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| In [[economics]], the '''marginal utility''' of a [[Good (economics)|good]] or [[Service (economics)|service]] is the gain from an increase or loss from a decrease in the [[Consumption (economics)|consumption]] of that good or service. Economists sometimes speak of a '''law of diminishing marginal utility''', meaning that the first [[units of measurement|unit]] of consumption of a good or service yields more utility than the second and subsequent units, with a continuing reduction for greater amounts{{huh|date=November 2013}}. The '''marginal decision rule''' states that a good or service should be consumed at a quantity at which the marginal utility is equal to the [[marginal cost]].<ref>Rittenberg and Trigarthen. Principles of Microeconomics: Chapter 6. pp. 3 [http://www.saylor.org/site/wp-content/uploads/2012/06/ECON101-3.1.pdf] Accessed June 20, 2012</ref>
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| The concept of marginal utility played a crucial role in the [[Marginalism#The Marginal Revolution|marginal revolution]] of the late 19th century, and led to the replacement of the [[labor theory of value]] by [[neoclassical economics|neoclassical]] [[value theory]] in which the [[relative prices]] of goods and services are simultaneously determined by [[marginal rate of substitution|marginal rates of substitution]] in consumption and [[marginal rate of transformation|marginal rates of transformation]] in [[Production (economics)|production]], which are equal in [[economic equilibrium]].{{citation needed|date=February 2012}}
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| == Marginality ==
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| The term ''marginal'' refers to a small change, starting from some baseline level. As [[Philip Wicksteed]] explained the term,
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| :"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]]; [http://www.econlib.org/library/Wicksteed/wkCS.html ''The Common Sense of Political Economy'' (1910),] [http://www.econlib.org/cgi-bin/searchbooks.pl?searchtype=BookSearchPara&id=wkCS&query=margin Bk I Ch 2 and elsewhere].</ref>
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| Frequently the marginal change is assumed to start from the [[Capital (economics)#Endowment|endowment]], meaning the total resources available for consumption (see [[Budget constraint]]). This endowment is determined by many things including physical laws (which constrain how forms of energy and matter may be transformed), accidents of nature (which determine the presence of natural resources), and the outcomes of past decisions made by the individual himself or herself and by others.
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| For reasons of tractability, it is often assumed in [[Neoclassical economics|neoclassical analysis]] that goods and services are [[Continuum (theory)|continuously divisible]]. Under this assumption, [[marginal concepts]], including marginal utility, may be expressed in terms of [[differential calculus]]. Marginal utility can then be defined as the first derivative of the total satisfaction obtained from consumption of a good or service, with respect to the amount of consumption of that good or service.
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| 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.
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| == Utility ==
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| {{Main|Utility}}
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| 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.<ref>[[George Stigler|Stigler, George Joseph]]; ''The Development of Utility Theory'', I and II, ''Journal of Political Economy'' (1950), issues 3 and 4.</ref><ref>[[George Stigler|Stigler, George Joseph]]; ''The Adoption of Marginal Utility Theory'', ''History of Political Economy'' (1972).</ref> 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.
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| 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>
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| Another conception is [[Utilitarianism|Benthamite philosophy]], which equated usefulness with the production of pleasure and avoidance of pain,<ref>[[Jeremy Bentham|Bentham, Jeremy]]; ''Introduction to the Principles of Morals and Legislation'', Chapter I §I-III.</ref> assumed subject to arithmetic operation.<ref>Bentham, Jeremy; ''Introduction to the Principles of Morals and Legislation'', Chapter IV.</ref> British economists, under the influence of this philosophy (especially by way of [[John Stuart Mill]]), viewed utility 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" (emphasis added).<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>
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| Though generally pursued outside of the mainstream methods, there are conceptions of utility that do not rely on quantification.
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| For example, the [[Austrian school]] generally attributes value to ''the satisfaction of needs'',<ref>Menger, Carl; ''Grundsätze der Volkswirtschaftslehre'' (''Principles of Economics'') Chapter 2 §2.</ref><ref name="mc_culloch" /><ref name="georgescu-rogen">[[Nicholas Georgescu-Roegen|Georgescu-Roegen, Nicholas]]; ''Utility'', ''International Encyclopedia of the Social Sciences'' (1968).</ref> and sometimes rejects even the ''possibility'' of quantification.<ref name="mises" >[[Ludwig von Mises|von Mises, Ludwig Heinrich]]; ''Theorie des Geldes und der Umlaufsmittel'' (1912).</ref>
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| It has been argued that the Austrian framework makes it possible to consider rational preferences that would otherwise be excluded.<ref name="mc_culloch">Mc Culloch, James Huston; [http://www.mises.org/etexts/mcCulloch.pdf “The Austrian Theory of the Marginal Use and of Ordinal Marginal Utility”,] ''Zeitschrift für Nationalökonomie'' 37 (1977) #3&4 (September).</ref>
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| 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 86-7.</ref>
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| == Diminishing marginal utility ==<!-- This section is linked from [[Law of diminishing marginal utility]],[[Diminishing-utility theory]], [[Diminishing utility]] -->
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| {{POV-section|date=July 2012}}
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| {{unreferenced section|date=July 2012}}
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| The notion that marginal utilities diminish across the ranges relevant to decision-making is called the "law of diminishing marginal utility" (and is also known as [[Hermann Heinrich Gossen|Gossen]]'s [[Gossen's laws|First Law]]). This refers to the utility which one obtains from an increase in the stock of an item that one already had. "The law of diminishing marginal utility is at the heart of the explanation of numerous economic phenomena, including [[time preference]] and the [[Value (economics)|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."<ref name=Mises/>
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| The law of diminishing marginal utility is similar to the law of [[diminishing returns]] which states that as the amount of one [[Factors of production|factor of production]] increases as all other factors of production are held the same, the marginal return (extra output gained by adding an extra unit) decreases.
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| As the rate of commodity acquisition increases, ''marginal'' utility decreases. If commodity consumption continues to rise, marginal utility at some point may fall to '''zero''', reaching '''maximum''' total utility. Further increase in consumption of units of commodities causes marginal utility to become '''negative'''; this signifies '''dissatisfaction'''. For example,
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| * beyond some point, further doses of antibiotics would kill no pathogens at all, and might even become harmful to the body.
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| * to satiate thirst a person drinks water but beyond a point consumption of more water might make the person vomit,hence leading to diminishing marginal utility
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| * it takes a certain amount of food energy to sustain a population, yet beyond a point, more calories cannot be consumed and are simply discarded (or cause disease).
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| Diminishing marginal utility is traditionally a microeconomic concept and often holds for an individual. For an individual, the marginal utility of a good or service might actually be ''increasing''. For example:
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| * bed sheets, which up to some number may only provide warmth, but after that point may be useful to allow one to effect an escape by being tied together into a rope;
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| * tickets, for travel or theatre, where a second ticket might allow one to take a date on an otherwise uninteresting outing;
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| * dosages of antibiotics, where having too few pills would leave bacteria with greater resistance, but a full supply could effect a cure.
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| * the third leg is more useful than the first two when building a chair.
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| As suggested elsewhere in this article, occasionally one may come across a situation in which marginal utility increases even at a macroeconomic level. For example the provision of a service may only be viable if it accessible to most or all of the population, and the marginal utility of a raw material required to provide such a service will increase at the "tipping point" at which this occurs. This is similar to the position with very large items such as aircraft carriers: the numbers of these items involved are so small that marginal utility is no longer a helpful concept, as there is merely a simple "yes" or "no" decision.
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| === Independence from presumptions of self-interested behavior ===
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| While the above example of water rations conforms to ordinary notions of [[Selfishness|self-interested behavior]], the concept and logic of marginal utility are independent of the presumption that people pursue self-interest.<ref>Wicksteed, Philip Henry; [http://books.google.com/books?id=drnRjsaxhfIC&pg=RA2-PR12-IA1&lpg=RA2-PR12-IA1&dq=economic+journal+march+1914+%22the+scope+and+method+of+political+economy%22&source=web&ots=UdPEWWpuOF&sig=jQfc2ItGLf_S7ndPYJB-gYmqjJo#PPP6,M1 ''The Scope and Method of Political Economy in the Light of the "Marginal" Theory of Value and Distribution'',] ''Economic Journal'' v24 (1914) #94.</ref> For example, one can conceive of an individual who gave highest priority to the rose bush, next highest to the dog, and last to himself. In that case, if the individual has three rations of water, then the marginal utility of any one of those rations is that of watering the person. With just two rations, the person is left unwatered and the marginal utility of either ration is that of watering the dog. Likewise, a person could give highest priority to the needs of one of her neighbors, next to another, and so forth, placing her own welfare last; the concept of diminishing marginal utility would still apply.
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| == Marginalist theory ==
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| [[Marginalism]] explains choice with the hypothesis that people decide whether to effect any given change based on the marginal utility of that change, with rival alternatives being chosen based upon which has the greatest marginal utility.
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| === Market price and diminishing marginal utility ===
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| 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.<ref name="mc_culloch" />) If any trader can better his position by offering a trade more favorable to complementary traders, then he will do so.
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| In an economy with [[money]], the marginal utility of a quantity is simply that of the best good or service that it could purchase. In this way it is useful for explaining [[supply and demand]], as well as essential aspects of models of [[imperfect competition]].
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| [[Image:AdamSmith.jpg|thumb|right|105px|Adam Smith]]
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| ==== The paradox of water and diamonds ====
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| {{Main|Paradox of value}}
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| The "paradox of water and diamonds", 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 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> is the apparent contradiction that water possesses a value far lower than diamonds, even though water is far more vital to a human being.
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| Price is determined by both marginal utility and marginal cost, and here the key to the "paradox" is that the marginal cost of water is far lower than that of diamonds.
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| That is not to say that the price of any good or service is simply a function of the marginal utility that it has for any one individual nor for some ostensibly typical individual. Rather, individuals are willing to trade based upon the respective marginal utilities of the goods that they have or desire (with these marginal utilities being distinct for each potential trader), and prices thus develop constrained by these marginal utilities.
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| == Quantified marginal utility ==
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| 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
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| :<math>\Delta U=U(S_2)-U(S_1)\,</math>
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| 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:
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| [[Image:UtilityQuantified.svg|thumb|right|400px|Diminishing marginal utility, given quantification]]
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| :<math>\left.\frac{\Delta U}{\Delta g}\right|_{c.p.}</math>
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| (where “[[ceteris paribus|c.p.]]” indicates that the ''only'' [[Dependent and independent variables|independent variable]] to change is <math>g\,</math>).
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| Mainstream neoclassical economics will typically assume that the limit
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| :<math>\lim_{\Delta g\to 0} \left.\frac{\Delta U}{\Delta g}\right|_{c.p.}</math>
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| exists, and use “marginal utility” to refer to the [[partial derivative]]
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| :<math>\frac{\partial U}{\partial g}=\lim_{\Delta g\to 0}\left.\frac{\Delta U}{\Delta g}\right|_{c.p.}</math>.
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| Accordingly, diminishing marginal utility corresponds to the condition
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| :<math>\frac{\partial^2 U}{\partial g^2}<0</math>.
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| == History ==
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| 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 School|Austrian]] economist [[Friedrich von Wieser]] by [[Alfred Marshall]],<ref>Marshall, Alfred; ''Principles of Economics'', [http://www.econlib.org/library/Marshall/marP11.html#n58 Bk 3 Ch 3 Note].</ref> was a translation of Wieser's term “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), Bk I Ch V “Marginal Utility” ([http://praxeology.net/FW-NV-I-5.htm HTML]).</ref>
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| === Proto-marginalist approaches ===
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| Perhaps the essence of a notion of diminishing marginal utility can be found in [[Aristotle]]'s [[Politics (Aristotle)|''Politics'']], wherein he writes {{Quotation|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'', Bk 7 Chapter 1.</ref>}} (There has been marked disagreement about the development and role of marginal considerations in Aristotle's value theory.<ref>Soudek, Josef; “Aristotle's Theory of Exchange: An Inquiry into the Origin of Economic Analysis”, ''Proceedings of the American Philosophical Society'' v 96 (1952) p 45-75.</ref><ref name="kauder">Kauder, Emil; “Genesis of the Marginal Utility Theory from Aristotle to the End of the Eighteenth Century”, ''Economic Journal'' v 63 (1953) p 638-50.</ref><ref>Gordon, Barry Lewis John; “Aristotle and the Development of Value Theory”, ''Quarterly Journal of Economics'' v 78 (1964).</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>)
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| 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.<ref>[[Karl Přibram|Přibram, Karl]]; ''A History of Economic Reasoning'' (1983).</ref>
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| 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.
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| [[Image:Richard Whately.jpg|thumb|right|105px|Richard Whately]]
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| [[Anne Robert Jacques Turgot]], in ''Réflexions sur la formation et la distribution de richesse'' (1769), held that value derived from the general utility of the class to which a good belonged, from comparison of present and future wants, and from anticipated difficulties in procurement.
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| 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 ''De commerce et le gouvernement'' (1776), Condillac emphasized that value is not based upon cost but that costs were paid because of value.
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| This last point was famously restated by the Nineteenth Century proto-marginalist, [[Richard Whately]], who in ''Introductory Lectures on Political Economy'' (1832) wrote {{Quotation|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.) | |
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| === Marginalists before the Revolution ===
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| [[Image:Gabriel Cramer.jpg|thumb|105px|Gabriel Cramer]]
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| The first unambiguous published statement of any sort of theory of marginal utility was by [[Daniel Bernoulli]], in “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> This paper appeared in 1738, but a draft had been written in 1731 or in 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]).</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]).</ref> In 1728, [[Gabriel Cramer]] had produced fundamentally the same theory in a private letter.<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]).</ref> Each had sought to resolve the [[St. Petersburg paradox]], and had concluded that the marginal desirability of money decreased as it was accumulated, more specifically such that the desirability of a sum were the [[natural logarithm]] (Bernoulli) or [[square root]] (Cramer) thereof. However, the more general implications of this hypothesis were not explicated, and the work fell into obscurity.
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| 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>[[Edwin Robert Anderson Seligman|Seligman, Edwin Robert Anderson]]; “On some neglected British economists”, ''Economic Journal'' v. 13 (September 1903).</ref>
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| 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>White, Michael V; “Diamonds Are Forever(?): Nassau Senior and Utility Theory” in ''The Manchester School of Economic & Social Studies'' 60 (1992) #1 (March).</ref>
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| In “De la mesure de l’utilité des travaux publics” (1844), [[Jules Dupuit]] applied a conception of marginal utility to the problem of determining bridge tolls.<ref>Dupuit, Jules; “De la mesure de l’utilité des travaux publics”, ''Annales des ponts et chaussées'', Second series, 8 (1844).</ref>
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| In 1854, [[Hermann Heinrich Gossen]] published ''Die Entwicklung der Gesetze des menschlichen Verkehrs und der daraus fließenden Regeln für menschliches Handeln'', which presented a marginal utility theory and to a very large extent worked-out its implications for the behavior of a market economy. However, Gossen's work was not well received in the Germany of his time, most copies were destroyed unsold, and he was virtually forgotten until rediscovered after the so-called Marginal Revolution.
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| === The Marginal Revolution ===
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| :''“Marginal revolution” redirects here. For the economics weblog, see [[Marginal Revolution (blog)]].''
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| Marginalism eventually found a foot-hold 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.
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| [[Image:Jevons.jpeg|thumb|105px|William Stanley Jevons]]
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| [[William Stanley Jevons]] first proposed the theory in [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]), 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.), [http://books.google.com/books?id=aYcBAAAAQAAJ&dq=jevons+%22the+theory+of+political+economy%22&printsec=frontcover&source=web&ots=IyxPG-thjm&sig=ta6Vv6bIPxNZVaqyxFoGfv39Od8#PPA203,M1 ''The Theory of Political Economy''], pp. 208.</ref><ref>R.D. Collison Brown (1987), "Jevons, William Stanley," [[The New Palgrave: A Dictionary of Economics]], v. 2, pp. 1008-09.</ref>
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| [[Carl Menger]] presented the theory in [http://docs.mises.de/Menger/Menger_Grundsaetze.pdf ''Grundsätze der Volkswirtschaftslehre''] (translated as [http://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" /> (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), p76.</ref>) Menger also developed the [[law of diminishing marginal utility]].<ref name=Mises>Polleit, Thorsten (2011-02-11) [http://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.
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| [[Léon Walras|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 [[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>
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| 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.
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| ==== The second generation ====
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| [[Image:Vilfredo Pareto.jpg|thumb|105px|Vilfredo Pareto]]
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| 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]].
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| 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.<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>
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| 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 [http://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>)
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| 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) Pt IV Ch 6 §4.</ref>)
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| ==== The Marginal Revolution and Marxism ====
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| [[Karl Marx]] acknowledged that "nothing can have value, without being an object of utility",<ref>Marx, Karl Heinrich; ''Capital'' V1 Ch 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), p276</ref> with labor being the principal measure of value under capitalism.
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| The doctrines of marginalism and the Marginal Revolution are often interpreted as somehow a response to [[Marxism|Marxist economics]]. However the first volume of ''[[Das Kapital]]'' was not published until July 1867, after the works of Jevons, Menger, and Walras were written or well under way; and Marx was still a relatively obscure figure when these works were completed. It is unlikely that any of them knew anything of him. (On the other hand, [[Friedrich Hayek|Hayek]] or [[William Warren Bartley|Bartley]] has suggested that Marx, voraciously reading at the [[British Museum]], may have come across the works of one or more of these figures, and that his inability to formulate a viable critique may account for his failure to complete any further volumes of ''Kapital'' before his death.<ref>Hayek, Friedrich August von, with [[William Warren Bartley|William Warren Bartley III]]; ''The Fatal Conceit: The Errors of Socialism'' (1988) p150.</ref>)
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| 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),<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 was Wicksteed's "The Marxian Theory of Value. ''Das Kapital'': a criticism" (1884,<ref>Wicksteed, Philip Henry; "Das Kapital: A Criticism", ''To-day'' 2 (1884) p. 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) p. 177-9.</ref>). Initially there were only a few Marxist responses to marginalism, of which the most famous were [[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 ekonomni rante'' (1914) by [[Nikolai Bukharin|Никола́й Ива́нович Буха́рин (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 considerable literature developed on the conflict between marginalism and the labour theory of value, with the work of the neo-Ricardian economist [[Piero Sraffa]] providing an important critique of marginalism.
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| It might also be noted that some followers of [[Henry George]] similarly consider marginalism and neoclassical economics a reaction to ''[[Progress and Poverty]]'', which was published in 1879.<ref>[[Mason Gaffney|Gaffney, Mason]], and Fred Harrison: ''The Corruption of Economics'' (1994).</ref>
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| In the 1980s [[John Roemer]] and other [[Analytical_Marxism#Exploitation|analytical Marxists]] have worked to rebuild Marxian theses on a marginalist foundation.
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| === Reformulation ===
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| In his 1881 work [http://socserv.mcmaster.ca/econ/ugcm/3ll3/edgeworth/mathpsychics.pdf ''Mathematical Psychics''], [[Francis Ysidro Edgeworth]] presented the [[indifference curve]], deriving its properties from marginalist theory which assumed utility to be a differentiable function of quantified goods and services. Later work attempted to generalize to the indifference curve formulations of utility and marginal utility in avoiding unobservable measures of utility.
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| 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 [[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 much the same results and found a significant audience. (Allen subsequently drew attention to Slutsky's earlier accomplishment.)
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| 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" /> 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, p23 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.
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| 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>
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| === Revival ===
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| [[Image:JohnvonNeumann-LosAlamos.gif|thumb|105px|[[John von Neumann]]]]
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| When Cramer and Bernoulli introduced the notion of diminishing marginal utility, it had been to address [[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.
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| 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]), 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).</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.
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| 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 simplify the analysis of risky decisions because, under quantified utility, diminishing marginal utility implies [[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>
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| 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" />
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| == See also ==
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| * [[Diminishing returns]]
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| * [[Economic subjectivism]]
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| * [[Marginalism]]
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| * [[Microeconomics]]
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| * [[Rivalry (economics)]]
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| * [[Theory of value (economics)]]
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| * [[Utility]]
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| == Footnotes ==
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| {{Reflist|colwidth=30em}}
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| ==Further reading==
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| * E.H. Downey, "The Futility of Marginal Utility," ''Journal of Political Economy,'' vol. 18, no. 4 (April 1910), pp. 253-268. [http://www.jstor.org/stable/1820794 In JSTOR]
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| {{DEFAULTSORT:Marginal Utility}}
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| [[Category:Marginal concepts]]
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| [[Category:Consumer theory]]
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| [[Category:Utility]]
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| [[Category:Welfare economics]]
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| [[Category:History of economic thought]]
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| [[de:Nutzenfunktion#Grenznutzen]]
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