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A marginal value is #a
value Value or values may refer to: Ethics and social * Value (ethics) wherein said concept may be construed as treating actions themselves as abstract objects, associating value to them ** Values (Western philosophy) expands the notion of value beyo ...
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 contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
'' 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 its ...
, 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 Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and intera ...
, 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 h ...
, 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 wa ...
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 :y=f\left(x_1 ,x_2 ,\ldots,x_n \right)


Discrete change

If the value of x_i is ''discretely'' changed from x_ to x_ while other independent variables remain unchanged, then the marginal value of the change in x_i is :\Delta x_i =x_-x_ and the “marginal value” of y may refer to :\Delta y=f\left(x_1 ,x_2 ,\ldots ,x_,\ldots,x_n \right)-f\left(x_1 ,x_2 ,\ldots ,x_,\ldots,x_n \right) or to :\frac=\frac


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 x_i would be dx_i, and the “marginal value” of y would typically refer to :\frac=\frac (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 *Y is
aggregate income Aggregate income is the total of all incomes in an economy without adjustments for inflation, taxation, or types of double counting. Aggregate income is a form of GDP that is equal to Consumption expenditure plus net profits. 'Aggregate income' in ...
. 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 t ...
'' is :MPC=\frac{dY}


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.{{citati ...


References

Marginal concepts