# ⓘ 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, u ..

## ⓘ Marginalism

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. 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 that of marginal utility, marginalists, following the lead of Alfred Marshall, drew upon the idea of marginal physical productivity in explanation of cost. The neoclassical tradition that emerged from British marginalism abandoned the concept of utility and gave marginal rates of substitution a more fundamental role in analysis. Marginalism is an integral part of mainstream economic theory.

### 1.1. Important marginal concepts Marginality

For issues of marginality, constraints are conceptualized as a border or margin. The location of the margin for any individual corresponds to his or her 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.

### 1.2. Important marginal concepts 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.

### 1.3. Important marginal concepts Marginal utility

The marginal utility of a good or service is the utility of its marginal use. Under the assumption of economic rationality, it is the utility of its least urgent possible use from the best feasible combination of actions in which its use is included.

In 20th century mainstream economics, the term "utility" has come to be formally defined as a quantification capturing preferences by assigning greater quantities to states, goods, services, or applications that are of higher priority. But marginalism and the concept of marginal utility predate the establishment of this convention within economics. The more general conception of utility is that of use or usefulness, and this conception is at the heart of marginalism; the term "marginal utility" arose from translation of the German "Grenznutzen", 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.

### 1.4. Important marginal concepts 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

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.}}}

is well defined, and use" marginal utility” to refer to a partial derivative

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

### 1.5. Important marginal concepts Law of diminishing marginal utility

The law of diminishing marginal utility, also known as a Gossens 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.

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

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

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