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| marginal utility | |
|---|---|
| Name | Marginal utility |
| Caption | Diminishing marginal utility illustrated by a concave utility curve |
| Field | Economics |
| Introduced | 19th century |
| Notable figures | William Stanley Jevons, Carl Menger, Leon Walras, Alfred Marshall, John Hicks |
marginal utility Marginal utility is the additional satisfaction or value a consumer obtains from consuming one more unit of a good or service, central to theories of choice and value. It underpins demand theory, price determination, and welfare comparisons in classical and neoclassical frameworks, connecting thinkers from Adam Smith and David Ricardo through the marginalist revolution led by William Stanley Jevons, Carl Menger, and Leon Walras. The concept interfaces with mathematical optimization and probability methods used by scholars at institutions such as Cambridge University and the London School of Economics.
Marginal utility denotes the incremental change in utility resulting from a small change in consumption of a particular commodity, used to explain how individuals allocate finite resources among alternatives such as consumption of goods, leisure, or investment in assets. Key early proponents like Alfred Marshall and later formalizers such as John Hicks and R. G. D. Allen linked marginal utility to demand curves and comparative statics, while modern treatments employ tools from Isaac Newton-style calculus and variational methods developed in mathematical economics at Princeton University and Harvard University. Practical policy and market analyses by organizations including the International Monetary Fund and World Bank often rely on marginal utility concepts when assessing welfare effects of transfers and taxation.
The marginal utility concept emerged during the 19th-century marginalist revolution, with parallel contributions by William Stanley Jevons in Britain, Carl Menger in Austria, and Leon Walras in Switzerland, reacting to the labor and cost theories associated with David Ricardo and later commentators like John Stuart Mill. Debates involving Alfred Marshall integrated marginal utility into price theory at Cambridge University, while controversies over interpersonal utility comparisons involved philosophers and economists such as Jeremy Bentham and John Nash. Twentieth-century refinements by Vilfredo Pareto, Léon Walras’s successors, and welfare economists connected marginal utility to social choice theory debates addressed by the LSE and the Cowles Commission.
Formally, if U(x) denotes a utility function over quantity x, marginal utility is dU/dx, a derivative used in optimization problems solved via first-order conditions; higher-dimensional consumption bundles invoke gradient vectors and Lagrange multipliers as in work by Kenneth Arrow and Gerard Debreu. The law of diminishing marginal utility—empirically observed and axiomatized in expected utility theory—states that d^2U/dx^2 < 0 for normal goods, an assumption used by John von Neumann and Oskar Morgenstern in expected utility formulations and by Milton Friedman in certain demand analyses. Intertemporal choice models by Paul Samuelson and asset-pricing frameworks by Fischer Black and Myron Scholes incorporate marginal utility of consumption into Euler equations and stochastic discount factors, linking to optimization under uncertainty studied at Bell Labs and the RAND Corporation.
Marginal utility underlies the derivation of individual demand curves via utility maximization subject to budget constraints, a method elaborated by Paul Samuelson and H. J. Davenport and taught across departments at Yale University and the University of Chicago. In applied welfare analysis, marginal utility determines compensating and equivalent variation measures used by agencies such as the OECD for policy evaluation, and shapes tax incidence studies influenced by theorists like Arthur Laffer and James Mirrlees. Marketing and pricing strategies at firms from Procter & Gamble to Amazon (company) exploit marginal utility insights for product bundling, while public finance programs, including social transfers analyzed by the European Commission, consider marginal utility to evaluate redistribution efficiency.
Critiques of marginal utility arise from philosophical and empirical challenges: the cardinal measurability of utility was disputed by utilitarians such as John Stuart Mill and later by ordinalists including Paul Samuelson; paradoxes like the St. Petersburg paradox questioned expected utility axioms, prompting contributions from Daniel Bernoulli and modern revisions by Leonard Savage. Behavioral findings by researchers at institutions like Harvard University and Stanford University, including Daniel Kahneman and Amos Tversky, highlight violations of diminishing marginal utility via prospect theory, loss aversion, and context-dependent preferences, prompting alternative models and critiques by scholars at the University of Chicago Booth School of Business.
Extensions include expected marginal utility in decision under risk developed by John von Neumann and Oskar Morgenstern, marginal rate of substitution linking bundles as formalized by Kenneth Arrow and Frank Hahn, and marginal utility of income applied in tax-smoothing literature by Robert Barro and Angus Deaton. Related constructs are the utility function in game theory studied by John Nash, cardinal vs ordinal utility debates associated with Amartya Sen, and welfare economics frameworks advanced by Vilfredo Pareto and Kenneth Arrow’s impossibility theorem, all taught in graduate programs at MIT and Princeton University.
Category:Economics concepts