# Marginal value

A marginal value is

1. a value that holds true given particular constraints,
2. the change in a value associated with a specific change in some independent variable, whether it be of that variable or of a dependent variable, or
3. [when underlying values are quantified] the ratio of the change of a dependent variable to that of the independent variable.

(This third case is actual a special case of the second).

In the case of differentiability, at the limit, a marginal change is a mathematical differential, or the corresponding mathematical derivative.

These uses of the term “marginal” are especially common in economics, and result from conceptualizing constraints as borders or as margins.[1] The sorts of marginal values most common to economic analysis are those associated with unit changes of resources and, in mainstream economics, those associated with instantaneous changes. Marginal values associated with units are considered because many decisions are made by unit, and marginalism explains unit price in terms of such marginal values. Mainstream economics uses instantaneous values in much of its analysis for reasons of mathematical tractability.

## Quantified conception

Assume a functional relationship

$y=f\left(x_1 ,x_2 ,\ldots,x_n \right)$

### Discrete change

If the value of xi is discretely changed from xi,0 to xi,1 while other independent variables remain unchanged, then the marginal value of the change in xi is

Δxi = xi,1xi,0

and the “marginal value” of y may refer to

$\Delta y=f\left(x_1 ,x_2 ,\ldots ,x_{i,1},\ldots,x_n \right)-f\left(x_1 ,x_2 ,\ldots ,x_{i,0},\ldots,x_n \right)$

or to

$\frac{\Delta y}{\Delta x}=\frac{f\left(x_1 ,x_2 ,\ldots ,x_{i,1},\ldots,x_n \right)-f\left(x_1 ,x_2 ,\ldots ,x_{i,0},\ldots,x_n \right)}{x_{i,1}-x_{i,0}}$

#### Example

If an individual saw her income increase from $50000 to$55000 per annum, and part of her response was to increase yearly purchases of amontillado from 2 casks to three casks, then

• the marginal increase in her income was $5000 • the marginal effect on her purchase of amontillado was an increase of 1 cask, or of 1 cask per$5000.

### Instantaneous margins

If instantaneous values are considered, then a marginal value of xi would be dxi, and the “marginal value” of y would typically refer to

$\frac{\partial y}{\partial x_i}=\frac{\partial f\left(x_1 ,x_2 ,\ldots,x_n \right)}{\partial x_i}$

(For a linear functional relationship $y = a + b\cdot x$, the marginal value of y will simply be the co-efficient of x (in this case, b) and this will not change as x changes. However, in the case where the functional relationship is non-linear, say $y = a\cdot b^x$, the marginal value of y will be different for different values of x.)

#### Example

Assume that, in some economy, aggregate consumption is well-approximated by

$C=C\left(Y\right)$

where

Then the marginal propensity to consume is

$MPC=\frac{dC}{dY}$

## References

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Marginal value theorem — The optimal time spent in a patch is given by the tangent to the resource intake curve that departs from the expected transit time value. Any other line crossing the resource intake curve has a shallower slope and thus a sub optimal resource… …   Wikipedia

• Marginal concepts — In economics, marginal concepts are associated with a specific change in the quantity used of a good or service, as opposed to some notion of the over all significance of that class of good or service, or of some total quantity thereof.… …   Wikipedia

• Value and Capital — is a book by the British economist John Richard Hicks, published in 1939. It is considered a classic exposition of microeconomic theory. A central result in consumer demand theory that the book builds on is that goods have value even with only… …   Wikipedia

• Marginal cost of capital schedule — Marginal Cost of Capital (MCC) Schedule is a graph that relates the firm’s weighted average cost of each dollar of capital to the total amount of new capital raised. The WACC is the minimum rate of return allowable, and still meeting financial… …   Wikipedia

• marginal product value — value of a product resulting from additional unit from a manufacturer …   English contemporary dictionary

• Marginal utility — In economics, the marginal utility of a good or service is the utility gained (or lost) from an increase (or decrease) in the consumption of that good or service. Economists sometimes speak of a law of diminishing marginal utility, meaning that… …   Wikipedia

• Marginal propensity to save — The marginal propensity to save (MPS) refers to the increase in saving (non purchase of current goods and services) that results from an increase in income i.e. The marginal propensity to save might be defined as the proportion of each additional …   Wikipedia

• Marginal propensity to consume — In economics, the marginal propensity to consume (MPC) is an empirical metric that quantifies induced consumption, the concept that the increase in personal consumer spending (consumption) occurs with an increase in disposable income (income… …   Wikipedia

• Value of life — The value of life (or price of life) is an economic or moral value assigned to life in general, or to specific living organisms. In social and political sciences, it is the marginal cost of death prevention in a certain class of circumstances. As …   Wikipedia

• Marginal product of labor — In economics, the marginal product of labor also known as MPL or MPN is the change in output from hiring one additional unit of labor. It is the increase in output added by the last unit of labor.[1] Ceteris paribus that no other inputs to… …   Wikipedia