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 water, for example, owes to the greater additional satisfaction of the diamonds over the water. Thus, while the water has greater total utility, the diamond has greater marginal utility.
Although the central concept of marginalism is marginal utility, marginalists, following the work of Alfred Marshall, drew upon the idea of marginal physical productivity in explanation of cost. The concept of marginalism came from Carl Menger, William Stanley Jevons, and Leon Walras when resolving the Diamond-Water Paradox propounded by Adam Smith by distinguishing between total utility and marginal utility. The location of the margin for any individual corresponds to their 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.
A value that holds true given particular constraints is a marginal value. A change that would be affected 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. Although 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 would not in any case be literally true. Frequently, economic analysis concerns the marginal values associated with a change of one unit of a resource, because decisions are often made in terms of units; marginalism seeks to explain unit prices in terms of such marginal values.
Marginal use
The marginal use of a good or service is the specific use to which an 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, economic rationality and an ordering of possible states-of-the-world, such that, for any given set of constraints, there is 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 affected 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 do not 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 did not still used an assumption of quantification for expository purposes. In this context, it is not 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 <math>S_1</math> to state <math>S_2</math> is
:<math>\Delta U=U(S_2)-U(S_1)\,</math>
Moreover, if <math>S_1</math> and <math>S_2</math> are distinguishable by values of just one variable <math>g\,</math> which is itself quantified, then it becomes possible to speak of the ratio of the marginal utility of the change in <math>g\,</math> to the size of that change:
:<math>\left.\frac{\Delta U}{\Delta g}\right|_{c.p.}</math>
(where "c.p." indicates that the only independent variable to change is <math>g\,</math>).
Mainstream neoclassical economics will typically assume that
:<math>\lim_{\Delta g\to 0}{\left.\frac{\Delta U}{\Delta g}\right|_{c.p.</math>
is well defined, and use "marginal utility" to refer to a partial derivative
:<math>\frac{\partial U}{\partial g}\approx\left.\frac{\Delta U}{\Delta g}\right|_{c.p.}</math>
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. It is not quite any of these things, although it may have aspects of each. The law does not hold under all circumstances, so it is 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 is 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 is on the margin, and not with a view to the big picture, that we make economic decisions.
thumb|right|Diminishing marginal utility, given quantification
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 should not 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.
When quantification of utility is assumed, diminishing marginal utility corresponds to a utility function whose slope is continually or continuously decreasing. In the latter case, if the function is also smooth, then the law may be expressed as
:<math>\frac{\partial^2 U}{\partial g^2}<0</math>
Neoclassical economics usually supplements or supplants discussion of marginal utility with indifference curves, which were originally derived as the level curves of utility functions, or can be produced without presumption of quantification, The shape of that curve is then determined by marginal rates of substitution of money for that good or service.
Markets
By confining themselves to limiting cases in which sellers or buyers are both "price takers" – so that demand functions ignore supply functions or vice versa – Marshallian marginalists and neoclassical economists produced tractable models of "pure" or "perfect" competition and of various forms of "imperfect" competition, which models are usually captured by relatively simple graphs. Other marginalists have sought to present what they thought of as more realistic explanations, but this work has been relatively uninfluential on the mainstream of economic thought.
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, although it was recognized by earlier thinkers. Human beings cannot even survive without water, whereas diamonds, in Smith's day, were ornamentation or engraving bits. Yet water had a very small price, and diamonds a very large price. Marginalists explained that it is 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 loss or gain was much greater.
That is not to say that the price of any good or service is simply a function of the marginal utility that it has for any one individual nor for some ostensibly typical individual. Rather, individuals are willing to trade based upon the respective marginal utilities of the goods that they have or desire (with these marginal utilities being distinct for each potential trader), and prices thus develop constrained by these marginal utilities.
History
Proto-marginalist approaches
Perhaps the essence of a notion of diminishing marginal utility can be found in Aristotle's Politics, wherein he writes
There has been marked disagreement about the development and role of marginal considerations in Aristotle's' value theory.
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.
Eighteenth-century Italian mercantilists, such as Antonio Genovesi, Giammaria Ortes, Pietro Verri, Cesare Beccaria, and Giovanni Rinaldo, 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. In Della Moneta (1751), Abbé Ferdinando Galiani, a pupil of Genovesi, attempted to explain value as a ratio of two ratios, utility and scarcity, with the latter component ratio being the ratio of quantity to use.
Anne Robert Jacques Turgot, in Réflexions sur la formation et la distribution de richesse (1769), held that value derived from the general utility of the class to which a good belonged, from comparison of present and future wants, and from anticipated difficulties in procurement.
Like the Italian mercantilists, Étienne Bonnot de Condillac saw value as determined by utility associated with the class to which the good belongs, and by estimated scarcity. In De commerce et le gouvernement (1776), Condillac emphasized that value is not based upon cost but that costs were paid because of value.
This last point was famously restated by the 19th-century proto-marginalist Richard Whately, who wrote as follows in Introductory Lectures on Political Economy (1832):
Whately's student Nassau William Senior is noted below as an early marginalist.
Frédéric Bastiat in chapters V and XI of his Economic Harmonies (1850) also develops a theory of value as ratio between services that increment utility, rather than between total utility.
Marginalists before the Revolution
The first unambiguous 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 as Distinguished Not Only from Utility, but also from Value in Exchange", delivered in 1833 and included in Lectures on Population, Value, Poor Laws and Rent (1837), William Forster Lloyd explicitly offered a general marginal utility theory, but did not offer its derivation nor elaborate its implications. The importance of his statement seems to have been lost on everyone (including Lloyd) until the early 20th century, by which time others had independently developed and popularized the same insight.
In An Outline of the Science of Political Economy (1836), Nassau William Senior asserted that marginal utilities were the ultimate determinant of demand, yet apparently did not pursue implications, though some interpret his work as indeed doing just that.
In "De la mesure de l'utilité des travaux publics" (1844), Jules Dupuit applied a conception of marginal utility to the problem of determining bridge tolls.
In 1854, Hermann Heinrich Gossen published Die Entwicklung der Gesetze des menschlichen Verkehrs und der daraus fließenden Regeln für menschliches Handeln, which presented a marginal utility theory and to a very large extent worked-out its implications for the behavior of a market economy. However, Gossen's work was not well received in the Germany of his time, most copies were destroyed unsold, and he was virtually forgotten until rediscovered after the so-called Marginal Revolution.
Marginal Revolution
Marginalism as a formal theory can be attributed to the work of three economists, Jevons in England, Menger in Austria, and Walras in Switzerland. William Stanley Jevons first proposed the theory in an article in 1862 and a book in 1871. Similarly, Carl Menger presented the theory in 1871. Menger explained why individuals use marginal utility to decide amongst trade-offs, but while his illustrative examples present utility as quantified, his essential assumptions do not. What the marginalists understood was that the exchange value of goods can be used to describe the use value of goods. Meghnad Desai puts it this way, "Individuals in their daily activity so managed their resources that they balanced the marginal utility--the utility (use value) derived from an extra unit of a commodity they consumed--with the price (exchange value) they paid for it". Thus, when consumption of a good goes up, the utility of that good decreases as it is consumed. Each person would continue to consume until the marginal utility would be equal to the price. Jevons also wanted to formulate a price theory that accounted for this marginal utility and discovered the following: cost production determines supply; supply determines final degree of utility; and final degree of utility determines value. Walras was able to articulate the utility maximization of the consumer far better than Jevons and Menger by assuming that utility was linked to the consumption of each good.
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 Wicksteed, by William Smart, and by Alfred Marshall; in Austria by Eugen Böhm von 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 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". 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. 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 productivity of time and with time preference. 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 did not see an explanation for supply in the theory of marginal utility, so he paired a marginal explanation of demand with a more classical explanation of supply, wherein costs were taken to be objectively determined. Marshall later actively mischaracterized the criticism that these costs were themselves ultimately determined by marginal utilities.
Marginal Revolution as a response to socialism
The doctrines of marginalism and the Marginal Revolution are often interpreted as a response to the rise of the worker's movement, Marxian economics and the earlier (Ricardian) socialist theories of the exploitation of labour. The first volume of Das Kapital was not published until July 1867, when marginalism was already developing, but before the advent of Marxian economics, proto-marginalist ideas such as those of Gossen had largely fallen on deaf ears. It was only in the 1880s, when Marxism had come to the fore as the main economic theory of the workers' movement, that Gossen found (posthumous) recognition.
Aside from the rise of Marxism, E. Screpanti and S. Zamagni point to a different 'external' reason for marginalism's success, which is its successful response to the Long Depression and the resurgence of class conflict in all developed capitalist economies after the 1848–1870 period of social peace. Marginalism, Screpanti and Zamagni argue, offered a theory of the free market as perfect, as performing optimal allocation of resources, while it allowed economists to blame any adverse effects of laissez-faire economics on the interference of workers' coalitions in the proper functioning of the market. 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). The most famous early Marxist responses were Rudolf Hilferding's (1904) and The Economic Theory of the Leisure Class (1914) by Nikolai Bukharin.
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, 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 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, 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, albeit 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 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, including Frank Ramsey (1926), John von Neumann and Oskar Morgenstern (1944), and Leonard 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.
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 is 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 role of production, further arguing:
: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 cannot explain how the distribution of income affects prices and consequently cannot 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.
See also
- Theory of value
References
External links
- Backhouse, Roger E. "Marginal Revolution." eds. Steven N. Durlauf and Lawrence E. Blume (2008). The New Palgrave Dictionary of Economics. Palgrave Macmillan. 2nd edition online