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| In [[economics]] and in particular [[neoclassical economics]], the '''marginal product''' or '''marginal physical product''' of an input ([[factor of production]]) is the extra output that can be produced by using one more unit of the input (for instance, the difference in output when a firm's labor usage is increased from five to six units), assuming that the quantities of no other inputs to production change.
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| <ref>{{cite book|title =The Making of the Classical Theory of Economic Growth|last=Brewer | |
| |first=Anthony
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| |url=http://books.google.co.uk/books?id=jBR4jmf75gYC&lpg=PA163&ots=JURDz1bm8d&dq=Edward%20West%20diminishing&pg=PA163#v=onepage&q=Edward%20West%20diminishing&f=false
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| |year=2010
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| |publisher =Routledge
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| |isbn=0415486203
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| |language = English
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| }}</ref>
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| The marginal product of a given input can be expressed
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| <ref>{{cite book
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| | last = Mukherjee | |
| | first = Sampat
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| | last2 = Mukherjee | |
| | first2 = Mallinath | |
| | last3 = Ghose | |
| | first3 = Amitava | |
| | title = Microeconomics
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| | publisher = Prentice-Hall of India
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| | place = New Delhi
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| | year = 2003
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| | isbn = 81-203-2318-1
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| | language = English
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| }}</ref>
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| as
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| :<math>MP = \frac{\Delta Y}{\Delta X}</math> | |
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| where <math>\Delta X</math> is the change in the firm's use of the input (conventionally a one-unit change) and <math>\Delta Y</math> is the change in quantity of output produced. Note that the quantity <math>Y</math> of the "product" is typically defined ignoring [[externalities|external costs and benefits]].
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| If the output and the input are infinitely divisible, so the marginal "units" are infinitesimal, the marginal product is the mathematical [[derivative]] of the [[production function]] with respect to that input. Suppose a firm's output ''Y'' is given by the production function
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| :<math>Y=F(K,L)</math>
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| where ''K'' and ''L'' are inputs to production (say, capital and labor). Then the marginal product of capital (''MPK'') and marginal product of labor (''MPL'') are given by:
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| :<math>MPK=\frac{\partial F}{\partial K}</math>
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| :<math>MPL=\frac{\partial F}{\partial L}</math>
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| In the "law" of [[diminishing returns|diminishing marginal returns]], the marginal product of one input is assumed to fall as one considers higher and higher starting points for the quantity of that input. The marginal product of labor is the slope of the [[total product]] curve, which is the production function plotted against labor usage for a fixed level of usage of the capital input.
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| In the neoclassical theory of [[perfect competition|competitive markets]], the [[marginal product of labor]] equals the [[real vs. nominal in economics|real]] wage. In aggregate models of perfect competition, in which a single good is produced and that good is used both in consumption and as a capital good, the [[marginal product of capital]] equals its [[rate of profit|rate of return]]. As was shown in the [[Cambridge capital controversy]], this proposition about the marginal product of capital cannot generally be sustained in multicommodity models in which capital and consumption goods are distinguished.
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| == See also ==
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| * [[Marginal product of capital]]
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| * [[Production theory]]
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| == References ==
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| <references />
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| * {{cite book|title = Volkswirtschaft verstehen
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| | last = Beck
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| | first = Bernhard
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| | url = http://books.google.de/books?id=ZX2P5h7C7cUC&pg=PA66&dq=Grenzprodukt&hl=de&ei=jE0cTrKvH4fu-gaOnp2cBA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCoQ6AEwAA#v=onepage&q=Grenzprodukt&f=false
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| | year = 2008
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| | isbn =
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| }}
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| * {{Cite book
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| | last = Rothbard
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| | first = Murray N.
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| | title = Classical Economics: An Austrian Perspective on the History of Economic Thought Volume II
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| | vydavatel = Ludwig von Mises Institute
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| | place = Auburn, Alabama
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| | year = 1995
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| | url = http://library.mises.org/books/Murray%20N%20Rothbard/Classical%20Economics%20An%20Austrian%20Perspective%20on%20the%20History%20of%20Economic%20Thought,%20Volume%20II.pdf
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| | language = English
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| | isbn = 0-945466-48-X
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| }}
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| {{DEFAULTSORT:Marginal Product}}
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| [[Category:Production economics]]
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| | |
| {{Economics-stub}}
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