Everything about Marginalism totally explained
Marginalism is the use of marginal concepts within
economics. The central concept of marginalism proper is that of
marginal utility, but marginalists following the lead of
Alfred Marshall were further heavily dependent upon the concept of
marginal physical productivity in their explanation of
cost; and the
neoclassical tradition that emerged from
British marginalism generally abandoned the concept of
utility and gave
marginal rates of substitution a more fundamental rôle in analysis.
Important marginal concepts
Marginality
Constraints are conceptualized as a
border or
margin. The location of the margin for any individual corresponds to his or her
endowment, broadly conceived to include opportunities. 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 both by others and by the individual himself or herself.
A value that holds true given particular constraints is a
marginal value. A change that would be effected as or by a specific loosening or tightening of those constraints is a
marginal change.
Neoclassical economics usually assumes that marginal changes are
infinitesimals or
limits. (Though this assumption makes the analysis less robust, it increases tractability.) One is therefore often told that “marginal” is synonymous with “very small”, though in more general analysis this may not be operationally true (and wouldn't in any case be literally true).
Marginal use
The
marginal use of a
good or service is the specific use to which an
economically rational agent would put a given increase, or the specific use of the good or service that would be abandoned in response to a given decrease.
Marginalism assumes, for any given agent, economically rationality and an
ordering of possible states-of-the-world, such that, for any given set of constraints, there's an attainable state which is best in the eyes of that agent.
Descriptive marginalism asserts that choice amongst the specific means by which various anticipated specific states-of-the-world (outcomes) might be effected is governed only by the distinctions amongst those specific outcomes;
prescriptive marginalism asserts that such choice
ought to be so governed.
On such assumptions, each increase would be put to the specific, feasible, previously unrealized use of greatest priority, and each decrease would result in abandonment of the use of lowest priority amongst the uses to which the good or service had been put. which literally means
border use, referring directly to the marginal use, and the more general formulations of marginal utility don't treat quantification as an
essential feature. On the other hand, none of the early marginalists insisted that utility were
not quantified, some indeed treated quantification as an essential feature, and those who didn't still used an assumption of quantification for expository purposes. In this context, it isn't surprising to find many presentations that fail to recognize a more general approach.
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:
»
The “law” of diminishing marginal utility
The “law” of diminishing marginal utility (also known as a “
Gossen's First Law”) is that,
ceteris paribus, as additional amounts of a good or service are added to available resources, their marginal utilities are decreasing. This “law” is sometimes treated as a tautology, sometimes as something proven by introspection, or sometimes as a mere
instrumental assumption, adopted only for its perceived predictive efficacy. Actually, it isn't quite any of these things, though it may have aspects of each. The “law” doesn't hold under all circumstances, so it's neither a tautology nor otherwise proveable; but it has a basis in prior observation.
An individual will typically be able to
partially order the potential uses of a good or service. If there's
scarcity, then a rational agent will satisfy wants of highest possible priority, so that no want is avoidably sacrificed to satisfy a want of
lower priority. In the absence of complementarity across the uses, this will imply that the priority of use of any additional amount will be lower than the priority of the established uses, as in this famous example:
» A pioneer farmer had five sacks of grain, with no way of selling them or buying more. He had five possible uses: as basic feed for himself, food to build strength, food for his chickens for dietary variation, an ingredient for making whisky and feed for his parrots to amuse him. Then the farmer lost one sack of grain. Instead of reducing every activity by a fifth, the farmer simply starved the parrots as they were of less utility than the other four uses; in other words they were on the margin. And it's on the margin, and not with a view to the big picture, that we make economic decisions.
However, if there
is a complementarity across uses, then an amount added can bring things past a desired
tipping point, or an amount subtracted cause them to fall short. In such cases, the marginal utility of a good or service might actually be
increasing.
Without the presumption that utility is quantified, the
diminishing of utility shouldn't be taken to be itself an
arithmetic subtraction. It is the movement from use of higher to lower priority, and may be no more than a purely
ordinal change. or can be produced without presumption of quantification, but this work has been relatively uninfluential on the mainstream of economic thought.
In any case buyers are modelled as pursuing generally lower quantities, and sellers offering generally higher quantities, as price is increased, with each being willing to trade until the marginal value of what they'd trade-away exceeds that of the thing for which they'd trade.
The paradox of water and diamonds
The “law” of diminishing marginal utility is said to explain the “paradox of water and diamonds”, most commonly associated with
Adam Smith (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 small price, and diamonds a very large price, by any normal measure. Marginalists explained that it's the
marginal usefulness of any given quantity that matters, 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 were 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” isn't about
geology or
cosmology, so 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 relative abundance affects the value imputed to a given diamond and the price of diamonds in a market.
Criticism
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.
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 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
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 little-noticed paper delivered in
1862 and published in
1863. He later presented the theory in
The Theory of Political Economy (
1871), which was fairly widely read but not much appreciated. Jevons' conception of utility was that in the
hedonic tradition of
Jeremy Bentham and of
John Stuart Mill, and Jevons explained demand but not supply by reference to marginal utility.
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. Menger's work found a significant and appreciative audience.
Marie-Esprit-Léon Walras introduced the theory in
Éléments d'économie politique pure, the first part of which was published in
1874. Walras's work found relatively few readers.
(An American,
John Bates Clark, is sometimes also mentioned in this context. 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
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. (On the other hand,
Hayek or
Bartley has suggested that Marx 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.)
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. 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). The most famous early Marxist responses were
Rudolf Hilferding's
Böhm-Bawerks Marx-Kritik (
1904) and
Политической экономии рантье (
The Economic Theory of the Leisure Class)(
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. But it came to be seen that indifference curves could be considered as somehow
given, without bothering with notions of 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 Slutksy'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, most economists presumed that utility must be a sort of quantity. Indifference curve analysis seemed to represent a way of dispensing with presumptions of quantification, albeït that a seemingly arbitrary assumption (admitted by Hicks to be a “rabbit out of a hat”) about decreasing marginal rates of substitution would then have to be introduced to have convexity of indifference curves.
For those who accepted that superseded marginal utility analysis had been superseded by indifference curve analysis, the former became at best somewhat analogous to the
Bohr model of the atom — 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, perhaps most notably
Ramsey (
1926),
v. Neumann and
Morgenstern (
1944), and
Savage (
1954). Although this hypothesis remains controversial, it brings not merely utility but a quantified conception thereof back into the mainstream of economic thought, and would dispatch the
Ockhamistic argument.
Criticisms of marginalism
Marginalism has been criticised for being extremely abstract, as “unobservable, unmeasurable and untestable”. Marginal utility is subjective, as the
value of an additional unit of consumption is based on the individual's circumstances. However, margins (constraints) are often observable, as are patterns of choice; hence the
general form of marginalism is in theory observable and testable. The special case of
quantification of utility is more problematic, but the
expected utility hypothesis represents a testable version of the theory with quantification. (Nonetheless, though confirmation of the
expected utility hypothesis might have confirm quantification, the specific measure wouldn't thus be found, as data that were fit by any proposed measure would be equally well fit by any
affine transformation of that proposed measure.)
However, observed patterns of choice in test situations often seem
not to correspond to an ordering, and the expected utility hypothesis has been falsified as description. (See
the article on behavior economics, and perhaps especially
that on the Ellsberg paradox or
that on the Allais problem.) Many behavioral economists argue that people often follow simple
rules of thumb instead of engaging in a mental process of maximizing some function. The reply from some marginalist and neoclassical economists is that these rules of thumb have been shaped by experience so that they give very nearly the same result as maximizing and that, moreover, use of rules of thumb is itself an act of optimization insofar as the decision-making process itself entails direct costs.
The theory is attacked for downplaying the rôle of
cost of production in price determination in favor of a focus on individual's tastes and preferences. In its most extreme
Austrian School version, marginalism denies that a purely objective, cost-based component exists at all. Rather, the Austrian School argues that costs of production pervasively involve individual preferences for labor vs. leisure and saving vs. consumption.
Marxist attacks on marginalism
Karl Marx died before marginalism became the accepted interpretation of economic value. His theory was based on the
labor theory of value, which distinguishes between
exchange value and
use value. In his
Capital he rejected the explanation of long-term market values by supply and demand:
» Nothing is easier than to realize the inconsistencies of demand and supply, and the resulting deviation of market-prices from market-values. The real difficulty consists in determining what is meant by the equation of supply and demand.
[...]
» If supply equals demand, they cease to act, and for this very reason commodities are sold at their market-values. Whenever two forces operate equally in opposite directions, they balance one another, exert no outside influence, and any phenomena taking place in these circumstances must be explained by causes other than the effect of these two forces. If supply and demand balance one another, they cease to explain anything, don't affect market-values, and therefore leave us so much more in the dark about the reasons why the market-value is expressed in just this sum of money and no other.
In his early response to marginalism,
Nikolai Bukharin argued that "the subjective evaluation from which price is to be derived really starts from this price", concluding:
» Whenever the Böhm-Bawerk theory, it appears, resorts to individual motives as a basis for the derivation of social phenomena, he's actually smuggling in the social content in a more or less disguised form in advance, so that the entire construction becomes a vicious circle, a continuous logical fallacy, a fallacy that can serve only specious ends, and demonstrating in reality nothing more than the complete barrenness of modern bourgeois theory.
Similarly a later Marxist critic,
Ernest Mandel, argued that marginalism was "divorced from reality", ignored the rôle of production, and that:
» It is, moreover, unable to explain how, from the clash of millions of different individual "needs" there emerge not only uniform prices, but prices which remain stable over long periods, even under perfect conditions of free competition. Rather than an explanation of constants, and of the basic evolution of economic life, the "marginal" technique provides at best an explanation of ephemeral, short-term variations.
Maurice Dobb argued that prices derived through marginalism depend on the distribution of income. The ability of consumers to express their preferences is dependent on their spending power. As the theory asserts that prices arise in the act of exchange, Dobb argues that it can't explain how the distribution of income affects prices and consequently can't explain prices.
Dobb also criticized the
motives behind marginal utility theory. Jevons wrote, for example, "so far as is consistent with the inequality of wealth in every community, all commodities are distributed by exchange so as to produce the maximum social benefit." (See
Fundamental theorems of welfare economics.) Dobb contended that this statement indicated that marginalism is intended to insulate market economics from criticism by making prices the natural result of the given income distribution.
Marxist adaptations to marginalism
Some economists strongly influenced by the
Marxian tradition such as
Oskar Lange,
Włodzimierz Brus, and
Michal Kalecki have attempted to integrate the insights of classical
political economy, marginalism, and
neoclassical economics. They believed that Marx lacked a sophisticated theory of prices, and neoclassical economics lacked a theory of the social frameworks of economic activity. Some other Marxists have also argued that on one level there's no conflict between marginalism and Marxism: one could employ a marginalist theory of supply and demand within the context of a “big picture” understanding of capitalist exploitation of labor.
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