# ⓘ Marginal utility. In economics, utility is the satisfaction or benefit derived by consuming a product; thus the marginal utility of a good or service is the cha ..

## ⓘ Marginal utility

In economics, utility is the satisfaction or benefit derived by consuming a product; thus the marginal utility of a good or service is the change in the utility from an increase in the consumption of that good or service.

In the context of cardinal utility, economists sometimes speak of a law of diminishing marginal utility, meaning that the first unit of consumption of a good or service yields more utility than the second and subsequent units, with a continuing reduction for greater amounts. Therefore, the fall in marginal utility as consumption increases is known as diminishing marginal utility. This concept is used by economists to determine how much of a good is a consumer willing to purchase.

## 1. 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.

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.

## 2. 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. 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.

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

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, and sometimes rejects even the possibility of quantification. It has been argued that the Austrian framework makes it possible to consider rational preferences that would otherwise be excluded.

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

## 3. 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 Gossens 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."

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 persons 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:

• tickets, for travel or theatre, where a second ticket might allow one to take a date on an otherwise uninteresting outing;
• 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;
• the third leg is more useful than the first two when building a chair.
• dosages of antibiotics, where having too few pills would leave bacteria with greater resistance, but a full supply could effect a cure.

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.

## 4. 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.

### 4.1. Marginalist theory 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. 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.

### 4.2. Marginalist theory Paradox of water and diamonds

The "paradox of water and diamonds", usually most commonly associated with Adam Smith, though recognized by earlier thinkers, is the apparent contradiction that water possesses a value far lower than diamonds, even though water is far more vital to a human being.

Price is determined by both marginal utility and marginal cost, and here the key to the "paradox" is that the marginal cost of water is far lower than that of diamonds.

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.

## 5. Quantified marginal utility

Under the special case in which usefulness can be quantified, the change in utility of moving from state S 1 {\displaystyle S_{1}} to state S 2 {\displaystyle S_{2}} is

Δ U = U S 2 − U S 1 {\displaystyle \Delta U=US_{2}-US_{1}\,}

Moreover, if S 1 {\displaystyle S_{1}} and S 2 {\displaystyle S_{2}} are distinguishable by values of just one variable g {\displaystyle g\,} which is itself quantified, then it becomes possible to speak of the ratio of the marginal utility of the change in g {\displaystyle g\,} to the size of that change:

Δ U Δ g | c. p. {\displaystyle \left.{\frac {\Delta U}{\Delta g}}\right|_{c.p.}}

where" c.p.” indicates that the only independent variable to change is g {\displaystyle g\,}.

Mainstream neoclassical economics will typically assume that the limit

lim Δ g → 0 Δ U Δ g | c. p. {\displaystyle \lim _{\Delta g\to 0}\left.{\frac {\Delta U}{\Delta g}}\right|_{c.p.}}

exists, and use" marginal utility” to refer to the partial derivative

∂ U ∂ g = lim Δ g → 0 Δ U Δ g | c. p. {\displaystyle {\frac {\partial U}{\partial g}}=\lim _{\Delta g\to 0}\left.{\frac {\Delta U}{\Delta g}}\right|_{c.p.}}.

Accordingly, diminishing marginal utility corresponds to the condition

∂ 2 U ∂ g 2 < 0 {\displaystyle {\frac {\partial ^{2}U}{\partial g^{2}}}

• the value of goods and services by reference to their secondary, or marginal utility The reason why the price of diamonds is higher than that of water
• terms of marginal utility and related concepts: Marginal utility Marginal Revolution Marginalism Marginal Revolution Marginal Revolution, an economics
• level of utility At equilibrium consumption levels assuming no externalities marginal rates of substitution are identical. The marginal rate of substitution
• response to a given decrease. In other words, marginal utility is the utility of the marginal use. The marginal rate of substitution is the rate of substitution
• demand Marginal product Marginal product of labor Marginal propensity to consume Marginal rate of substitution Marginal use Marginal utility Marginal rate
• about the origin. The utility function is concave in the positive region, reflecting the phenomenon of diminishing marginal utility The boundedness reflects
• diminishing marginal utility will obtain. The Austrian School of economics explicitly arrives at its conception of marginal utility as the utility of the marginal
• we call the final utility According to the law of marginal utility the value of each good in a stock of identical goods is utility of the last and most
• positive marginal utility for the goods you are essentially climbing a mound of utility The higher you go the greater the level of utility The non - satiation
• expenditures such that the ratio of the marginal utility of each good or service to its price the marginal expenditure necessary for its acquisition
• which case there is often said to be diminishing marginal utility Thus the use of cardinal utility imposes the assumption that levels of absolute satisfaction