A marginal value is
#a
value that holds true given particular constraints,
#the ''change'' in a value associated with a specific change in some
independent variable
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand ...
, whether it be of that variable or of a
dependent variable
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand ...
, or
#
hen underlying values are quantifiedthe ''
ratio
In mathematics, a ratio shows how many times one number
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in lan ...
'' of the change of a dependent variable to that of the independent variable.
(This third case is actually a special case of the second).
In the case of
differentiability
In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non- vertical tangent line at each interior point in i ...
, 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''.
[ Wicksteed, Philip Henry; ''The Common Sense of Political Economy'' (1910),] Bk I Ch 2 and elsewhere.] The sorts of marginal values most common to economic analysis are those associated with ''unit'' changes of resources and, in
mainstream economics
Mainstream economics is the body of knowledge, theories, and models of economics, as taught by universities worldwide, that are generally accepted by economists as a basis for discussion. Also known as orthodox economics, it can be contrasted to ...
, those associated with ''infinitesimal'' changes. Marginal values associated with units are considered because many decisions are made by unit, and
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. It states that the reason why the price of diamonds is higher than that of w ...
explains ''unit price'' in terms of such marginal values. Mainstream economics uses infinitesimal values in much of its analysis for reasons of mathematical tractability.
Quantified conception
Assume a functional relationship
:
Discrete change
If the value of
is ''discretely'' changed from
to
while other independent variables remain unchanged, then the marginal value of the change in
is
:
and the “marginal value” of
may refer to
:
or to
:
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
Amontillado () is a variety of sherry wine characterised by being darker than fino but lighter than oloroso. It is named after the Montilla region of Spain, where the style originated in the 18th century, although the name "Amontillado" is somet ...
from two 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 one cask, or of one cask per $5000.
Infinitesimal margins
If ''infinitesimal'' values are considered, then a marginal value of
would be
, and the “marginal value” of
would typically refer to
:
(For a linear functional relationship
, the marginal value of
will simply be the co-efficient of
(in this case,
) and this will not change as
changes. However, in the case where the functional relationship is non-linear, say
, the marginal value of
will be different for different values of
.)
Example
Assume that, in some economy, aggregate consumption is well-approximated by
:
where
*
is
aggregate income.
Then the ''
marginal propensity to consume
In economics, the marginal propensity to consume (MPC) is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending ( consumption) occurs with an increase in disposable income (income after taxes and ...
'' is
:
See also
*
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.{{citat ...
References
Marginal concepts