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| A '''marginal value''' is
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| #a [[Value (mathematics)|value]] that holds true given particular constraints,
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| #the ''change'' in a value associated with a specific change in some [[Dependent and independent variables|independent variable]], whether it be of that variable or of a [[Dependent and independent variables|dependent variable]], or
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| #[when underlying values are quantified] the ''[[ratio]]'' of the change of a dependent variable to that of the independent variable.
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| (This third case is actually a special case of the second).
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| In the case of [[Differentiability#Continuity and differentiability|differentiability]], at the limit, a marginal change is a [[Differential (infinitesimal)|mathematical differential]], or the corresponding [[Derivative (calculus)|mathematical derivative]].
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| These uses of the term “marginal” are especially common in [[economics]], and result from conceptualizing constraints as ''borders'' or as ''margins''.<ref>[[Philip Wicksteed|Wicksteed, Philip Henry]]; [http://www.econlib.org/library/Wicksteed/wkCS.html ''The Common Sense of Political Economy'' (1910),] [http://www.econlib.org/cgi-bin/searchbooks.pl?searchtype=BookSearchPara&id=wkCS&query=margin Bk I Ch 2 and elsewhere].</ref> 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.
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| == Quantified conception ==
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| Assume a functional relationship
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| :<math>y=f\left(x_1 ,x_2 ,\ldots,x_n \right)</math>
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| === Discrete change ===
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| If the value of <math>x_i</math> is ''discretely'' changed from <math>x_{i,0}</math> to <math>x_{i,1}</math> while other independent variables remain unchanged, then the marginal value of the change in <math>x_i</math> is
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| :<math>\Delta x_i =x_{i,1}-x_{i,0}</math>
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| and the “marginal value” of <math>y</math> may refer to
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| :<math>\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)</math>
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| or to
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| :<math>\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}}</math>
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| ==== Example ====
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| 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
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| *the marginal increase in her income was $5000
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| *the marginal effect on her purchase of amontillado was an increase of 1 cask, or of 1 cask per $5000.
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| === Instantaneous margins ===
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| If ''instantaneous'' values are considered, then a marginal value of <math>x_i</math> would be <math>dx_i</math>, and the “marginal value” of <math>y</math> would typically refer to
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| :<math>\frac{\partial y}{\partial x_i}=\frac{\partial f\left(x_1 ,x_2 ,\ldots,x_n \right)}{\partial x_i}</math>
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| (For a linear functional relationship <math>y = a + b\cdot x</math>, the marginal value of <math>y</math> will simply be the co-efficient of <math>x</math> (in this case, <math>b</math>) and this will not change as <math>x</math> changes. However, in the case where the functional relationship is non-linear, say <math>y = a\cdot b^x</math>, the marginal value of <math>y</math> will be different for different values of <math>x</math>.)
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| ==== Example ====
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| Assume that, in some economy, aggregate consumption is well-approximated by
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| :<math>C=C\left(Y\right)</math>
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| where
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| *<math>Y</math> is [[Measures of national income and output|aggregate income]].
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| Then the ''[[marginal propensity to consume]]'' is
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| :<math>MPC=\frac{dC}{dY}</math>
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| == See also ==
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| *[[Marginal concepts]]
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| == References ==
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| <references />
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| [[Category:Economics terminology]]
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| [[Category:Marginal concepts]]
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Hi there, I am Alyson Boon although it is not the name on my beginning certificate. Alaska is where he's always been residing. To perform lacross is some thing I truly appreciate doing. I am currently a travel agent.
Feel free to surf to my weblog ... tarot card readings (myoceancounty.net)