Everything about Marginal Utility totally explained
In
economics, the
marginal utility of a
good or service is the
utility of the specific use to which an
economically rational agent would put a given increase in that good or service, or of the specific use that would be abandoned in response to a given decrease. In other words, marginal utility is the utility of the
marginal use — the least urgent use of the good or service, from the best feasible combination of actions in which its use is included. Under the mainstream assumptions, the marginal utility of a good or service is the posited
quantified change in utility obtained by using one more or one less unit of that good or service.
This concept grew out of attempts by economists to explain the determination of price. The term “marginal utility”, credited to the
Austrian economist
Friedrich von Wieser by
Alfred Marshall, was a translation of Wieser's term “Grenznutzen” (
border-use). This has significantly affected the development and reception of theories of marginal utility. Conceptions of utility that entail quantification allow familiar arithmetic operations, and further assumptions of continuity and differentiability greatly increase tractability. However, conceptions without even weak quantification are able to consider rational preferences that would otherwise be excluded.
Benthamite philosophy equated usefulness with the production of pleasure and avoidance of pain, conceptualized as subject to arithmetic operation. British economists, under the influence of this philosophy (especially by way of
John Stuart Mill), conceptualized utility as “the feelings of pleasure and pain” and further as a “
quantity of feeling” (emphasis added).
The Austrian School more generally attributes value to
the satisfaction of needs, didn't depend upon a presumption of quantification,
The mainstream of contemporary economic theory frequently defers ontological questions, and merely notes or assumes that preference structures conforming to certain rules can be usefully
proxied by associating goods, services, or uses thereof with quantities, and
defines “utility” as such a quantification. Recognizing that
preference may be taken as the determinant of
usefulness, this conception doesn't depart from the concept of usefulness.
Under any standard conception, the same object may have different marginal utilities for different people, reflecting different preferences or individual circumstances.
The “law” of diminishing marginal utility
An individual will typically be able to
partially order the potential uses of a good or service. For example, a ration of water might be used to sustain oneself, a dog, or a rose bush. Say that a given person gives her own sustenance highest priority, that of the dog next highest priority, and lowest priority to saving the roses. In that case, if the individual has two rations of water, then the
marginal utility of either of those rations is that of sustaining the dog. The marginal utility of a third unit would be that of watering the roses.
(The
diminishing of utility shouldn't necessarily be taken to be itself an
arithmetic subtraction. It may be no more than a purely
ordinal change. (though recognized by earlier thinkers). Human beings can't even survive without water, whereas diamonds were in Smith's day mere ornamentation or engraving bits. Yet water had a very low price, and diamonds a very high price, by any normal measure. Marginalists explained that it's the
marginal usefulness of any given quantity that determines its price, rather than the usefulness of a
class or of a
totality. For most people, water was sufficiently abundant that the loss or gain of a gallon would withdraw or add only some very minor use if any; whereas diamonds were in much more restricted supply, so that the lost or gained use would be much greater.
That isn't 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've or desire (with these marginal utilities being distinct for each potential trader), and prices thus develop constrained by these marginal utilities.
The “law” doesn't tell us such things as why diamonds are naturally less abundant on the earth than is water, but helps us to understand how this affects the value imputed to a given diamond and the price of diamonds in a market.
Criticism of the marginalist explanation of the paradox of water and diamonds
Many critics of marginalism would reply that the reason that diamonds are more expensive than water isn't because of their relative natural abundance but because of their cost of production. The reason water is available abundantly and diamonds in relatively smaller quantities is because one is inexpensive to produce and one very expensive. Critics claim that thus the reason water is cheaper than diamonds is simply because it costs less to produce. If diamonds could be produced cheaply from carbon, as modern technology may make possible in the short term, then the price of diamonds will fall, even though the demand for their use hasn't altered. Therefore, as these critics would claim, it's the cost of production which determines price, not the marginal utility.
Marginalists simply respond that if this were true then, rather than our seeing some goods and services not produced because their costs exceeded their prices, consumers would make a practice of seeking expensive wares without regard to their use. (As proto-marginalist
Richard Whately put it, “It isn't 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.”) Marginalists explain that
costs of production may be what limit supply, but that these costs of production are themselves sacrificed marginal uses, and won't be borne when they're expected to exceed the marginal use of what is produced. In other words, the marginalist certainly does
not explain
price as a simple function of the marginal utility of a single good for one person or for some “average” person, but nonetheless insists that it results from the trade-offs that each participant would be willing to make for the various goods and services at stake, with those trade-offs being determined by marginal uses. The critics who believe that costs of production determine price, by assuming a demand that will bear the cost, have begged the essential question that the marginalists purport to answer.
Quantified marginal utility
Under the
special case in which usefulness can be quantified, the change in utility of moving from state
to state
is
»
Moreover, if
and
are distinguishable by values of just one variable
which is itself quantified, then it becomes possible to speak of the ratio of the marginal utility of the change in
to the size of that change:
»
History
Proto-marginalist approaches
A great variety of economists concluded that there was
some sort of inter-relationship between utility and rarity that effected economic decisions, and in turn informed the determination of prices.
Marginalists before the Revolution
The first published statement of any sort of theory of marginal utility was by
Daniel Bernoulli, 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 had produced fundamentally the same theory in a private letter. Each had sought to resolve the
St. Petersburg paradox, and had concluded that the marginal desirability of money decreased as it was accumulated, more specifically such that the desirability of a sum were the
natural logarithm (Bernoulli) or
square root (Cramer) thereof. However, the more general implications of this hypothesis were not explicated, and the work fell into obscurity.
In “A Lecture on the Notion of Value”, 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 didn't 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 asserted that marginal utilities were the ultimate determinant of demand, yet apparently didn't pursue implications, though some interpret his work as indeed doing just that.
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 wasn't 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.
The Marginal Revolution
» “Marginal revolution” redirects here. For the economics weblog, see Marginal Revolution (blog).
Marginalism eventually found a foot-hold by way of the work of three economists,
Jevons in England,
Menger in Austria, and
Walras in Switzerland.
William Stanley Jevons first proposed the theory in
“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 tradition of
Jeremy Bentham and of
John Stuart Mill, but he differed from his
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." He later qualified this in deriving the result that in a model of exchange equilibrium, price ratios would be proportional to not only to ratios of "final degrees of utility" but costs of production.
Carl Menger presented the theory in
Grundsätze der Volkswirtschaftslehre (translated as
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're 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.
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.
The 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; 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 A. Fetter.
There were significant, distinguishing features amongst the approaches of Jevons, Menger, and Walras, but the second generation didn't 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.
Böhm-Bawerk was perhaps the most able expositor of Menger's conception. (This theory was adopted in full and then further developed by
Knut Wicksell and, with modifications including formal disregard for time-preference, by Wicksell's American rival
Irving Fisher.)
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 didn't 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.)
The Marginal Revolution and Marxism
In his critique of
political economy, Marx discussed “use-value”, a concept analogous to utility:
» A use-value has value only in use, and is realized only in the process of consumption. One and the same use-value can be used in various ways. But the extent of its possible application is limited by its existence as an object with distinct properties. It is, moreover, determined not only qualitatively but also quantitatively. Different use-values have different measures appropriate to their physical characteristics; for example, a bushel of wheat, a quire of paper, a yard of linen.
He acknowledged that the value of a commodity is dependent on the use that can be garnered from it, but, in his analysis, utility was considered as all or nothing; it was unnecessary to describe variable use-value; to Marx labor was the ultimate source of value.
The doctrines of marginalism and the Marginal Revolution are often interpreted as somehow a response to
Marxist economics. In fact, the first volume of
Das Kapital wasn't published until
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,
Hayek or
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.)
Nonetheless, it isn't unreasonable to suggest that part of what contributed to the success of the generation who followed the preceptors of the Revolution was their ability to formulate straight-forward responses to Marxist economic theory. The most famous of these was that of Böhm-Bawerk, “Zum Abschluss des Marxschen Systems” (
1896), but the first was Wicksteed's “The Marxian Theory of Value.
Das Kapital: a criticism” (
1884, followed by “The Jevonian criticism of Marx: a rejoinder” in
1885). Only a few Marxist replies were made to marginalism, of which the most famous were
Rudolf Hilferding's
Böhm-Bawerks Marx-Kritik (
1904) and
Политической экономии рантье (
1914) by
Никола́й Ива́нович Буха́рин (Nikolai Bukharin).
(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.)
Eclipse
In his
1881 work
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 the indifference-curve formulation of utility and marginal utility.
In
1915,
Евгений Евгениевич Слуцкий (Eugen Slutsky) derived a theory of consumer choice solely from properties of indifference curves. Because of
the World War, the
Bolshevik Revolution, and his own subsequent loss of interest, Slutsky's work drew almost no notice, but similar work in
1934 by
John Richard Hicks and
R. G. D. Allen derived much 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,) about decreasing marginal rates of substitution would then have to be introduced to have convexity of indifference curves.
For those who accepted that indifference curve analysis superseded marginal utility analysis, the latter became at best perhaps pedagogically useful, but “old fashioned” and ultimately incorrect.
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 marginalists of the revolution, however, had been formally concerned with problems in which there was neither
risk nor
uncertainty. So too with the indifference curve analysis of Slutsky, Hicks, and Allen.
The
expected utility hypothesis of Bernoulli
et alii was revived by various
20th century thinkers, with early contributions by
Ramsey (
1926),
v. Neumann and
Morgenstern (
1944), and
Savage (
1954). Although this hypothesis remains controversial, it not only brings utility, but a quantified conception of 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 to “
risk aversion”. In fact, many contemporary analyses of saving and portfolio choice require stronger assumptions than diminishing marginal utility, such as the assumption of “
prudence”, which means
convex marginal utility.
Meanwhile, the Austrian School continues to develop its ordinalist notions of marginal utility analysis, formally demonstrating that from them proceed the decreasing marginal rates of substitution of indifference curves.
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