# Marginal utility theory (1870S)

Proposed in the late 19th century by the Marginalist group of economists, who used differential calculus to study the impact of small changes in economic quantities, marginal utility refers to the additional satisfaction a consumer derives from the consumption of one extra unit of a product.

Thus, an individual’s demand for a product is determined not by the total utility of it but by its marginal utility. Therefore, the greater the supply of a product, the smaller its marginal utility.

The Marginalists rejected the labor theory of value which had previously been central to classical economics.

Source:
R D Black, A W Coats and C D W Goodwin, The Marginal Revolution in Economics (Durham, NC, 1973)

## Marginality

The term marginal refers to a small change, starting from some baseline level. Philip Wicksteed explained the term as follows:

Marginal considerations are considerations which concern a slight increase or diminution of the stock of anything which we possess or are considering.[1]

Frequently the marginal change is assumed to start from the endowment, meaning the total resources available for consumption (see Budget constraint). 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 by the individual himself or herself and by others.

For reasons of tractability, it is often assumed in neoclassical analysis that goods and services are continuously divisible. Under this assumption, marginal concepts, including marginal utility, may be expressed in terms of differential calculus. Marginal utility can then be defined as the first derivative of total utility—the total satisfaction obtained from consumption of a good or service—with respect to the amount of consumption of that good or service.

In practice the smallest relevant division may be quite large. Sometimes economic analysis concerns the marginal values associated with a change of one unit of a discrete good or service, such as a motor vehicle or a haircut. For a motor vehicle, the total number of motor vehicles produced is large enough for a continuous assumption to be reasonable: this may not be true for, say, an aircraft carrier.

## Utility

Depending on which theory of utility is used, the interpretation of marginal utility can be meaningful or not. Economists have commonly described utility as if it were quantifiable, that is, as if different levels of utility could be compared along a numerical scale.[2][3] This has affected the development and reception of theories of marginal utility. Quantitative concepts of utility allow familiar arithmetic operations, and further assumptions of continuity and differentiability greatly increase tractability.

Contemporary mainstream economic theory frequently defers metaphysical questions, and merely notes or assumes that preference structures conforming to certain rules can be usefully proxied by associating goods, services, or their uses with quantities, and defines “utility” as such a quantification.[4]

Another conception is Benthamite philosophy, which equated usefulness with the production of pleasure and avoidance of pain,[5] assumed subject to arithmetic operation.[6] British economists, under the influence of this philosophy (especially by way of John Stuart Mill), viewed utility as “the feelings of pleasure and pain”[7] and further as a “quantity of feeling” (emphasis added).[8]

Though generally pursued outside of the mainstream methods, there are conceptions of utility that do not rely on quantification. For example, the Austrian school generally attributes value to the satisfaction of wants,[9][10][11] and sometimes rejects even the possibility of quantification.[12] It has been argued that the Austrian framework makes it possible to consider rational preferences that would otherwise be excluded.[10]

In any standard framework, the same object may have different marginal utilities for different people, reflecting different preferences or individual circumstances.[13]

## Diminishing marginal utility

The concept in cardinal utility theory that marginal utilities diminish across the ranges relevant to decision-making is called the “law of diminishing marginal utility” (and is also known as Gossen’s First Law). This refers to the increase in utility an individual gains from increasing their consumption of a particular good. “The law of diminishing marginal utility is at the heart of the explanation of numerous economic phenomena, including time preference and the value of goods … The law says, first, that the marginal utility of each homogenous unit decreases as the supply of units increases (and vice versa); second, that the marginal utility of a larger-sized unit is greater than the marginal utility of a smaller-sized unit (and vice versa). The first law denotes the law of diminishing marginal utility, the second law denotes the law of increasing total utility.”[14]

In modern economics, choice under conditions of certainty at a single point in time is modeled via ordinal utility, in which the numbers assigned to the utility of a particular circumstance of the individual have no meaning by themselves, but which of two alternative circumstances has higher utility is meaningful. With ordinal utility, a person’s preferences have no unique marginal utility, and thus whether or not marginal utility is diminishing is not meaningful. In contrast, the concept of diminishing marginal utility is meaningful in the context of cardinal utility, which in modern economics is used in analyzing intertemporal choice, choice under uncertainty, and social welfare.

The law of diminishing marginal utility is similar to the law of diminishing returns which states that as the amount of one factor of production increases as all other factors of production are held the same, the marginal return (extra output gained by adding an extra unit) decreases.

As the rate of commodity acquisition increases, marginal utility decreases. If commodity consumption continues to rise, marginal utility at some point may fall to zero, reaching maximum total utility. Further increase in the consumption of units of commodities causes the marginal utility to become negative; this signifies dissatisfaction. For example,

• beyond some point, further doses of antibiotics would kill no pathogens at all, and might even become harmful to the body.
• to satiate thirst a person drinks water but beyond a point, consumption of more water might make the person vomit, hence leading to negative marginal and thus diminished total utility
• it takes a certain amount of food energy to sustain a population, yet beyond a point, more calories cannot be consumed and are simply discarded (or cause disease).

Diminishing marginal utility is traditionally a microeconomic concept and often holds for an individual, although the marginal utility of a good or service might be increasing as well. For example:

• bed sheets, which up to some number may only provide warmth, but after that point may be useful to allow one to effect an escape by being tied together into a rope;
• tickets, for travel or theatre, where a second ticket might allow one to take a date on an otherwise uninteresting outing;
• dosages of antibiotics, where having too few pills would leave bacteria with greater resistance, but a full supply could effect a cure.
• the third leg is more useful than the first two when building a chair.

As suggested elsewhere in this article, occasionally one may come across a situation in which marginal utility increases even at a macroeconomic level. For example, the provision of a service may only be viable if it is accessible to most or all of the population, and the marginal utility of a raw material required to provide such a service will increase at the “tipping point” at which this occurs. This is similar to the position with very large items such as aircraft carriers: the numbers of these items involved are so small that marginal utility is no longer a helpful concept, as there is merely a simple “yes” or “no” decision.

## Marginalist theory

Marginalism explains choice with the hypothesis that people decide whether to effect any given change based on the marginal utility of that change, with rival alternatives being chosen based upon which has the greatest marginal utility.

### Market price and diminishing marginal utility

If an individual possesses a good or service whose marginal utility to him is less than that of some other good or service for which he could trade it, then it is in his interest to effect that trade. Of course, as one thing is sold and another is bought, the respective marginal gains or losses from further trades will change. If the marginal utility of one thing is diminishing, and the other is not increasing, all else being equal, an individual will demand an increasing ratio of that which is acquired to that which is sacrificed. One important way in which all else might not be equal is when the use of the one good or service complements that of the other. In such cases, exchange ratios might be constant.[10] If any trader can better his position by offering a trade more favorable to complementary traders, then he will do so.

In an economy with money, the marginal utility of a quantity is simply that of the best good or service that it could purchase. In this way it is useful for explaining supply and demand, as well as essential aspects of models of imperfect competition.