Marginal Utility Theory
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In
economics Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and intera ...
,
utility As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosopher ...
is the satisfaction or benefit derived by consuming a product. The marginal utility of a
good In most contexts, the concept of good denotes the conduct that should be preferred when posed with a choice between possible actions. Good is generally considered to be the opposite of evil and is of interest in the study of ethics, morality, ph ...
or service describes how much pleasure or satisfaction is gained by consumers as a result of the increase or decrease in
consumption Consumption may refer to: *Resource consumption *Tuberculosis, an infectious disease, historically * Consumption (ecology), receipt of energy by consuming other organisms * Consumption (economics), the purchasing of newly produced goods for curren ...
by one unit. There are three types of marginal utility. They are positive, negative, or zero marginal utility. For instance, you like eating pizza, the second piece of pizza brings you more satisfaction than only eating one piece of pizza. It means your marginal utility from purchasing pizza is positive. However, after eating the second piece you feel full, and you would not feel any better from eating the third piece. This means your marginal utility from eating pizza is zero. Moreover, you might feel sick if you eat more than three pieces of pizza. At this time, your marginal utility is negative. In other words, a negative marginal utility indicates that every unit of goods or service consumed will do more harm than good, which will lead to the decrease of overall utility level, while the positive marginal utility indicates that every unit of goods or services consumed will increase the overall utility level. In the context of
cardinal utility In economics, a cardinal utility function or scale is a utility index that preserves preference orderings uniquely up to positive affine transformations. Two utility indices are related by an affine transformation if for the value u(x_i) of one ind ...
, economists postulate a law of diminishing marginal utility, which describes how the first
unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatrical presentation Music * ''Unit'' (alb ...
of consumption of a particular good or service yields more utility than the second and subsequent units, with a continuing reduction for greater amounts. Therefore, the fall in marginal utility as consumption increases is known as diminishing marginal utility. Economists use this concept to determine how much of a good or service that a consumer is willing to purchase.


Marginality

In the study of Economics, the term
marginal Marginal may refer to: * ''Marginal'' (album), the third album of the Belgian rock band Dead Man Ray, released in 2001 * ''Marginal'' (manga) * '' El Marginal'', Argentine TV series * Marginal seat or marginal constituency or marginal, in polit ...
refers to a small change, starting from some baseline level.
Philip Wicksteed Philip Henry Wicksteed (25 October 1844 – 18 March 1927) is known primarily as an economist. He was also a Georgist, Unitarian theologian, classicist, medievalist, and literary critic. Family background He was the son of Charles Wicksteed ...
explained the term as follows:
Marginal considerations are considerations which concern a slight increase or diminution of the stock of anything which we possess or are considering. 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 Marginalism is a theory of economics that attempts to explain the discrepancy in the value of goods and services by reference to their secondary, or marginal, utility. It states that the reason why the price of diamonds is higher than that of wa ...
. 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 Maximization is a style of decision-making characterized by seeking the best option through an exhaustive search through alternatives. It is contrasted with satisficing, in which individuals evaluate options until they find one that is "good enough" ...
their potential profits and often used when making decisions about expanding or reducing production.


Utility

As a topic of economics,
utility As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosopher ...
is used to measure worth or value. 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. Initially, the term utility is equated usefulness with the production of pleasure and avoidance of pain by moral philosophers such as Jeremy Bentham and John Stuart Mill. Moreover, under the influence of this philosophy, viewed utility as "the feelings of pleasure and pain" and further as a "''quantity'' of feeling". 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. In any standard framework, the same object may have different marginal utilities for different people, reflecting different preferences or individual circumstances.


Law of diminishing marginal utility

The British economist
Alfred Marshall Alfred Marshall (26 July 1842 – 13 July 1924) was an English economist, and was one of the most influential economists of his time. His book '' Principles of Economics'' (1890) was the dominant economic textbook in England for many years. I ...
believed that the more of something you have, the less of it you want. This phenomenon is referred to as diminishing marginal utility by economists. Diminishing marginal utility refers to the phenomenon that each additional unit of gain leads to an ever-smaller increase in subjective value. For example, three bites of candy are better than two bites, but the twentieth bite does not add much to the experience beyond the nineteenth (and could even make it worse). This effect is so well established that it is referred to as the "law of diminishing marginal utility" in economics (Gossen, 1854/1983), and is reflected in the concave shape of most subjective utility functions. This refers to the increase in utility an individual gains from increasing their consumption of a particular good. "The law of diminishing marginal utility is at the heart of the explanation of numerous economic phenomena, including
time preference In economics, time preference (or time discounting, delay discounting, temporal discounting, long-term orientation) is the current relative valuation placed on receiving a good or some cash at an earlier date compared with receiving it at a later ...
and the value of goods ... The law says, first, that the marginal utility of each homogeneous unit decreases as the supply of units increases (and vice versa); second, that the marginal utility of a larger-sized unit is greater than the marginal utility of a smaller-sized unit (and vice versa). The first law denotes the law of diminishing marginal utility; the second law denotes the law of increasing total utility." In modern economics, choice under conditions of certainty at a single point in time is modelled via
ordinal utility In economics, an ordinal utility function is a function representing the preferences of an agent on an ordinal scale. Ordinal utility theory claims that it is only meaningful to ask which option is better than the other, but it is meaningless to ask ...
, in which the numbers assigned to the utility of a particular circumstance of the individual have no meaning by themselves, but which of two alternative circumstances has higher utility ''is'' meaningful. With the ordinal utility, a person's preferences have no unique marginal utility, and thus whether or not the marginal utility is diminishing is not meaningful. In contrast, the concept of diminishing marginal utility is meaningful in the context of
cardinal utility In economics, a cardinal utility function or scale is a utility index that preserves preference orderings uniquely up to positive affine transformations. Two utility indices are related by an affine transformation if for the value u(x_i) of one ind ...
, which in modern economics is used in analyzing
intertemporal choice Intertemporal choice is the process by which people make decisions about what and how much to do at various points in time, when choices at one time influence the possibilities available at other points in time. These choices are influenced by the ...
,
choice under uncertainty Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical ...
, and
social welfare Welfare, or commonly social welfare, is a type of government support intended to ensure that members of a society can meet Basic needs, basic human needs such as food and shelter. Social security may either be synonymous with welfare, or refe ...
. The law of diminishing marginal utility is that subjective value changes most dynamically near the zero points and quickly levels off as gains (or losses) accumulate. And it is reflected in the concave shape of most subjective utility functions. Given a concave relationship between objective gains (x-axis) and subjective value (y-axis), each one-unit gain produces a smaller increase in subjective value than the previous gain of an equal unit. The marginal utility, or the change in subjective value above the existing level, diminishes as gains increase. As the rate of commodity acquisition increases, the ''marginal'' utility decreases. If commodity consumption continues to rise, marginal utility at some point may fall to zero, reaching maximum total utility. Further increase in the consumption of commodities causes the marginal utility to become negative; this signifies dissatisfaction. For example, beyond some point, further doses of antibiotics would kill no pathogens at all and might even become harmful to the body. Diminishing marginal utility is traditionally a microeconomic concept and often holds for an individual, although the marginal utility of a good or service might be ''increasing'' as well. For example, dosages of antibiotics, where having too few pills would leave bacteria with greater resistance, but a full supply could effect a cure. As suggested elsewhere in this article, occasionally, one may come across a situation where marginal utility increases even at a macroeconomic level. For example, providing a service may only be viable if it is accessible to most or all of the population. The marginal utility of a raw material required to provide such a service will increase at the "tipping point" at which this occurs. This is similar to the position with huge items such as aircraft carriers: the numbers of these items involved are so small that marginal utility is no longer a helpful concept, as there is merely a simple "yes" or "no" decision.


Marginalist theory

Marginalism Marginalism is a theory of economics that attempts to explain the discrepancy in the value of goods and services by reference to their secondary, or marginal, utility. It states that the reason why the price of diamonds is higher than that of wa ...
explains choice with the hypothesis that people decide whether to effect any given change based on the marginal utility of that change, with rival alternatives being chosen based upon which has the greatest marginal utility.


Market price and diminishing marginal utility

If an individual possesses a good or service whose marginal utility to him is less than that of some other good or service for which he could trade it, then it is in his interest to effect that trade. Of course, as one thing is sold and another is bought, the respective marginal gains or losses from further trades will change. If the marginal utility of one thing is diminishing, and the other is not increasing, all else being equal, an individual will demand an increasing ratio of that which is acquired to that which is sacrificed. One important way in which all else might not be equal is when the use of the one good or service complements that of the other. In such cases, exchange ratios might be constant.Mc Culloch, James Huston
"The Austrian Theory of the Marginal Use and of Ordinal Marginal Utility"
''Zeitschrift für Nationalökonomie'' 37 (1977) #3&4 (September).
If any trader can better his position by offering a trade more favorable to complementary traders, then he will do so. In an economy with
money Money is any item or verifiable record that is generally accepted as payment for goods and services and repayment of debts, such as taxes, in a particular country or socio-economic context. The primary functions which distinguish money are as ...
, the marginal utility of a quantity is simply that of the best good or service that it could purchase. In this way it is useful for explaining
supply and demand In microeconomics, supply and demand is an economic model of price determination in a Market (economics), market. It postulates that, Ceteris paribus, holding all else equal, in a perfect competition, competitive market, the unit price for a ...
, as well as essential aspects of models of
imperfect competition In economics, imperfect competition refers to a situation where the characteristics of an economic market do not fulfil all the necessary conditions of a perfectly competitive market. Imperfect competition will cause market inefficiency when it hap ...
.


Paradox of water and diamonds

The "paradox of water and diamonds" is most commonly associated with
Adam Smith Adam Smith (baptized 1723 – 17 July 1790) was a Scottish economist and philosopher who was a pioneer in the thinking of political economy and key figure during the Scottish Enlightenment. Seen by some as "The Father of Economics"——— ...
, though it was recognized by earlier thinkers. The apparent contradiction lies in the fact that water possesses a lower economic value than diamonds, even though water is far more vital to human existence. Smith suggested that there was an irrational divide between the 'use value' of something and the 'exchange value'. The things which have the greatest value in use frequently have little or no value in exchange; and likewise, things which have the greatest value in exchange have frequently little or no value in use. Nothing is more useful than water: but it will purchase scarcely anything. A diamond has hardly any practical value in use, but a great quantity of other goods may be had in exchange for it. Price is determined by both marginal utility and marginal cost, and here is the key to the 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.


Marginalism limitations

Marginalism Marginalism is a theory of economics that attempts to explain the discrepancy in the value of goods and services by reference to their secondary, or marginal, utility. It states that the reason why the price of diamonds is higher than that of wa ...
has many limitations like many economic theories.
Economists An economist is a professional and practitioner in the social science discipline of economics. The individual may also study, develop, and apply theories and concepts from economics and write about economic policy. Within this field there are ...
often question the if people act as they are portrayed within the theory. Understanding what is giving someone a specific amount of utility is extremely complex and varies from person to person and may not be stable. Another limitation is in regard to the way marginal change is measured. Measuring money is one of the simplest ways to analyse marginalism due to not having any other substitute. Although the limitation can be seen when attempting to measure the utility derived from other consumables such as food as there are too many substitutes and once again preferences can limit the accuracy.


Quantified marginal utility

Under the
special case In logic, especially as applied in mathematics, concept is a special case or specialization of concept precisely if every instance of is also an instance of but not vice versa, or equivalently, if is a generalization of . A limiting case is ...
in which usefulness can be quantified, the change in utility of moving from state S_1 to state S_2 is :\Delta U=U(S_2)-U(S_1)\, Moreover, if S_1 and S_2 are distinguishable by values of just one variable g\, which is itself quantified, then it becomes possible to speak of the ratio of the marginal utility of the change in g\, to the size of that change: :\left.\frac\_ (where " c.p." indicates that the ''only''
independent variable Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand ...
to change is g\,). Mainstream neoclassical economics will typically assume that the limit :\lim_ \left.\frac\_ exists, and use "marginal utility" to refer to the
partial derivative In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Part ...
:\frac=\lim_\left.\frac\_. Accordingly, diminishing marginal utility corresponds to the condition :\frac<0.


History

The concept of marginal utility grew out of attempts by economists to explain the determination of price. The term "marginal utility", credited to the
Austrian Austrian may refer to: * Austrians, someone from Austria or of Austrian descent ** Someone who is considered an Austrian citizen, see Austrian nationality law * Austrian German dialect * Something associated with the country Austria, for example: ...
economist
Friedrich von Wieser Friedrich Freiherr von Wieser (; 10 July 1851 – 22 July 1926) was an early (so-called "first generation") economist of the Austrian School of economics. Born in Vienna, the son of Privy Councillor Leopold von Wieser, a high official in the war m ...
by
Alfred Marshall Alfred Marshall (26 July 1842 – 13 July 1924) was an English economist, and was one of the most influential economists of his time. His book '' Principles of Economics'' (1890) was the dominant economic textbook in England for many years. I ...
, was a translation of Wieser's term ("border-use").von Wieser, Friedrich; ''Über den Ursprung und die Hauptgesetze des wirtschaftlichen Wertes'' /nowiki>''The Nature and Essence of Theoretical Economics''/nowiki> (1884), p. 128.Wieser, Friedrich von; ''Der natürliche Werth'' /nowiki>''Natural Value''/nowiki> (1889), Bk I Ch V "Marginal Utility"
HTML
.


Proto-marginalist approaches

Perhaps the essence of a notion of diminishing marginal utility can be found in
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of phil ...
's ''Politics'', wherein he writes There has been marked disagreement about the development and role of marginal considerations in Aristotle's value theory.Schumpeter, Joseph Alois; ''History of Economic Analysis'' (1954) Part II Chapter 1 §3. A great variety of economists have concluded that there is ''some'' sort of interrelationship between utility and rarity that affects economic decisions, and in turn informs the determination of prices. Diamonds are priced higher than water because their marginal utility is higher than water . Eighteenth-century Italian
mercantilists Mercantilism is an economic policy that is designed to maximize the exports and minimize the imports for an economy. It promotes imperialism, colonialism, tariffs and subsidies on traded goods to achieve that goal. The policy aims to reduce ...
, such as
Antonio Genovesi Antonio Genovesi (1 November 171322 September 1769) was an Italian writer on philosophy and political economy. Biography Son of Salvatore Genovese, a shoemaker, and Adriana Alfinito of San Mango, Antonio Genovesi was born in Castiglione, near ...
,
Giammaria Ortes Abbé Giovanni Maria Ortes (March 1713 – 1790) was a Venetian composer, economist, mathematician, Camaldolese monk A monk (, from el, μοναχός, ''monachos'', "single, solitary" via Latin ) is a person who practices religious a ...
,
Pietro Verri Count Pietro Verri (12 December 1728 – 28 June 1797) was an economist, historian, philosopher and writer. Among the most important personalities of the 18th-century Italian culture, he is considered among the fathers of the Lombard reformist E ...
, Marchese Cesare di Beccaria, and Count Giovanni Rinaldo Carli, held that value was explained in terms of the general utility and of scarcity, though they did not typically work-out a theory of how these interacted.Pribram, Karl; ''A History of Economic Reasoning'' (1983), Chapter 5 "Refined Mercantilism", "Italian Mercantilists". In ''Della moneta'' (1751), Abbé
Ferdinando Galiani Ferdinando Galiani (2 December 1728, Chieti, Kingdom of Naples – 30 October 1787, Naples, Kingdom of Naples) was an Italian economist, a leading Italian figure of the Enlightenment. Friedrich Nietzsche referred to him as "a most fastidious and ...
, a pupil of Genovesi, attempted to explain value as a ratio of two ratios, ''utility'' and ''scarcity'', with the latter component ratio being the ratio of quantity to use.
Anne Robert Jacques Turgot Anne Robert Jacques Turgot, Baron de l'Aulne ( ; ; 10 May 172718 March 1781), commonly known as Turgot, was a French economist and statesman. Originally considered a physiocrat, he is today best remembered as an early advocate for economic libe ...
, in ' (1769), held that value derived from the general utility of the class to which a good belonged, from comparison of present and future wants, and from anticipated difficulties in procurement. Like the Italian mercantists, Étienne Bonnot, Abbé de Condillac, saw value as determined by utility associated with the class to which the good belong, and by estimated scarcity. In ' (1776), Condillac emphasized that value is not based upon cost but that costs were paid because of value. This last point was famously restated by the Nineteenth Century proto-marginalist,
Richard Whately Richard Whately (1 February 1787 – 8 October 1863) was an English academic, rhetorician, logician, philosopher, economist, and theologian who also served as a reforming Church of Ireland Archbishop of Dublin. He was a leading Broad Churchman ...
, who in ''Introductory Lectures on Political Economy'' (1832) wrote: (Whatley's student
Senior Senior (shortened as Sr.) means "the elder" in Latin and is often used as a suffix for the elder of two or more people in the same family with the same given name, usually a parent or grandparent. It may also refer to: * Senior (name), a surname ...
is noted below as an early marginalist.)


Marginalists before the Revolution

The first unambiguous published statement of any sort of theory of marginal utility was by
Daniel Bernoulli Daniel Bernoulli FRS (; – 27 March 1782) was a Swiss mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family from Basel. He is particularly remembered for his applications of mathematics to mechan ...
, in "Specimen theoriae novae de mensura sortis". This paper appeared in 1738, but a draft had been written in 1731 or in 1732. In 1728,
Gabriel Cramer Gabriel Cramer (; 31 July 1704 – 4 January 1752) was a Genevan mathematician. He was the son of physician Jean Cramer and Anne Mallet Cramer. Biography Cramer showed promise in mathematics from an early age. At 18 he received his doctorate ...
had produced fundamentally the same theory in a private letter. Each had sought to resolve the
St. Petersburg paradox The St. Petersburg paradox or St. Petersburg lottery is a paradox involving the game of flipping a coin where the expected payoff of the theoretical lottery game approaches infinity but nevertheless seems to be worth only a very small amount to t ...
, and had concluded that the marginal desirability of money decreased as it was accumulated, more specifically such that the desirability of a sum were the
natural logarithm The natural logarithm of a number is its logarithm to the base of the mathematical constant , which is an irrational and transcendental number approximately equal to . The natural logarithm of is generally written as , , or sometimes, if ...
(Bernoulli) or
square root In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or  ⋅ ) is . For example, 4 and −4 are square roots of 16, because . E ...
(Cramer) thereof. However, the more general implications of this hypothesis were not explicated, and the work fell into obscurity. I
"A Lecture on the Notion of Value as Distinguished Not Only from Utility, but also from Value in Exchange"
delivered in 1833 and included in ''Lectures on Population, Value, Poor Laws and Rent'' (1837),
William Forster Lloyd William Forster Lloyd FRS (1794 – 2 June 1852) was a British writer on economics. He is best known today for one of his 1833 lectures on population control which have influenced writers in modern economic theory. Life Born in 1794 at Bradenh ...
explicitly offered a general marginal utility theory, but did not offer its derivation nor elaborate its implications. The importance of his statement seems to have been lost on everyone (including Lloyd) until the early 20th century, by which time others had independently developed and popularized the same insight. In ''An Outline of the Science of Political Economy'' (1836),
Nassau William Senior Nassau William Senior (; 26 September 1790 – 4 June 1864), was an English lawyer known as an economist. He was also a government adviser over several decades on economic and social policy on which he wrote extensively. Early life He was born ...
asserted that marginal utilities were the ultimate determinant of demand, yet apparently did not pursue implications, though some interpret his work as indeed doing just that. In "'" (1844),
Jules Dupuit Arsène Jules Étienne Juvenel Dupuit (18 May 1804 – 5 September 1866) was an Italian-born French civil engineer and economist. He was born in Fossano, Italy then under the rule of Napoleon Bonaparte. At the age of ten he emigrated to Franc ...
applied a conception of marginal utility to the problem of determining bridge tolls. In 1854,
Hermann Heinrich Gossen Hermann Heinrich Gossen (7 September 1810 – 13 February 1858) was a Prussian economist who is often regarded as the first to elaborate a general theory of marginal utility. Life and work Gossen studied in Bonn, then worked in the Prussian admin ...
published , which presented a marginal utility theory and to a very large extent worked-out its implications for the behavior of a market economy. However, Gossen's work was not well received in the Germany of his time, most copies were destroyed unsold, and he was virtually forgotten until rediscovered after the so-called Marginal Revolution.


Marginal Revolution

Marginalism eventually found a foothold by way of the work of three economists, Jevons in England, Menger in Austria, and Walras in Switzerland.
William Stanley Jevons William Stanley Jevons (; 1 September 183513 August 1882) was an English economist and logician. Irving Fisher described Jevons's book ''A General Mathematical Theory of Political Economy'' (1862) as the start of the mathematical method in ec ...
first proposed the theory i
"A General Mathematical Theory of Political Economy"PDF
, a paper presented in 1862 and published in 1863, followed by a series of works culminating in his book ''The Theory of Political Economy'' in 1871 that established his reputation as a leading political economist and logician of the time. Jevons' conception of utility was in the
utilitarian In ethical philosophy, utilitarianism is a family of normative ethical theories that prescribe actions that maximize happiness and well-being for all affected individuals. Although different varieties of utilitarianism admit different charac ...
tradition of
Jeremy Bentham Jeremy Bentham (; 15 February 1748 Old_Style_and_New_Style_dates">O.S._4_February_1747.html" ;"title="Old_Style_and_New_Style_dates.html" ;"title="nowiki/>Old Style and New Style dates">O.S. 4 February 1747">Old_Style_and_New_Style_dates.htm ...
and of
John Stuart Mill John Stuart Mill (20 May 1806 – 7 May 1873) was an English philosopher, political economist, Member of Parliament (MP) and civil servant. One of the most influential thinkers in the history of classical liberalism, he contributed widely to ...
, but he differed from his classical predecessors in emphasizing that "value depends entirely upon utility", in particular, on "
final utility Final Utility is the utility of a good when applied to our least desirable use of it. It is the estimated utility of the last use of a supply, i.e., the least important use of that supply. For example, if a ''use'' of a good must be given up, it wil ...
upon which the theory of Economics will be found to turn." He later qualified this in deriving the result that in a model of exchange equilibrium, price ratios would be proportional not only to ratios of "final degrees of utility," but also to costs of production.
Carl Menger Carl Menger von Wolfensgrün (; ; 28 February 1840 – 26 February 1921) was an Austrian economist and the founder of the Austrian School of economics. Menger contributed to the development of the theories of marginalism and marginal utility ...
presented the theory i
''Grundsätze der Volkswirtschaftslehre''
(translated a
''Principles of Economics''
in 1871. Menger's presentation is peculiarly notable on two points. First, he took special pains to explain ''why'' individuals should be expected to rank possible uses and then to use marginal utility to decide amongst trade-offs. (For this reason, Menger and his followers are sometimes called "the Psychological School", though they are more frequently known as "the
Austrian School The Austrian School is a heterodox school of economic thought that advocates strict adherence to methodological individualism, the concept that social phenomena result exclusively from the motivations and actions of individuals. Austrian school ...
" or as "the Vienna School".) Second, while his illustrative examples present utility as quantified, his essential assumptions do not. Georgescu-Roegen, Nicholas; ''Utility'', ''International Encyclopedia of the Social Sciences'' (1968). (Menger in fact crossed-out the numerical tables in his own copy of the published ''Grundsätze''.) Menger also developed the
law of diminishing marginal utility In economics, utility is the satisfaction or benefit derived by consuming a product. The marginal utility of a good or service describes how much pleasure or satisfaction is gained by consumers as a result of the increase or decrease in consumpti ...
.Polleit, Thorsten (2011-02-11
What Can the Law of Diminishing Marginal Utility Teach Us?
''
Mises Institute Ludwig von Mises Institute for Austrian Economics, or Mises Institute, is a libertarian nonprofit think tank headquartered in Auburn, Alabama, United States. It is named after the Austrian School economist Ludwig von Mises (1881–1973). It wa ...
''
Menger's work found a significant and appreciative audience. Marie-Esprit-Léon Walras introduced the theory in ', the first part of which was published in 1874 in a relatively mathematical exposition. Walras's work found relatively few readers at the time but was recognized and incorporated two decades later in the work of Pareto and Barone. An American,
John Bates Clark John Bates Clark (January 26, 1847 – March 21, 1938) was an American neoclassical economist. He was one of the pioneers of the marginalist revolution and opponent to the Institutionalist school of economics, and spent most of his career as ...
, is sometimes also mentioned. But, while Clark independently arrived at a marginal utility theory, he did little to advance it until it was clear that the followers of Jevons, Menger, and Walras were revolutionizing economics. Nonetheless, his contributions thereafter were profound.


Second generation

Although the Marginal Revolution flowed from the work of Jevons, Menger, and Walras, their work might have failed to enter the mainstream were it not for a second generation of economists. In England, the second generation were exemplified by Philip Henry Wicksteed, by William Smart, and by
Alfred Marshall Alfred Marshall (26 July 1842 – 13 July 1924) was an English economist, and was one of the most influential economists of his time. His book '' Principles of Economics'' (1890) was the dominant economic textbook in England for many years. I ...
; in Austria by
Eugen von Böhm-Bawerk Eugen Ritter von Böhm-Bawerk (; born Eugen Böhm, 12 February 185127 August 1914) was an Austrian economist who made important contributions to the development of the Austrian School of Economics and neoclassical economics. He served intermitten ...
and by
Friedrich von Wieser Friedrich Freiherr von Wieser (; 10 July 1851 – 22 July 1926) was an early (so-called "first generation") economist of the Austrian School of economics. Born in Vienna, the son of Privy Councillor Leopold von Wieser, a high official in the war m ...
; in Switzerland by
Vilfredo Pareto Vilfredo Federico Damaso Pareto ( , , , ; born Wilfried Fritz Pareto; 15 July 1848 – 19 August 1923) was an Italian polymath (civil engineer, sociologist, economist, political scientist, and philosopher). He made several important contribut ...
; and in America by Herbert Joseph Davenport and by
Frank A. Fetter Frank Albert Fetter (; March 8, 1863 – March 21, 1949) was an American economist of the Austrian School. Fetter's treatise, ''The Principles of Economics'', contributed to an increased American interest in the Austrian School, including the th ...
. There were significant, distinguishing features amongst the approaches of Jevons, Menger, and Walras, but the second generation did not maintain distinctions along national or linguistic lines. The work of von Wieser was heavily influenced by that of Walras. Wicksteed was heavily influenced by Menger. Fetter referred to himself and Davenport as part of "the American Psychological School", named in imitation of the Austrian "Psychological School". (And Clark's work from this period onward similarly shows heavy influence by Menger.) William Smart began as a conveyor of Austrian School theory to English-language readers, though he fell increasingly under the influence of Marshall.Salerno, Joseph T. 1999; "The Place of Mises's Human Action in the Development of Modern Economic Thought." ''Quarterly Journal of Economic Thought'' v. 2 (1). Böhm-Bawerk was perhaps the most able expositor of Menger's conception. He was further noted for producing a theory of interest and of profit in equilibrium based upon the interaction of diminishing marginal utility with diminishing
marginal product In economics and in particular neoclassical economics, the marginal product or marginal physical productivity of an input (factor of production) is the change in output resulting from employing one more unit of a particular input (for instance, th ...
ivity of time and with
time preference In economics, time preference (or time discounting, delay discounting, temporal discounting, long-term orientation) is the current relative valuation placed on receiving a good or some cash at an earlier date compared with receiving it at a later ...
. This theory was adopted in full and then further developed by
Knut Wicksell Johan Gustaf Knut Wicksell (December 20, 1851 – May 3, 1926) was a leading Swedish economist of the Stockholm school. His economic contributions would influence both the Keynesian and Austrian schools of economic thought. He was married to th ...
and with modifications including formal disregard for time-preference by Wicksell's American rival
Irving Fisher Irving Fisher (February 27, 1867 – April 29, 1947) was an American economist, statistician, inventor, eugenicist and progressive social campaigner. He was one of the earliest American neoclassical economists, though his later work on debt def ...
. Marshall was the second-generation marginalist whose work on marginal utility came most to inform the mainstream of neoclassical economics, especially by way of his ''Principles of Economics'', the first volume of which was published in 1890. Marshall constructed the demand curve with the aid of assumptions that utility was quantified, and that the marginal utility of money was constant (or nearly so). Like Jevons, Marshall did not see an explanation for supply in the theory of marginal utility, so he synthesized an explanation of demand thus explained with supply explained in a more classical manner, determined by costs which were taken to be objectively determined. Marshall later actively mischaracterized the criticism that these costs were themselves ultimately determined by marginal utilities.Schumpeter, Joseph Alois; ''History of Economic Analysis'' (1954) Pt IV Ch 6 §4.


Marginal Revolution and Marxism

Karl Marx Karl Heinrich Marx (; 5 May 1818 – 14 March 1883) was a German philosopher, economist, historian, sociologist, political theorist, journalist, critic of political economy, and socialist revolutionary. His best-known titles are the 1848 ...
acknowledged that "nothing can have value, without being an object of utility", but in his analysis "use-value as such lies outside the sphere of investigation of political economy", with labor being the principal determinant of value under capitalism. The doctrines of marginalism and the Marginal Revolution are often interpreted as somehow a response to
Marxist economics Marxian economics, or the Marxian school of economics, is a heterodox school of political economic thought. Its foundations can be traced back to Karl Marx's critique of political economy. However, unlike critics of political economy, Marxian e ...
. However the first volume of ''
Das Kapital ''Das Kapital'', also known as ''Capital: A Critique of Political Economy'' or sometimes simply ''Capital'' (german: Das Kapital. Kritik der politischen Ökonomie, link=no, ; 1867–1883), is a foundational theoretical text in Historical mater ...
'' was not published until July 1867, after the works of Jevons, Menger, and Walras were written or well under way (Walras published in 1874 and Carl Menger published ''Principles of Economics'' in 1871); and Marx was still a relatively minor figure when these works were completed. It is unlikely that any of them knew anything of him. (On the other hand,
Friedrich Hayek Friedrich August von Hayek ( , ; 8 May 189923 March 1992), often referred to by his initials F. A. Hayek, was an Austrian–British economist, legal theorist and philosopher who is best known for his defense of classical liberalism. Haye ...
and
W. W. Bartley III William Warren Bartley III (October 2, 1934 – February 5, 1990), known as W. W. Bartley III, was an American philosopher specializing in 20th century philosophy, language and logic, and the Vienna Circle. Early life and education Born in Wilk ...
have suggested that Marx, voraciously reading at the
British Museum The British Museum is a public museum dedicated to human history, art and culture located in the Bloomsbury area of London. Its permanent collection of eight million works is among the largest and most comprehensive in existence. It docum ...
, may have come across the works of one or more of these figures, and that his inability to formulate a viable critique may account for his failure to complete any further volumes of ''Kapital'' before his death. Nonetheless, it is not unreasonable to suggest that the generation who followed the preceptors of the Revolution succeeded partly because they could formulate straightforward responses to Marxist economic theory. The most famous of these was that of Böhm-Bawerk, (1896), but the first was Wicksteed's "The Marxian Theory of Value. ''Das Kapital'': a criticism" (1884, followed by "The Jevonian criticism of Marx: a rejoinder" in 1885). Initially there were only a few Marxist responses to marginalism, of which the most famous were
Rudolf Hilferding Rudolf Hilferding (10 August 1877 – 11 February 1941) was an Austrian-born Marxism, Marxist economist, Socialism, socialist theorist,International Institute of Social History, ''Rodolf Hilferding Papers''. http://www.iisg.nl/archives/en/files ...
's ''Böhm-Bawerks Marx-Kritik'' (1904) and ''Politicheskoy ekonomii rante'' (1914) by
Nikolai Bukharin Nikolai Ivanovich Bukharin (russian: Никола́й Ива́нович Буха́рин) ( – 15 March 1938) was a Bolshevik revolutionary, Soviet politician, Marxist philosopher and economist and prolific author on revolutionary theory. ...
. However, over the course of the 20th century a considerable literature developed on the conflict between marginalism and the labour theory of value, with the work of the neo-Ricardian economist
Piero Sraffa Piero Sraffa (5 August 1898 – 3 September 1983) was an influential Italian economist who served as lecturer of economics at the University of Cambridge. His book ''Production of Commodities by Means of Commodities'' is taken as founding the neo- ...
providing an important critique of marginalism. It might also be noted that some followers of
Henry George Henry George (September 2, 1839 – October 29, 1897) was an American political economist and journalist. His writing was immensely popular in 19th-century America and sparked several reform movements of the Progressive Era. He inspired the eco ...
similarly consider marginalism and neoclassical economics a reaction to ''
Progress and Poverty ''Progress and Poverty: An Inquiry into the Cause of Industrial Depressions and of Increase of Want with Increase of Wealth: The Remedy'' is an 1879 book by social theorist and economist Henry George. It is a treatise on the questions of why pover ...
'', which was published in 1879. In the 1980s
John Roemer John E. Roemer (; born February 1, 1945 in Washington, D.C., to Ruth Roemer and Milton Roemer, namesake of Roemer's law) is an American economist and political scientist. He is the Elizabeth S. and A. Varick Stout Professor of Political Scienc ...
and other
analytical Marxists Analytical Marxism is an approach to Marxist theory that was prominent amongst English-speaking philosophers and social scientists during the 1980s. Described by G. A. Cohen as "non-bullshit Marxism", members of this school seek to apply the t ...
have worked to rebuild Marxian theses on a marginalist foundation.


Reformulation

In his 1881 wor
''Mathematical Psychics''
Francis Ysidro Edgeworth Francis Ysidro Edgeworth (8 February 1845 – 13 February 1926) was an Anglo-Irish philosopher and political economist who made significant contributions to the methods of statistics during the 1880s. From 1891 onward, he was appointed the ...
presented the
indifference curve In economics, an indifference curve connects points on a graph representing different quantities of two goods, points between which a consumer is ''indifferent''. That is, any combinations of two products indicated by the curve will provide the c ...
, deriving its properties from marginalist theory which assumed utility to be a differentiable function of quantified goods and services. Later work attempted to generalize to the indifference curve formulations of utility and marginal utility in avoiding unobservable measures of utility. In 1915,
Eugen Slutsky Evgeny "Eugen" Evgenievich Slutsky (russian: Евге́ний Евге́ньевич Слу́цкий; – 10 March 1948) was a Russian and Soviet mathematical statistician, economist and political economist. Work in economics Slutsky is principa ...
derived a theory of consumer choice solely from properties of indifference curves. Because of the World War, the
Bolshevik Revolution The October Revolution,. officially known as the Great October Socialist Revolution. in the Soviet Union, also known as the Bolshevik Revolution, was a revolution in Russia led by the Bolsheviks, Bolshevik Party of Vladimir Lenin that was ...
, and his own subsequent loss of interest, Slutsky's work drew almost no notice, but similar work in 1934 by
John Richard Hicks Sir John Richards Hicks (8 April 1904 – 20 May 1989) was a British economist. He is considered one of the most important and influential economists of the twentieth century. The most familiar of his many contributions in the field of economic ...
and
R. G. D. Allen Sir Roy George Douglas Allen, CBE, FBA (3 June 1906 – 29 September 1983) was an English economist, mathematician and statistician, also member of the International Statistical Institute. Life Allen was born in Worcester and educated at t ...
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, von Mises, Ludwig Heinrich; ''Theorie des Geldes und der Umlaufsmittel'' (1912). most economists presumed that utility must be a sort of quantity. Indifference curve analysis seemed to represent a way to dispense with presumptions of quantification, albeit that a seemingly arbitrary assumption (admitted by Hicks to be a "rabbit out of a hat") about decreasing marginal rates of substitutionHicks, Sir John Richard; ''Value and Capital'', Chapter I. "Utility and Preference" §7–8. would then have to be introduced to have convexity of indifference curves. For those who accepted that indifference curve analysis superseded earlier marginal utility analysis, the latter became at best perhaps pedagogically useful, but "old fashioned" and observationally unnecessary.Samuelson, Paul Anthony; "Complementarity: An Essay on the 40th Anniversary of the Hicks-Allen Revolution in Demand Theory", ''Journal of Economic Literature'' vol 12 (1974).


Revival

When Cramer and Bernoulli introduced the notion of diminishing marginal utility, it had been to address a paradox of gambling, rather than the
paradox of value The paradox of value (also known as the diamond–water paradox) is the contradiction that, although water is on the whole more useful, in terms of survival, than diamonds, diamonds command a higher price in the market. The philosopher Adam Smith ...
. The marginalists of the revolution, however, had been formally concerned with problems in which there was neither
risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environme ...
nor
uncertainty Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or ...
. So too with the indifference curve analysis of Slutsky, Hicks, and Allen. The
expected utility hypothesis The expected utility hypothesis is a popular concept in economics that serves as a reference guide for decisions when the payoff is uncertain. The theory recommends which option rational individuals should choose in a complex situation, based on the ...
of Bernoulli and others was revived by various 20th century thinkers, with early contributions by
Ramsey Ramsey may refer to: Geography British Isles * Ramsey, Cambridgeshire, a small market town in England * Ramsey, Essex, a village near Harwich, England ** Ramsey and Parkeston, a civil parish formerly called just "Ramsey" * Ramsey, Isle of Man, t ...
(1926),
von Neumann Von Neumann may refer to: * John von Neumann (1903–1957), a Hungarian American mathematician * Von Neumann family * Von Neumann (surname), a German surname * Von Neumann (crater), a lunar impact crater See also

* Von Neumann algebra * Von Ne ...
and Morgenstern (1944), and
Savage Savage may refer to: Places Antarctica * Savage Glacier, Ellsworth Land * Savage Nunatak, Marie Byrd Land * Savage Ridge, Victoria Land United States * Savage, Maryland, an unincorporated community * Savage, Minnesota, a city * Savage, Mi ...
(1954). Although this hypothesis remains controversial, it brings not only utility, but a quantified conception of utility (cardinal utility), back into the mainstream of economic thought. A major reason why quantified models of utility are influential today is that risk and uncertainty have been recognized as central topics in contemporary economic theory. Quantified utility models simplify the analysis of risky decisions because, under quantified utility, diminishing marginal utility implies
risk aversion In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more ce ...
. In fact, many contemporary analyses of saving and portfolio choice require stronger assumptions than diminishing marginal utility, such as the assumption of
prudence Prudence ( la, prudentia, Contraction (grammar), contracted from meaning "seeing ahead, sagacity") is the ability to govern and discipline oneself by the use of reason. It is classically considered to be a virtue, and in particular one of th ...
, which means
convex Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytope ...
marginal utility.Kimball, Miles (1990), "Precautionary Saving in the Small and in the Large", ''
Econometrica ''Econometrica'' is a peer-reviewed academic journal of economics, publishing articles in many areas of economics, especially econometrics. It is published by Wiley-Blackwell on behalf of the Econometric Society. The current editor-in-chief is Gui ...
'', 58 (1) pp. 53–73.
Meanwhile, the Austrian School continued to develop its ordinalist notions of marginal utility analysis, formally demonstrating that from them proceed the decreasing marginal rates of substitution of indifference curves.


See also

*
Diminishing returns In economics, diminishing returns are the decrease in marginal (incremental) output of a production process as the amount of a single factor of production is incrementally increased, holding all other factors of production equal ( ceteris paribu ...
*
Economic subjectivism The subjective theory of value is an theory of value (economics), economic theory which proposes the idea that the value (economics), value of any good is not determined by the utility value of the object, nor by the cumulative value of components ...
*
Marginalism Marginalism is a theory of economics that attempts to explain the discrepancy in the value of goods and services by reference to their secondary, or marginal, utility. It states that the reason why the price of diamonds is higher than that of wa ...
*
Microeconomics Microeconomics is a branch of mainstream economics that studies the behavior of individuals and firms in making decisions regarding the allocation of scarce resources and the interactions among these individuals and firms. Microeconomics fo ...
*
Paradox of value The paradox of value (also known as the diamond–water paradox) is the contradiction that, although water is on the whole more useful, in terms of survival, than diamonds, diamonds command a higher price in the market. The philosopher Adam Smith ...
*
Rivalry (economics) In economics, a good is said to be rivalrous or a rival if its consumption by one consumer prevents simultaneous consumption by other consumers, or if consumption by one party reduces the ability of another party to consume it. A good is consider ...
*
Shadow price A shadow price is the monetary value assigned to an abstract or intangible commodity which is not traded in the marketplace. This often takes the form of an externality. Shadow prices are also known as the recalculation of known market prices in o ...
*
Theory of value (economics) A theory of value is any economic theory that attempts to explain the exchange value or price of goods and services. Key questions in economic theory include why goods and services are priced as they are, how the value of goods and services comes ...
*
Utility As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosopher ...


References


Further reading

*


External links

*
Maximization of Originality
{{Authority control Marginal concepts Utility Welfare economics Economics laws Austrian School