown (1987), "Jevons, William Stanley", [[The New Palgrave: A Dictionary of Economics]], v. 2, pp. 1008–9.</ref>

[[Carl Menger]] presented the theory in ''Grundsätze der Volkswirtschaftslehre''<ref>{{Cite web |last=Menger |first=Carl |date=1871 |title=Grundsätze der Volkswirthschaftslehre |url=http://docs.mises.de/Menger/Menger_Grundsaetze.pdf |url-status=dead |archive-url=https://web.archive.org/web/20080528063159/http://docs.mises.de/Menger/Menger_Grundsaetze.pdf |archive-date=2008-05-28}}</ref> (translated as ''Principles of Economics''<ref>{{Cite web |title=Principles of Economics by Carl Menger |url=https://www.mises.org/etexts/menger/principles.asp |url-status=dead |archive-url=http://web.archive.org/web/20110303023807/https://www.mises.org/etexts/menger/principles.asp |archive-date=2011-03-03 |website=Ludwig von Mises Institute}}</ref>) 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.<ref name="georgescu-rogen">[[Nicholas Georgescu-Roegen|Georgescu-Roegen, Nicholas]]; ''Utility'', ''International Encyclopedia of the Social Sciences'' (1968).</ref> (Menger in fact crossed-out the numerical tables in his own copy of the published ''Grundsätze''.<ref>Kauder, Emil; ''A History of Marginal Utility Theory'' (1965), p. 76.</ref>) Menger also developed the [[law of diminishing marginal utility]].<ref name="Mises">Polleit, Thorsten (2011-02-11) [https://mises.org/daily/5014/What-Can-the-Law-of-Diminishing-Marginal-Utility-Teach-Us What Can the Law of Diminishing Marginal Utility Teach Us?], ''[[Mises Institute]].''</ref> Menger's work found a significant and appreciative audience.

[[Léon Walras|Marie-Esprit-Léon Walras]] introduced the theory in ''{{Lang|fr|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 [[Vilfredo Pareto|Pareto]] and [[Enrico Barone|Barone]].<ref>Donald A. Walker  (1987), "Walras, Léon" ''The New Palgrave: A Dictionary of Economics, v. 4, p. 862.</ref>

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 ====
[[Image:Vilfredo Pareto 1870s2.jpg|thumb|105px|[[Vilfredo Pareto]]]]
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 Wicksteed|Philip Henry Wicksteed]], by [[William Smart (economist)|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 Fetter|Frank A. Fetter]].

While the approaches of Jevons, Menger, and Walras had notable differences, the second generation of economists did not maintain these distinctions based on national or linguistic boundaries. Von Wieser's work was significantly influenced by Walras, while Wicksteed was strongly influenced by Menger. Fetter and Davenport identified themselves as part of the "American Psychological School", named after the "Austrian Psychological School", while Clark's work during this period was also heavily influenced by Menger. William Smart initially served as a conduit for Austrian School ideas to English-speaking readers but gradually came under the sway of Marshall's ideas.<ref name="salerno">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).</ref>

Böhm-Bawerk was perhaps the most able expositor of Menger's conception.<ref name="salerno" /><ref>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''.</ref> 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]]ivity of time and with [[time preference]].<ref>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''.</ref> This theory was adopted in full and then further developed by [[Knut Wicksell]]<ref>Wicksell, Johan Gustaf Knut; ''Über Wert, Kapital unde Rente'' (1893). Translated as [https://www.mises.org/books/valuecapital.pdf ''Value, Capital and Rent''.]</ref> and with modifications including formal disregard for time-preference by Wicksell's American rival [[Irving Fisher]].<ref>Fisher, Irving; ''Theory of Interest'' (1930).</ref>

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 economics|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.<ref name="schumMarshScis">Schumpeter, Joseph Alois; ''History of Economic Analysis'' (1954) Part IV, Chapter 6, §4.</ref>

==== Marginal Revolution and Marxism ====
[[Karl Marx]] acknowledged that "nothing can have value, without being an object of utility",<ref>Marx, Karl Heinrich; ''Capital'', Volume 1, Chapter 1, §1.</ref><ref>Marx, Karl Heinrich; [http://www.marxists.org/archive/marx/works/1857/grundrisse/f239-289.htm ''Grundrisse''] (Completed in 1857 though not published until much later.)</ref> but in his analysis "use-value as such lies outside the sphere of investigation of political economy",<ref>[[Karl Marx|Marx, Karl Heinrich]]: ''A Contribution to the Critique of Political Economy'' (1859), p. 276.</ref> with labor being the principal determinant of value under capitalism.{{primary source inline|date=October 2021}}

[[Ernesto Screpanti]] and [[Stefano Zamagni]] interpret the doctrines of marginalism and the Marginal Revolution as a response to [[Marxism|Marxist economics]].<ref name=":02">{{cite book |author-last1=Screpanti |author-first1=Ernesto |author-link1=Ernesto Screpanti |url=https://academic.oup.com/book/1668/chapter/141233045 |title=An Outline of the History of Economic Theory |author-last2=Zamagni |author-first2=Stefano |author-link2=Stefano Zamagni |publisher=[[Oxford University Press]] |year=2005 |pages=170–173 |chapter=5. The Triumph of Utilitarianism and the Marginalist Revolution |quote=It was against Marx's classical economics that the marginalists made a revolution, not against that of Mill.}}</ref> However, this view is somewhat flawed, as the first volume of ''[[Das Kapital]]'' was not published until July 1867, which was after the works of Jevons, Menger, and Walras had either been written or were under way (Walras published {{Lang|fr|Éléments d'économie politique pure}} in 1874 and Carl Menger published ''Principles of Economics'' in 1871); Marx was still a relatively minor figure when these works were completed and it is unlikely that any of these economists knew anything about him. Some scholars, such as [[Friedrich Hayek]] and [[W. W. Bartley III]], have speculated that Marx may have come across the works of one or more of these economists while reading at the [[British Museum]]. However, it is also possible that Marx's inability to formulate a viable critique may account for his failure to complete any further volumes of ''Kapital'' before his death.<ref>{{Cite book |last=Hayek |first=Friedrich August von |author-link=Friedrich August von Hayek |title=[[The Fatal Conceit: The Errors of Socialism]] |last2=Bartley III |first2=William Warren |author-link2=William Warren Bartley |date=1988 |publisher=University of Chicago Press |year=1988 |pages=150}}</ref>

Despite the fact the Marxist economics was not an immediate target for the marginalists, it is possible to argue that the new generation of economists succeeded partly because they were able to provide simple responses to Marxist economic theory. One of the best known responses was Böhm-Bawerk, {{Lang|de|Zum Abschluss des Marxschen Systems}} (1896),<ref>Böhm-Bawerk, Eugen Ritter von: "''Zum Abschluss des Marxschen Systems''" <nowiki>[</nowiki>"On the Closure of the Marxist System"<nowiki>]</nowiki>, ''Staatswiss. Arbeiten. Festgabe für [[Karl Knies|K. Knies]]'' (1896).</ref> but the first response was actually Wicksteed's "The Marxian Theory of Value. ''Das Kapital'': A Criticism" (1884),<ref>Wicksteed, Philip Henry; "Das Kapital: A Criticism", ''To-Day'' 2 (1884) pp. 388–409.</ref> followed by "The Jevonian Criticism of Marx: A Rejoinder" in 1885.<ref>Wicksteed, Philip Henry; "The Jevonian Criticism of Marx: A Rejoinder", ''To-Day'' 3 (1885) pp. 177–9.</ref> At first, there were only a few Marxist responses to marginalism, including [[Rudolf Hilferding]]'s ''Böhm-Bawerks Marx-Kritik'' (1904)<ref>Hilferding, Rudolf: ''Böhm-Bawerks Marx-Kritik'' (1904). Translated as ''Böhm-Bawerk's Criticism of Marx''.</ref> and ''Politicheskoy ekonomii rante'' (1914) by [[Nikolai Bukharin]].<ref>[[Nikolai Bukharin|Буха́рин, Никола́й Ива́нович (Nikolai Ivanovich Bukharin)]]; ''Политической экономии рантье'' (1914). Translated as [http://www.marxists.org/archive/bukharin/works/1927/leisure-economics/ ''The Economic Theory of the Leisure Class''].</ref> However, over the course of the 20th century, a significant body of literature emerged on the conflict between marginalism and labour theory of value. One important critique of marginalism came from neo-Ricardian economist [[Piero Sraffa]].

Followers of [[Henry George]]'s ideas such as [[Mason Gaffney]] view marginalism and neoclassical economics as a response to ''[[Progress and Poverty]]'', which was published in 1879.<ref>{{Cite book |last=Gaffney |first=Mason |author-link=Mason Gaffney |url=https://masongaffney.org/publications/K1Neo-classical_Stratagem.CV.pdf |title=Neo-classical Economics as a Stratagem Against Henry George |date=1993 |publisher=Macquarie University School of Economic and Financial Studies |year=1993}}</ref>

In the 1980s [[John Roemer]] and other [[Analytical Marxism#Exploitation|analytical Marxists]] have worked to rebuild Marxian theses on a marginalist foundation.

=== Reformulation ===
In his 1881 work ''Mathematical Psychics'',<ref>{{Cite web |last=Edgeworth |first=Francis Ysidro |date=1881 |title=Mathematical psychics |url=https://socialsciences.mcmaster.ca/econ/ugcm/3ll3/edgeworth/mathpsychics.pdf |url-status=dead |archive-url=http://web.archive.org/web/20180323203128/https://socialsciences.mcmaster.ca/econ/ugcm/3ll3/edgeworth/mathpsychics.pdf |archive-date=2018-03-23 |website=socialsciences.mcmaster.ca}}</ref> [[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.<ref>[[Eugen Slutsky|Слуцкий, Евгений Евгениевич (Slutsky, Yevgyeniy Ye.)]]; "Sulla teoria del bilancio del consumatore", ''Giornale degli Economisti'' 51 (1915).</ref> Because of the [[World War I|World War]], the [[October Revolution|Bolshevik Revolution]], and his own subsequent loss of interest, Slutsky's work drew almost no notice, but similar work in 1934 by [[John Hicks|John Richard Hicks]] and [[R. G. D. Allen]]<ref>Hicks, John Richard, and Roy George Douglas Allen; "A Reconsideration of the Theory of Value", ''Economica'' 54 (1934).</ref> 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,<ref name="mises" >[[Ludwig von Mises|von Mises, Ludwig Heinrich]]; ''Theorie des Geldes und der Umlaufsmittel'' (1912).</ref> 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"<ref>Hicks, Sir John Richard; ''Value and Capital'', Chapter I. "Utility and Preference" §8, p. 23 in the 2nd edition.</ref>) about decreasing marginal rates of substitution<ref name="hicks_vc">Hicks, Sir John Richard; ''Value and Capital'', Chapter I. "Utility and Preference" §7–8.</ref> 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.<ref name="hicks_vc" /><ref name="samuelson">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).</ref>

=== Revival ===
[[Image:JohnvonNeumann-LosAlamos.gif|thumb|105px|[[John von Neumann]]]]
When Cramer and Bernoulli introduced the notion of diminishing marginal utility, it had been to address a [[St. Petersburg paradox|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 [[Frank P. Ramsey|Ramsey]] (1926),<ref>Ramsey, Frank Plumpton; "Truth and Probability" ([http://cepa.newschool.edu/het//texts/ramsey/ramsess.pdf PDF] {{webarchive|url=https://web.archive.org/web/20080227205205/http://cepa.newschool.edu/het//texts/ramsey/ramsess.pdf|date=2008-02-27}}), Chapter VII in ''The Foundations of Mathematics and Other Logical Essays'' (1931).</ref> [[John von Neumann|von Neumann]] and [[Oskar Morgenstern|Morgenstern]] (1944),<ref>von Neumann, John and Oskar Morgenstern; ''[[Theory of Games and Economic Behavior]]'' (1944).</ref> and [[Leonard Jimmie Savage|Savage]] (1954).<ref>Savage, Leonard Jimmie: ''Foundations of Statistics'' (1954), New York: John Wiley & Sons.</ref> 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.<ref>Diamond, Peter, and Michael Rothschild, eds.: ''Uncertainty in Economics'' (1989). Academic Press.</ref> Quantified utility models provide a simplified approach to analysing risky decision by establishing a link between diminishing marginal utility and [[risk aversion]].<ref>Demange, Gabriel, and Guy Laroque: ''Finance and the Economics of Uncertainty'' (2006), Ch. 3, pp. 71–72. Blackwell Publishing.</ref> In fact, many contemporary analyses of saving and portfolio choice require stronger assumptions than diminishing marginal utility, such as the assumption of [[Prudence#Prudence in economics and finance|prudence]], which means [[convex function|convex]] marginal utility.<ref>Kimball, Miles (1990), "Precautionary Saving in the Small and in the Large", ''[[Econometrica]]'', 58 (1) pp. 53–73.</ref>

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.<ref name="mc_culloch" />

== See also ==
{{colbegin|colwidth=22em}}
* [[Diminishing returns]]
* [[Economic subjectivism]]
* [[Marginalism]]
* [[Microeconomics]]
* [[Paradox of value]]
* [[Pareto efficiency]]
* [[Rivalry (economics)]]
* [[Shadow price]]
* [[Theory of value (economics)]]
* [[Utility]]
{{colend}}

== References ==
{{reflist|colwidth=30em}}

== Further reading ==
* {{cite journal|first=E. H.|last=Downey|title=The Futility of Marginal Utility|journal=[[Journal of Political Economy]]|volume=18|issue=4|year=1910|pages=253–268|jstor=1820794|doi=10.1086/251690|url=https://zenodo.org/record/1431301|doi-access=free}}

== External links ==
* {{commons category-inline}}
* [http://philpapers.org/archive/BRAMOO-2.pdf Maximization of Originality]

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