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Marginal utility

Marginal utility is a fundamental concept in economics that refers to the additional satisfaction, benefit, or pleasure a consumer derives from consuming one more unit of a good or service, assuming all else remains constant.^[1] This measure is typically expressed in subjective terms and forms the basis for understanding individual decision-making in resource allocation. The theory of marginal utility emerged prominently during the marginal revolution in economics in the 1870s, when it was independently developed by key figures including William Stanley Jevons in his work The Theory of Political Economy (1871), Carl Menger in Principles of Economics (1871), and Léon Walras in Elements of Pure Economics (1874).^[1] Earlier precursors to the idea appeared in the mid-19th century, notably in Hermann Heinrich Gossen's The Laws of Human Relations (1854), where he articulated the principle that enjoyment from additional consumption diminishes progressively.^[2] These contributions shifted economic analysis from classical labor theories of value to subjective valuations based on utility maximization, profoundly influencing neoclassical economics.^[1] A central implication of marginal utility is the law of diminishing marginal utility, which posits that the incremental benefit from successive units of a good decreases as consumption increases, leading to a downward-sloping demand curve.^[3] For instance, the first slice of pizza may provide high satisfaction, but additional slices yield progressively less until the marginal utility becomes zero or negative.^[2] This law underpins consumer equilibrium, where individuals allocate resources until the marginal utility per dollar spent is equal across goods.^[1] The concept extends to broader applications, such as public policy on taxation and redistribution, where diminishing marginal utility of income justifies progressive systems to equalize welfare.^[4]

Core Concepts

Utility

In economics, utility refers to the satisfaction, usefulness, or pleasure that a consumer derives from the consumption of goods and services.^[5] This concept serves as a foundational measure of individual welfare and preference fulfillment within economic decision-making.^[6] The historical roots of utility in economics trace back to the philosophical tradition of utilitarianism, particularly Jeremy Bentham's "greatest happiness principle," which posited that actions are right if they promote happiness and wrong if they produce the reverse, providing a basis for evaluating economic choices by their contribution to overall well-being.^[7] Economists distinguish between two primary approaches to utility: cardinal utility, which assumes satisfaction can be measured in absolute, quantifiable units (such as utils), allowing for interpersonal comparisons; and ordinal utility, which views utility as a ranking of preferences without requiring precise measurement, focusing instead on relative orderings of bundles of goods.^[8] Cardinal utility was prominent in early economic thought, while ordinal utility became more dominant in modern analysis due to its feasibility in modeling observed behavior.^[9] Utility plays a central role in consumer choice theory, where individuals are modeled as seeking to maximize their total utility subject to budget constraints, thereby determining the demand for goods and services based on preferences and prices. For instance, the total utility from consuming multiple units of a good, such as slices of pizza, typically increases with each additional slice up to a satiation point, reflecting how preferences shape consumption patterns.^[5] Marginal utility, in turn, represents the change in total utility from consuming one additional unit.

Marginality

Marginal analysis in economics refers to the examination of the additional or incremental effects arising from a small change in the quantity of an input or output, often conceptualized as the rate of change between related economic variables.^[10] This approach focuses on the impact of one more unit, enabling precise evaluation of how variables like cost, revenue, or output respond to adjustments at the "margin."^[11] Beyond its application to utility—which involves assessing the extra satisfaction from one additional unit of consumption—marginal analysis extends to broader economic contexts.^[12] In production theory, it includes marginal cost, the added expense of producing one more unit of output; marginal revenue, the increase in total revenue from selling one additional unit; and marginal product, the extra output generated by employing one more unit of an input such as labor or capital.^[13]^[14] These concepts guide firms in optimizing resource allocation and output levels. The importance of marginal analysis lies in its role in rational decision-making, where economic agents compare marginal benefits against marginal costs to identify optimal choices.^[15] For producers, this means expanding output until marginal revenue equals marginal cost, maximizing profit; for consumers, it involves allocating spending to equate marginal utility per dollar across goods.^[6] By focusing on incremental trade-offs, it ensures decisions enhance net gains without relying on holistic aggregates. In contrast to average measures, which divide totals by quantity to yield per-unit summaries (e.g., average cost as total cost divided by output), or total measures that capture overall magnitudes, marginal analysis is crucial for optimization because it reveals the tipping point for actions.^[16] Average metrics can mislead by smoothing variations, whereas marginal ones pinpoint when benefits cease to outweigh costs—such as halting consumption precisely when marginal utility aligns with price, avoiding over- or under-allocation.^[13] Early economic thought incorporated marginal concepts implicitly, particularly in classical analyses of resource distribution. For instance, David Ricardo's theory of rent treated the productivity of the least fertile "marginal land" as the benchmark, with rents on more productive inframarginal lands arising from their surplus output relative to this margin. Such uses highlighted incremental differences without fully systematizing the marginal approach that later became central to economic theory.^[17]

Key Principles

Law of Diminishing Marginal Utility

The law of diminishing marginal utility states that, all else being equal (ceteris paribus), the additional satisfaction or utility derived from consuming successive units of a good or service decreases as the total quantity consumed increases.^[18] This principle posits that the marginal utility of the first unit is typically the highest, with each subsequent unit providing progressively less incremental benefit until satiation is approached or reached.^[19] Psychologically, this law arises from satiation effects, where repeated consumption reduces the perceived value or pleasure from additional units due to physiological limits or habituation.^[20] Empirically, it is supported by behavioral observations and introspective reports, such as individuals deriving greater satisfaction from the first few bites of food when hungry compared to later ones, reflecting a natural tapering of desire.^[21] Graphically, the marginal utility curve is represented as downward-sloping, starting high on the vertical axis (utility) and declining as quantity consumed increases along the horizontal axis, illustrating the progressive reduction in added value per unit.^[6] This diminishing pattern has key implications for consumer behavior, as individuals will only purchase additional units if the price falls to match the lower marginal utility, resulting in a negatively sloped demand curve at the individual level.^[22] For instance, a thirsty person experiences high marginal utility from the first glass of water but far less from the tenth, leading to reduced willingness to pay for extras; this dynamic also helps illustrate the diamond-water paradox, where water's abundant supply yields low marginal utility despite high total utility, while diamonds command high prices due to scarcity-driven high marginal utility.^[21] However, behavioral economics highlights that in addiction, individuals may continue consuming even when marginal utility is low or negative due to time-inconsistent preferences, such as hyperbolic discounting, although the law of diminishing marginal utility generally holds for successive units.^[23]

Diamond-Water Paradox

The diamond-water paradox, also known as the paradox of value, questions why water, which is essential for human survival and provides immense total utility, is typically cheap, while diamonds, which offer little practical use, command high prices. This puzzle was articulated by Adam Smith in his seminal work An Inquiry into the Nature and Causes of the Wealth of Nations (1776), where he distinguished between "value in use" (utility derived from consumption) and "value in exchange" (market price). Smith illustrated the contradiction by noting that "nothing is more useful than water: but it will purchase scarce any thing," whereas "a diamond... has scarce any value in use; but a very great quantity of other goods may frequently be had in exchange for it." He attributed this to factors like scarcity and labor costs but could not fully resolve it under his labor theory of value, which emphasized production effort over consumer perception.^[24] The paradox was resolved in the late 19th century through the development of marginal utility theory by economists William Stanley Jevons, Carl Menger, and Léon Walras during the Marginal Revolution. Under this framework, value is determined not by total utility—the overall benefit from all units of a good—but by marginal utility, the additional satisfaction from consuming one more unit. Water has high total utility due to its necessity but low marginal utility in most contexts because it is abundant, making additional units less valuable. Conversely, diamonds have low total utility but high marginal utility due to their scarcity, where each additional diamond provides significant incremental benefit to the consumer. This relies on the law of diminishing marginal utility, where the value of successive units decreases as quantity increases. Jevons formalized this in The Theory of Political Economy (1871), arguing that utility "varies with the quantity of commodity, and ultimately decreases as the quantity increases." Similarly, Menger in Principles of Economics (1871) emphasized subjective valuation based on individual needs and scarcity. To illustrate, consider a hypothetical scenario in a desert where water is scarce: the first cup provides life-saving utility (high marginal utility, perhaps worth a fortune), the second adds substantial relief, but further cups yield diminishing returns until abundance lowers the value of additional units to near zero. In a modern city with plentiful water supply, even the first extra glass after daily needs offers little incremental benefit, aligning with low market prices. For diamonds, scarcity drives high marginal utility; in a world with few available, acquiring one more—whether for adornment or status—carries substantial subjective value, justifying elevated exchange prices despite limited total utility. These schedules highlight how abundance flattens the marginal utility curve for water, while rarity steepens it for diamonds.^[25] The paradox exposed limitations in the classical labor theory of value, which struggled to explain exchange values disconnected from production costs or total usefulness, as seen in Smith's own analysis. It paved the way for the subjective theory of value, central to neoclassical economics, by shifting focus to individual preferences and marginal increments rather than objective labor inputs. Menger's contributions, in particular, underscored that value emerges from human judgments of scarcity relative to needs, influencing the broader Austrian school and challenging cost-based theories.^[26]^[27] In modern environmental economics, the paradox informs water pricing strategies amid scarcity, emphasizing that undervaluing water's marginal utility in arid regions leads to overuse and depletion. For instance, in drought-prone areas, policies adjust prices to reflect higher marginal value during shortages, promoting conservation and equitable allocation. A World Wildlife Fund report highlights how treating water as "cheap" ignores its ecosystem and health benefits, advocating multidimensional pricing to capture true scarcity costs. Academic analyses further apply this to resource management, where full-cost recovery pricing balances supply reliability with demand constraints in water-scarce basins.^[28]^[29]

Theoretical Framework

Marginalist Theory

The marginalist theory asserts that the value of a good derives from its marginal utility—the additional satisfaction derived from consuming one more unit—rather than from intrinsic properties or the amount of labor embodied in production. This subjective valuation forms the core tenet, emphasizing that economic decisions hinge on incremental changes at the margin. Equilibrium in exchange arises when consumers allocate resources such that the marginal utilities of different goods are proportional to their prices, ensuring optimal satisfaction under budget constraints.^[30] Key components of the theory include consumer equilibrium, achieved when the ratio of marginal utility to price is equal across all goods, expressed as \frac{MU_x}{P_x} = \frac{MU_y}{P_y} = \lambda, where \lambda represents the marginal utility of income. For producers, equilibrium occurs at the point where marginal cost equals marginal revenue, maximizing profit by balancing the additional cost of production with the additional revenue from selling one more unit. These principles rely on the assumption of diminishing marginal utility, where each additional unit provides less satisfaction than the previous one.^[30]^[31] Marginalist theory marked a fundamental shift from classical economics, rejecting cost-of-production theories like the labor theory of value in favor of demand-side explanations rooted in individual preferences and subjective scarcity. This pivot redirected economic analysis toward how consumers' valuations drive resource allocation, rather than focusing solely on supply factors.^[30] In applications, marginalism underpins general equilibrium theory, where interconnected markets achieve balance through successive marginal adjustments in prices and quantities, coordinating supply and demand across the economy. The theory's influence extends to modern economics as the bedrock of microeconomics, providing analytical frameworks for studying efficiency, resource distribution, and policy impacts in welfare economics.^[32]

Price Determination

In market economies, prices emerge as the outcome of consumers seeking to equalize the marginal utility per dollar spent across different goods, ensuring that the additional satisfaction from the last unit purchased of each good is proportional to its cost. This consumer optimization leads to individual demand schedules where the quantity demanded decreases as price rises, reflecting the law of diminishing marginal utility. Aggregating these individual schedules across consumers forms the market demand curve, which slopes downward because marginal utility decreases as the quantity consumed increases, leading to lower willingness to pay at greater quantities.^[33] On the supply side, producers respond to prices by equating them to their marginal costs, the additional expense of producing one more unit, generating an upward-sloping supply curve that reflects increasing production costs. Market equilibrium occurs where this supply curve intersects the demand curve, balancing the quantity supplied with the quantity demanded at a price where marginal utility-derived willingness to pay equals marginal cost. At this equilibrium, consumer surplus—the difference between what consumers are willing to pay (based on total utility) and what they actually pay—represents the net benefit to buyers above the market price, while producer surplus captures the net gain to sellers below the price they receive, together maximizing total economic welfare under competitive conditions.^[33]^[18] Scarcity plays a key role in elevating marginal utility and thus prices; for instance, a rare piece of art commands a high price because its limited availability heightens the additional satisfaction it provides to the marginal buyer, whereas abundant common bread yields low marginal utility and a correspondingly low price due to plentiful supply reducing its perceived value per unit. This dynamic underscores how relative scarcity drives price differences for goods with similar total utility potential.^[18] Empirical evidence from auction markets supports this framework, as bidders' willingness to pay—directly tied to the marginal utility of acquiring the item—reveals demand schedules through escalating bids until equilibrium is reached with the highest valuation. Studies on willingness to pay in experimental and real-world settings, such as transportation improvements, confirm that consumers' bids align with diminishing marginal utility, providing measurable validation of how individual valuations aggregate to influence market prices.^[34]^[35]

Limitations of Marginalism

Marginal utility theory, a cornerstone of neoclassical economics, relies on several key assumptions that have faced significant critique from behavioral economics. Chief among these is the postulate of perfect rationality, where individuals are presumed to make consistent, utility-maximizing choices based on complete information and stable preferences. However, prospect theory, developed by Daniel Kahneman and Amos Tversky, demonstrates that decision-making under risk deviates from this model, with individuals exhibiting loss aversion—valuing losses more than equivalent gains—and reference-dependent preferences that violate the stability assumption.^[36] Furthermore, the measurability of utility, central to marginalist analysis, is challenged by evidence of inconsistent rankings and context-dependent valuations, undermining the theory's foundational interpersonal comparisons. Empirical applications of marginal utility reveal further inconsistencies, particularly through the lens of revealed preference theory, which infers preferences from observed choices. Studies show that choices often fail to satisfy the axioms of revealed preference, such as the weak axiom, due to dynamic inconsistencies where past decisions do not predict future behavior under changing circumstances.^[37] This is especially pronounced in contexts like public goods and externalities, where marginal utility is difficult to observe directly because individual contributions cannot be isolated from collective outcomes, leading to free-rider problems and market failures that marginalist models struggle to predict accurately.^[38] Marginalism also exhibits institutional blind spots by overlooking power dynamics, advertising influences, and historical contexts that shape pricing and consumption. Critics argue that the theory treats markets as atomistic and equilibrium-driven, ignoring how monopolistic structures or asymmetric information—exacerbated by advertising—distort marginal utility calculations and lead to non-competitive outcomes.^[39] For instance, advertising can artificially inflate perceived marginal utility without corresponding changes in underlying preferences, a factor absent from standard marginalist frameworks.^[40] Recent advancements attempt to address these limitations through integration with neuroscience and considerations of incomplete markets. Functional magnetic resonance imaging (fMRI) studies have shown that brain activity in regions like the dorsal striatum encodes marginal utility, providing neural correlates that validate diminishing returns at a biological level while highlighting deviations from rational choice predictions. In incomplete markets, where assets or information are not fully tradable, marginal utility equalization across agents becomes infeasible, prompting extensions like stochastic models that incorporate uncertainty but reveal the theory's inadequacy in non-Walrasian settings. As alternatives, institutional economics emphasizes evolving social norms and habits over static marginal calculations, critiquing marginalism for its ahistorical individualism, while post-Keynesian approaches highlight fundamental uncertainty and effective demand, arguing that marginal utility cannot reliably determine prices in capitalist economies prone to instability.^[41]^[42]

Formalization

Quantifying Marginal Utility

Quantifying marginal utility involves empirical methods to approximate the additional satisfaction derived from consuming one more unit of a good or service, despite the inherent subjectivity of utility. Economists employ various techniques to infer marginal utility, often through observable behaviors or stated preferences, as direct introspection is unreliable. These approaches distinguish between cardinal utility, which assigns numerical values, and ordinal utility, which ranks preferences without magnitudes. Measurement techniques for marginal utility include surveys assessing willingness-to-pay (WTP), where individuals state the maximum price they would pay for an additional unit, providing an estimate of its marginal value. Revealed preference methods analyze market data, such as consumer choices and expenditure patterns, to infer marginal utility from actual behaviors under budget constraints, as pioneered by Paul Samuelson in his foundational work on observable demand. Experimental economics uses controlled lab settings, like auctions or trading games, to elicit marginal utilities through participants' decisions, revealing preferences in simulated markets.^[43] Cardinal approaches attempt to assign numerical "utils" to marginal utility, most notably through von Neumann-Morgenstern expected utility theory, which scales utility based on choices under risk, such as lottery preferences, to create an interpersonally comparable measure up to affine transformations. This method operationalizes marginal utility by equating it to the change in expected utility from marginal consumption increments. Ordinal approximations avoid numerical assignment by using indifference curve analysis, where the slope of the curve at a point represents the marginal rate of substitution (MRS), indicating the rate at which a consumer is willing to trade one good for another while maintaining constant total utility. This infers diminishing marginal utility from the convex shape of indifference curves, reflecting trade-offs without quantifying absolute levels. Challenges in quantifying marginal utility include interpersonal comparability, as utilities are subjective and cannot be directly compared across individuals without ethical or empirical assumptions, complicating aggregation for social welfare. Subjectivity and context-dependence further hinder measurement, as preferences vary with framing, mood, or cultural factors, leading to inconsistencies between stated and revealed preferences.^[44] In applications, such as cost-benefit analysis for policy, marginal utility quantification values environmental goods like clean air through contingent valuation surveys, estimating societal willingness-to-pay to inform regulations on pollution or conservation. These methods adjust for income distribution by incorporating diminishing marginal utility of income, ensuring equitable weighting in public decisions.

Mathematical Models

Marginal utility is formally defined as the change in total utility derived from consuming an additional unit of a good or service, expressed mathematically as MU = \frac{\Delta TU}{\Delta Q}, where TU represents total utility and Q is the quantity consumed.^[45] This discrete formulation approximates the partial derivative MU_x = \frac{\partial U}{\partial x} in continuous models, capturing the incremental satisfaction from one more unit of good x.^[46] In consumer optimization, individuals maximize utility subject to a budget constraint. The Lagrangian function for this problem is \mathcal{L} = U(x, y) + \lambda (I - p_x x - p_y y), where U(x, y) is the utility function, I is income, p_x and p_y are prices, and \lambda is the Lagrange multiplier.^[47] The first-order conditions yield \frac{\partial U}{\partial x} = \lambda p_x and \frac{\partial U}{\partial y} = \lambda p_y, implying \frac{MU_x}{p_x} = \frac{MU_y}{p_y} = \lambda, where \lambda represents the marginal utility of income.^[48] This equi-marginal principle ensures optimal allocation by equalizing the utility per dollar spent across goods. The law of diminishing marginal utility underpins the concavity of the utility function, ensuring interior solutions.^[49] From the optimization condition MU_x = \lambda p_x, and given \lambda as the marginal utility of income, the demand for good x emerges when MU_x = p_x in equilibrium for a representative consumer.^[50] As price p_x varies, the quantity demanded adjusts such that marginal utility equals price, tracing out an individual demand curve. Aggregating across consumers yields the market demand function, reflecting collective marginal utilities.^[49] Indifference curve analysis formalizes trade-offs between goods. The marginal rate of substitution (MRS), which measures the rate at which a consumer is willing to substitute one good for another while maintaining constant utility, is given by MRS_{xy} = -\frac{MU_x}{MU_y} = -\frac{\partial U / \partial x}{\partial U / \partial y}.^[51] This ratio equals the slope of the indifference curve and declines along the curve due to diminishing marginal utilities, ensuring convexity.^[52] An advanced example is the Cobb-Douglas utility function U(x, y) = x^a y^b, where a > 0, b > 0, and often a + b = 1 for constant returns. The marginal utility of x is MU_x = a \frac{U}{x} = a x^{a-1} y^b, illustrating diminishing marginal utility as MU_x decreases with higher x.^[53] Similarly, MU_y = b x^a y^{b-1}, and the MRS simplifies to MRS_{xy} = \frac{a}{b} \frac{y}{x}.^[54] This functional form is widely used for its tractability in deriving demand functions proportional to income shares.^[53]

Historical Development

Precursors

Early economic thought contained nascent ideas that foreshadowed the concept of marginal utility, though these were often embedded within broader discussions of value and exchange rather than forming a coherent theory. In ancient Greece, Aristotle distinguished between use value—the practical utility of a good for satisfying needs—and exchange value, which arises from trading goods in markets to obtain what one lacks.^[55] This differentiation, articulated in his Nicomachean Ethics (Book V) and Politics (Book I), recognized that a good's worth in use could differ markedly from its market price, laying a conceptual groundwork for later utility-based analyses, albeit without quantifying incremental satisfaction. Medieval scholastic economists built on Aristotelian foundations, particularly in debates over equitable exchange. Thomas Aquinas, in his Summa Theologica (II-II, Q. 77), developed the notion of the "just price" as one that reflects the good's intrinsic worth based on its usefulness and the labor or costs involved in production, ensuring fairness in transactions without exploitation.^[56] Aquinas argued that prices should align with communal needs and moral equity, hinting at utility's role in valuation but tying it more to total production costs than to individual increments of satisfaction.^[57] Among classical economists, Adam Smith primarily adhered to a labor theory of value in An Inquiry into the Nature and Causes of the Wealth of Nations (1776), positing that a good's exchange value derives from the labor required to produce it.^[58] However, Smith introduced demand-side considerations through the famous diamond-water paradox, observing that water, essential for life and thus high in use value, commands a low market price due to its abundance, while diamonds, of lesser practical utility, fetch high prices from scarcity and desire.^[25] This highlighted a tension between total utility and exchange value, suggesting an intuitive grasp of how abundance diminishes perceived worth, though Smith did not formalize it as marginal increments. Nassau William Senior extended such ideas in An Outline of the Science of Political Economy (1836), where his "abstinence theory" of capital and interest implied that the utility of goods diminishes with increased supply, as additional units provide less satisfaction relative to the sacrifices of forgoing consumption.^[59] In the early 19th century, mathematicians and economists began incorporating marginal concepts more explicitly. Antoine Augustin Cournot, in Researches into the Mathematical Principles of the Theory of Wealth (1838), analyzed firm behavior in oligopoly using marginal revenue and marginal cost equalization for profit maximization, laying groundwork for marginal analysis on the supply side without directly addressing consumer utility.^[60] Jules Dupuit advanced demand-side insights in his 1844 essay on taxation and public works, introducing the concept of consumer surplus and recognizing that the utility of additional units of a good (e.g., water or bridges) diminishes, with value determined by the maximum willingness to pay for marginal units.^[61] Hermann Heinrich Gossen provided one of the most direct precursors in The Laws of Human Relations (1854), formulating the first law of diminishing marginal utility—where successive units yield progressively less satisfaction—and the second law of equimarginal utility for optimal resource allocation across goods.^[2] In the 18th century, further proto-marginalist insights emerged in addressing specific puzzles. Daniel Bernoulli, in his 1738 paper "Exposition of a New Theory on the Measurement of Risk," resolved the St. Petersburg paradox—a gambling scenario with infinite expected monetary value but finite willingness to pay—by proposing that the utility of wealth increases at a decreasing rate, often modeled logarithmically, so marginal gains in wealth yield progressively less additional satisfaction.^[62] This introduced a subjective, diminishing utility function for wealth, applied to decision-making under uncertainty, though it remained focused on total rather than unit-by-unit analysis. Similarly, Anne Robert Jacques Turgot, in Reflections on the Formation and Distribution of Riches (1766), advanced a subjective theory of value emphasizing utility and scarcity, arguing that a good's worth stems from its ability to satisfy wants, with prices equilibrating based on consumers' estimations of usefulness rather than solely labor or production.^[63] Despite these contributions, ideas on utility prior to the 1870s were limited by their emphasis on total or average satisfaction rather than a systematic framework for marginal increments, lacking integration into price determination or consumer behavior. Key texts like Aristotle's ethical treatises, Aquinas's theological summas, Smith's Wealth of Nations, Senior's Outline, Bernoulli's risk essay, Turgot's Reflections, Cournot's Researches, Dupuit's essays, and Gossen's Laws offered scattered insights into value's subjective dimensions but stopped short of a comprehensive marginal approach.

Marginal Revolution

The Marginal Revolution refers to the pivotal intellectual transformation in economic thought during the early 1870s, marked by the independent development of marginal utility theory by several economists who shifted the focus from objective cost-based explanations of value to subjective, incremental assessments of utility. This revolution emerged amid growing dissatisfaction with classical economics' labor and cost-of-production theories, particularly in explaining paradoxes like the diamond-water puzzle, and coincided with economic turbulence including the onset of the Long Depression in 1873.^[64]^[65] The core publications appeared between 1871 and 1874, laying the groundwork for modern microeconomics by emphasizing how value derives from the additional satisfaction (marginal utility) gained from the last unit of a good consumed. Central to this shift were three key figures whose near-simultaneous works formalized marginal utility as the determinant of economic value. Carl Menger, an Austrian economist, published Grundsätze der Volkswirtschaftslehre (Principles of Economics) in 1871, introducing a subjective theory of value where the worth of goods stems from individuals' personal valuations based on their ability to satisfy needs, diminishing with additional units due to marginal utility. William Stanley Jevons, from England, released The Theory of Political Economy the same year, defining utility in mathematical terms and coining the "final degree of utility" to describe the marginal increment of satisfaction from consuming one more unit of a commodity, which decreases as consumption rises. Léon Walras, a French-Swiss economist, contributed Éléments d'économie politique pure (Elements of Pure Economics) in 1874, integrating marginal utility into a system of general equilibrium where prices adjust across all markets to equate supply and demand, ensuring that marginal utilities per unit of expenditure are equalized for consumers.^[66]^[67]^[68] These ideas spread rapidly through distinct schools of thought, fostering a global dialogue that reshaped economics. Menger's work founded the Austrian School, emphasizing methodological individualism and subjective valuation without heavy reliance on mathematics. Jevons influenced the English (or Cambridge) School, later advanced by Alfred Marshall, who blended marginalism with partial equilibrium analysis. Walras established the Lausanne School, focusing on mathematical general equilibrium models, with successors like Vilfredo Pareto refining them. The dissemination was aided by academic journals, such as the Economic Journal launched in 1891, which published translations, reviews, and debates, facilitating the exchange of ideas across linguistic and national boundaries.^[69]^[70] The immediate impact of the Marginal Revolution was profound, effectively overthrowing the classical cost-of-production theories—such as the labor theory of value championed by Adam Smith and David Ricardo—by demonstrating that prices are determined by subjective marginal utilities rather than production inputs alone. By the 1890s, marginalist principles had permeated mainstream economics, appearing in influential textbooks like Marshall's Principles of Economics (1890), which synthesized and popularized the approach for a broader audience and solidified its role as the foundation of neoclassical economics.^[71]^[72]

Post-Revolution Evolution

Following the Marginal Revolution, the second generation of economists refined marginal utility theory by integrating it with classical elements. Alfred Marshall's Principles of Economics (1890) synthesized marginal utility with supply-side costs of production, emphasizing that market prices equilibrate at the intersection of marginal utility-derived demand and marginal cost-derived supply, thus bridging subjective value with objective production factors.^[73]^[74] Concurrently, Philip Wicksteed advanced marginal productivity theory in The Common Sense of Political Economy (1910), arguing that factor incomes, including wages and rents, are determined by the marginal contribution of each input to total output, extending marginal utility principles to distribution.^[75]^[76] Reformulations in the early 20th century shifted marginal utility toward ordinalism, reducing reliance on cardinal measurement. Vilfredo Pareto's Manual of Political Economy (1906) introduced ordinal utility, positing that consumer preferences could be ranked without quantifying utility levels, thereby abandoning the assumption of interpersonal comparability and intercardinal measurability central to earlier marginalists.^[77] This ordinal approach influenced welfare economics by focusing on preference orderings for efficiency analysis. Irving Fisher, in works like Mathematical Investigations in the Theory of Value and Prices (1892) and later refinements, proposed a utility index to operationalize cardinal utility through observable choices and price data, aiming to make utility more empirically tractable via index number methods.^[78]^[79] Rivalries emerged between marginalism and alternative paradigms, particularly Marxism. Eugen von Böhm-Bawerk's Karl Marx and the Close of His System (1896) critiqued Marx's labor theory of value, arguing that it failed to explain exchange values and profits, as marginal utility better accounted for subjective valuations and time preferences in production. The Austrian school, building on this, emphasized methodological individualism, insisting that economic phenomena arise from individual purposeful actions rather than aggregate or class-based forces, reinforcing marginal utility's subjectivist core against holistic theories.^[80]^[81] Marginal utility experienced revival and mainstreaming in the 1930s through the neoclassical synthesis, which integrated it with Keynesian macroeconomics while retaining microfoundations in utility maximization.^[82] Lionel Robbins' An Essay on the Nature and Significance of Economic Science (1932) redefined economics as the study of human behavior under scarcity, aligning marginal utility with resource allocation choices and solidifying its role in positive economic analysis. Twentieth-century extensions challenged and adapted marginal utility. Paul Samuelson's revealed preference theory (1948) offered a non-utility-based alternative, deriving demand consistency from observed choices without assuming underlying utility functions, thus providing an axiomatic foundation for consumer theory that bypassed cardinal or ordinal utility measurement.^[83] Post-1970s behavioral economics critiques, led by figures like Daniel Kahneman and Amos Tversky, highlighted violations of marginal utility assumptions, such as diminishing sensitivity and rationality in prospect theory, revealing how cognitive biases undermine the theory's predictive power in real decision-making.^[84]^[85]

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[PDF] The Principles of Economics - UT liberal arts
And. thus the law just given may be worded:- The marginal utility of a thing to anyone diminishes with every increase in. the amount of it he already has.(2*) ...
[19]
2.3 Utility - Front Matter
Assumption A4 (Diminishing Marginal Utility): As the number of units consumed increases, additional units add less and less consumer satisfaction.
[20]
[PDF] Determinants of Experienced Utility: Laws and Implications
The concept of diminishing marginal utility has been a corner-stone of theories both in economics and psychology. Satiation carries the principle of diminishing ...
[21]
Theory of Demand
Utility is a term applied by economists to the benefits or satisfaction obtained from a good or service (also from a particular course of action). Utility ...
[22]
[PDF] Consumer Choice: the Demand Side of the Market - CSUN
The optimal purchase rule for more than 1 good is to set the ratio of marginal utility (MU) to the price (P) of the good equal for every good purchased. The ...Missing: optimization | Show results with:optimization
[23]
An Inquiry Into the Nature and Causes of the Wealth of Nations (Cannan ed.), vol. 1 | Online Library of Liberty
### Summary of Relevant Content
[24]
The Value of Diamonds and Water Paradox - Investopedia
He described this problem in The Wealth of Nations by comparing the high value of a diamond, which is unessential to human life, to the low value of water, ...Missing: origin | Show results with:origin
[25]
The value of value theory for ecological economics - PMC
Aug 25, 2020 · “The classical economists, such as Smith and Ricardo, could not resolve it [the diamond-water paradox] using their labor theories of value.
[26]
Adam Smith and the Austrian School of Economics - ResearchGate
While Adam Smith was not able to solve the value paradox, his – especially Austrian – successors developed theories of marginal utility and put the individual ...Missing: seminal | Show results with:seminal
[27]
https://www.researchgate.net/publication/331646692_Adam_Smith_and_the_Austrian_School_of_Economics_The_Problem_of_Diamonds_and_Water
[28]
The paradox of water pricing: dichotomies, dilemmas, and decisions
Jan 6, 2020 · The water pricing paradox is that water's price almost never equals its value and rarely covers its costs, due to its inability to be ...
[29]
Outline Nineteen - Marginal Revolution - Jevons, Menger and Walras
The diamond/water example we did earlier – can use water for very low valued uses, therefore, every marginal unit of water is valued as the least important ...
[30]
8.2 How Perfectly Competitive Firms Make Output Decisions
The profit-maximizing choice for a perfectly competitive firm will occur where marginal revenue is equal to marginal cost—that is, where MR = MC. A profit- ...
[31]
[PDF] Regulation and the Marginalist Revolution
The marginalist revolution in economics became the foundation for the modern regulatory State with its “mixed” economy. For the classical political economists, ...
[32]
[PDF] 14.01 F23 Full Lecture Summaries - MIT OpenCourseWare
Diminishing marginal utility of income means that the next dollar is worth less to you than the last one was in terms of happiness you gain. 9.1.2 Risk ...
[33]
[PDF] Measuring willingness to pay for transportation improvements
Jul 1, 1997 · Consumers' Willingness-to-Pay (WTP) for transportation improvements can be estimated by analyzing travel choices in real or hypothetical markets ...
[34]
[PDF] Marginal Utility and the Coase Theorem
When economic considerations such as efficiency are used to define the scope of pri- vate endowment, these endowments may as easily include the right to health ...
[35]
[PDF] Prospect Theory: An Analysis of Decision under Risk - MIT
BY DANIEL KAHNEMAN AND AMOS TVERSKY'. This paper presents a critique of expected utility theory as a descriptive model of decision making under risk, ...
[36]
[PDF] REVEALED MISTAKES AND REVEALED PREFERENCES
That is, there may be multiple natural theories of preferences and mistakes that can explain a person's revealed mistakes.
[37]
Revealed Preferences - an overview | ScienceDirect Topics
Revealed preference methods infer the trade-offs that people make between health and money indirectly by observing everyday behavior, such as when people accept ...<|control11|><|separator|>
[38]
Two Critics of Marginalist Theory: Piero Sraffa and John Maynard ...
The paper discusses the contributions of two major critics of marginalist theory: John Maynard Keynes and Piero Sraffa.
[39]
Marginalist Theory (Arguments for and against ... - Your Article Library
ADVERTISEMENTS: This led to a controversy for and against the neo-classical theory of the firm. There were economists like ...
[40]
Institutionalist Economics
Dec 18, 2016 · This text presents a perspective of Pluralist Economics. In the orientation section you can learn about and compare ten different perspectives of Pluralist ...Missing: advertising | Show results with:advertising<|control11|><|separator|>
[41]
[PDF] Post-Keynesian Institutionalism after the Great Recession
It explicitly offers PKI as an alternative to conventional economics and other economic paradigms. In particular, it describes PKI as holistic (in other words, ...
[42]
How Should Consumers' Willingness to Pay be Measured? An ...
This study compares the performance of four commonly used approaches to measure consumers' willingness to pay with real purchase data (REAL).<|control11|><|separator|>
[43]
[PDF] INTERPERSONAL COMPARISONS OF UTILITY - Stanford University
The main exception has been the almost certainly unethical comparisons that result from weighing all individuals' dollars equally.
[44]
Understanding Marginal Utility: Definition, Types, and Economic ...
Marginal utility is useful in explaining how consumers make choices to get the most benefit from their limited budgets. In general, people will continue ...What Is Marginal Utility? · How It Works · History · Marginal Utility vs. Total Utility
[45]
[PDF] Lecture 4 - Utility Maximization - MIT OpenCourseWare
This expression says that at the utility-maximizing point, the next dollar spent on each good yields the same marginal utility. thesis are zero. λ equals the “ ...
[46]
[PDF] economic applications of lagrange multipliers
Lagrange multipliers are used in economics for maximizing utility with wealth constraints, and as the rate of change of output with respect to a constraint. ...
[47]
[PDF] Utility Maximisation Problem - UCLA Economics
The price ratio equals the number of x2 the agent has to give up in order to get one more unit of x1 if she wishes to stay within her budget. If MRS > p1/p2, ...Missing: optimization | Show results with:optimization
[48]
5.1: The Demand Curve and Utility - Social Sci LibreTexts
Jul 17, 2023 · Marginal utility of a good or service is the gain from an increase or loss from a decrease in the consumption of that good or service. Learning ...
[49]
Deriving demand curve from tweaking marginal utility per dollar
Mar 23, 2014 · In this video, we derive the individual's demand curve for a good by tweaking the marginal utility per dollar spent.
[50]
MRS in Economics: What It Is and the Formula for Calculating It
The MRS, or marginal rate of substitution, represents how easy it is to replace one good with another and retain the same level of consumer satisfaction.Marginal Rate of Substitution... · Formula and Calculation · Example · MRS vs. MRT
[51]
[PDF] MARGINAL UTILITY AND MRS (detailed notes)
Definition: Marginal Utility (MU) - the change in utility associated with a small change in the amount of one of the goods consumed holding the quantity of the ...
[52]
4.11 The Cobb-Douglas Utility Function - EconGraphs
The Cobb-Douglas functional form was first proposed as a production function in a macroeconomic setting, but its mathematical properties are also useful as a ...
[53]
[PDF] Utility Maximization Steps
In this case the marginal rate of substitution for the Cobb-Douglas utility function is. MRS = ³ab´³yx´ regardless of the values of a and b. Solving the ...
[54]
Aristotle on Money - jstor
Aristotle's distinction between the two kinds of wealth is aligned, in turn, with the distinction between use value and exchange value (1257a6-13), which he ...
[55]
A Defense of a Thomistic Concept of the Just Price
Thomas Aquinas was one of the first scholastics to analyze the idea of a “just price,” economists, economic historians and philosophers inter- ested in the ...
[56]
The Concept of the Just Price: Theory and Economic Policy - jstor
Besides, Thomas Aquinas himself recognizes that the just price cannot be determined with precision, but can vary within a certain range, so that minor ...
[57]
nassau w. senior, british economist, in the
The marginal- utility theory of value is usually illustrated in modern textbooks on economics by references to the supposed thoughts and activities of ...
[58]
the St. Petersburg paradox - Stanford Encyclopedia of Philosophy
Jul 30, 2019 · As stressed by Cramér and Daniel Bernoulli, more money is always better than less, but the utility gained from each extra dollar is decreasing.The History of the St... · The Modern St. Petersburg... · Ignore Small Probabilities?
[59]
(PDF) Anne-Robert-Jacques Turgot (1727-1781) - ResearchGate
Sep 25, 2023 · Turgot developed instead a subjective theory of value, equilibrium prices and the interest rate, as well as a theory of capitalist ...<|control11|><|separator|>
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[PDF] Macroeconomic Crises since 1870 - Brookings Institution
ABSTRACT We build on Angus Maddison's data by assembling inter- national time series from before 1914 on real per capita personal consumer.Missing: catalysts | Show results with:catalysts
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The deflation of 1873-1896 - Marginal REVOLUTION
Aug 28, 2011 · I think its clear that deflation during this period was the result of rapid economic growth rather than a fall in the money supply or velocity.Missing: catalysts | Show results with:catalysts
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[PDF] PRINCIPLES OF ECONOMICS - Carl Menger - MIT
Erich Streissler, “To What Extent Was the Austrian School Marginalist?” The Marginalist. Revolution in Economics: Interpretation and Evolution ed. by R.D. ...
[63]
The Theory of Political Economy | Online Library of Liberty
In ordinary circumstances, too, the final degree of utility will not be great compared with what it might be. Only in famine or other extreme circumstances ...
[64]
Léon Walras | Marginal Utility, General Equilibrium & Mathematical ...
... (1874–77; Elements of Pure Economics) was one of the first comprehensive mathematical analyses of general economic equilibrium. Because Walras wrote in ...
[65]
HET: Phases of the Marginalist Revolution
The Cambridge Neoclassicals followed Marshall's approach, the Austrian School followed Menger Böhm-Bawerk and Wieser, while the Chicago School followed a ...
[66]
Austrian economics and its reception in different countries
Apr 20, 2018 · The Marginal revolution is traditionally divided into three different “schools” as follows: the Austrian school, the Lausanne school, and the “English” school.
[67]
The Marginal Revolution and the Birth of the Austrian School
Jul 14, 2020 · In the Marginal Revolution, economics abandoned the cost- of- production theory of value used by the classical economists in favor of the modern, marginal ...
[68]
[PDF] The 'Marginalist Revolution' in Historical Context
This understanding of social life as a derivative of the natural life of the species posed the context for the subsequent development of the classical tradition ...
[69]
Principles of Economics (8th ed.) | Online Library of Liberty
This is the 8th edition of what is regarded to be the first “modern” economics textbook, leading in various editions from the 19th into the 20th century.Missing: synthesis | Show results with:synthesis
[70]
MARSHALL'S PRINCIPLES AFTER ONE HUNDRED YEARS - jstor
of Marshall's book wholly be imputed to its powers of synthesis. Marshall succeeded to a degree in integrating marginal utility with the classical cost-of- ...
[71]
The Commonsense of Political Economy | Online Library of Liberty
Wicksteed substantively furthered the work of John Bates Clark on marginal productivity theory. Although Marshall's Principles generally receives more attention ...
[72]
THE CO-ORDINATION OF THE LAWS OF DISTRIBUTION
Wicksteed's classic work, The Co-ordination of the Laws of Distribution, has a central place within the development of marginal productivity theory.
[73]
Manual of Political Economy - Vilfredo Pareto - Oxford University Press
Free delivery 25-day returnsVilfredo Pareto's Manual of Political Economy is a classic study in the history of economic thought for many reasons.
[74]
[PDF] irving fisher, ragnar frisch, and the elusive quest for measurable utility
Fisher's candidate for such an index would be the Fisher ideal index, the geometric mean of the Paasche and Laspeyres indexes (Fisher 1922), which satisfied ...
[75]
IRVING FISHER AND INDEX NUMBER THEORY
May 10, 2013 · There are four main approaches to bilateral index number theory: the fixed basket, stochastic, test, and economic approaches.
[76]
Methodological Individualism - Stanford Encyclopedia of Philosophy
Feb 3, 2005 · It amounts to the claim that social phenomena must be explained by showing how they result from individual actions.Origins of the Doctrine · Austrian School and the... · Criticism
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[PDF] The Methodology of the Austrian School Economists - Mises Institute
Subjectivism has been, in short, the distinctive Method of the Austrian School economists. If the Austrians continue to stand apart from mainstream neoclassical.
[78]
Neoclassical Synthesis - an overview | ScienceDirect Topics
Walras, Jevons, and Menger thus are considered to be the leaders of the neoclassical or marginalist revolution, whose key elements are marginal utility (and ...
[79]
Consumption Theory in Terms of Revealed Preference - jstor
If the preference field has simple concavity, " indifference " will never explicitly reveal itself to us except as the results of an infinite limiting process.
[80]
Measuring Utility: From the Marginal Revolution to Behavioral ...
Measuring Utility tells the story of a fundamental problem in the history of economics that arose after the labor theory of value gave way to a theory that took ...
[81]
[PDF] Moscati, I. (2018). Measuring utility: From the marginal revolution to
Ivan Moscati has written a definitive treatment of the intellectual evolution of the measurement of utility from the mid-19th century to 1985.Missing: critiques post-