Marginal utility: Difference between revisions

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In the study of Economicseconomics, the term '''[[Marginalism|marginal]]''' refers to a small change, starting from some baseline level. [[Philip Wicksteed]] explained the term as follows:

'''[[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 quantifiesquantified 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}}

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's 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" />

: <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:

: <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>).

: <math>\lim_{\Delta g\to 0} \left.\frac{\Delta U}{\Delta g}\right|_\text{c.p.}</math>

: <math>\frac{\partial U}{\partial g} = \lim_{\Delta g\to 0}\left.\frac{\Delta U}{\Delta g}\right|_\text{c.p.}.</math>.

: <math>\frac{\partial^2 U}{\partial g^2} < 0.</math>.

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, ChNote 3 Note.</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'' <nowiki>[</nowiki>''Natural Value''<nowiki>]</nowiki> (1889), BkBook I, ChChapter V , "Marginal Utility" ([http://praxeology.net/FW-NV-I-5.htm HTML]).</ref>

Perhaps the essence of a notion of diminishing marginal utility can be found in [[Aristotle]]'s [[Politics (Aristotle)|''Politics'']], wherein he writes {{Blockquote|externalExternal 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'', BkBook 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.

[[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 newNew theoryTheory on the measurementMeasurement of riskRisk" 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 excerptedExcerpted 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 excerptedExcerpted 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 excerptedExcerpted 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 "''{{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 surplusSurplus and pricingPricing of transportTransport infrastructuresInfrastructures: The legacyLegacy of Jules Dupuit |journal=University of Lyon |year=2017 }}</ref>

[[William Stanley Jevons]] first proposed the theory in [https://web.archive.org/web/20061215140931/http://socserv2.socsci.mcmaster.ca/~econ/ugcm/3ll3/jevons/mathem.txt "A General Mathematical Theory of Political Economy"] ([http://www.eco.utexas.edu/~hmcleave/jevonsmath.pdf PDF]{{Dead link|date=October 2022 |bot=InternetArchiveBot |fix-attempted=yes }}), 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>W. 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. 1008–091008–9.</ref>

[[Carl Menger]] presented the theory in [https://web.archive.org/web/20080528063159/http://docs.mises.de/Menger/Menger_Grundsaetze.pdf ''Grundsätze der Volkswirtschaftslehre''] (translated as [https://www.mises.org/etexts/menger/principles.asp ''Principles of Economics'']) in 1871. Menger's presentation is peculiarly notable on two points. First, he took special pains to explain ''why'' individuals should be expected to rank possible uses and then to use marginal utility to decide amongst trade-offs. (For this reason, Menger and his followers are sometimes called "the Psychological School", though they are more frequently known as "the [[Austrian School]]" or as "the Vienna School".) Second, while his illustrative examples present utility as quantified, his essential assumptions do not.<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.

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.

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 Undund 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) PtPart IV, ChChapter 6, §4.</ref>

[[Karl Marx]] acknowledged that "nothing can have value, without being an object of utility",<ref>Marx, Karl Heinrich; ''Capital'', V1Volume Ch1, Chapter 1, §1.</ref><ref>Marx, Karl Heinrich; [http://www.marxists.org/archive/marx/works/1857/grundrisse/f239-289.htm ''Grundrisse''] (completedCompleted 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}}

Many scholars 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 |title=An Outline of the History of Economic Theory |author-last2=Zamagni |author-first2=Stefano |publisher=[[Oxford University Press]] |year=2005 |pages=170–173 |author-link1=Ernesto Screpanti |author-link2=Stefano Zamagni}}</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 writterwritten 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 suggested 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>Hayek, Friedrich August von, with [[William Warren Bartley|William Warren Bartley III]]; ''The Fatal Conceit: The Errors of Socialism'' (1988) p. 150.</ref>

Despite the fact the Marxist economics wasn'twas 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 most wellbest knowknown 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'': aA criticismCriticism" (1884),<ref>Wicksteed, Philip Henry; "Das Kapital: A Criticism", ''To-dayDay'' 2 (1884) pp. 388–409.</ref> followed by "The Jevonian criticismCriticism of Marx: aA rejoinderRejoinder" in 1885).<ref>Wicksteed, Philip Henry; "The Jevonian criticismCriticism of Marx: aA rejoinderRejoinder", ''To-dayDay'' 3 (1885) pp. 177–79177–9.</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 marginalisemarginalism came from neo-Ricardian economist [[Piero Sraffa]].

It is noteworthy to mention that certain followers of [[Henry George|Henry George]]'s]] ideas view marginalism and neoclassical economics as a response to ''[[Progress and Poverty]]'', which was published in 1879.<ref>[[Mason Gaffney|Gaffney, Mason]], and Fred Harrison: ''The Corruption of Economics'' (1994).</ref>

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|the 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. 2"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.

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

The [[expected utility hypothesis]] of Bernoulli and others was revived by various 20th century thinkers, with early contributions by [[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 otherOther 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.