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en:elasticity-of-production [2017/08/31 14:50]
federico [Example: Elasticity of Production of a Cobb Douglas Production Function]
en:elasticity-of-production [2019/02/06 07:52] (current)
federico [Elasticity of Production]
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 ====== Elasticity of Production ====== ====== Elasticity of Production ======
  
-The elasticity of production, also called **output elasticity**,​ is the percentaje change in the production of a good by a firm, divided the percentaje ​change in an input used for the production of that good, for example, labor or capital.+The elasticity of production, also called **output elasticity**,​ is the percentaje change in the production of a good by a firm, divided the percentage ​change in an input used for the production of that good, for example, labor or capital.
  
-The elasticity of production shows the **responsiveness** of the output when there is a change in one input. It is defined as de proportional change in the product, divided the proportional change in the quantity of an input. ​+The elasticity of production shows the **responsiveness** of the output when there is a change in one input. 
 + 
 +It is defined as de proportional change in the product, divided the proportional change in the quantity of an input.
  
 **For example**, if a factory employs 10 people, and produces 100 chairs per day. If the number of people employed in the factory increases to 12, that is, a 20% increase, and the number of chairs produced per day increases to 110 (that is, a 10% increase), the elasticity of production is: **For example**, if a factory employs 10 people, and produces 100 chairs per day. If the number of people employed in the factory increases to 12, that is, a 20% increase, and the number of chairs produced per day increases to 110 (that is, a 10% increase), the elasticity of production is:
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 **ΔQ/Q / ΔL/L** = 10/100 / 2/10 = 0.1 / 0.2 = 0.5 **ΔQ/Q / ΔL/L** = 10/100 / 2/10 = 0.1 / 0.2 = 0.5
  
-If the production function contains only one input, the elasticity of production measures the degree of [[returns to scale]]. In this case: +If the production function contains only one input, the elasticity of production measures the degree of [[https://​www.econowiki.com/​doku.php?​id=en:​returns-to-scale|returns to scale]]. In this case:  
-- if the elasticity of production is 1, the production has constant ​return ​to scale, at that point. + 
-- if the elasticity of production is greater than one, the production has increasing returns to scale at that point. +- if the elasticity of production is 1, the production has **constant ​returns ​to scale**, at that point. ​ 
-- if the elasticity of production is less than one, the production has decreasing returns to scale at that point.+ 
 +- if the elasticity of production is greater than one, the production has **increasing returns to scale** at that point. ​ 
 + 
 +- if the elasticity of production is less than one, the production has **decreasing returns to scale** at that point. 
  
 ===== Using a production function ===== ===== Using a production function =====
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 ==== Example: Elasticity of Production of a Cobb Douglas Production Function ==== ==== Example: Elasticity of Production of a Cobb Douglas Production Function ====
  
-The [[en:​cobb-douglas-production-function|Cobb-Douglas production function]] is a function that is used a lot in economics. The form of a Cobb-Douglas production function is:+The [[:en:​cobb-douglas-production-function|Cobb-Douglas production function]] is a function that is used a lot in economics. The form of a Cobb-Douglas production function is: 
 + 
 +Q(L,K) = A L<​sup>​β</​sup> ​ K<​sup>​α</​sup>​
  
-Q(L,K) = A L<​sup>​β</​sup> ​K<​sup>​α</​sup>​+To calculate the [[:​en:​cobb-douglas-output-elasticity|elasticity of production of the Cobb-Douglas production function]]with respect to K, we must find the proportional change in the production, divided the proportional change in K:
  
-To calculate the [[en:​cobb-douglas-output-elasticity|elasticity of production of the Cobb-Douglas production function]], with respect to K, we must find the proportional change in the production, divided the proportional change in K:+\begin{equation} \frac {\frac{\partial Q}{Q}} {\frac{\partial K}{K}} = \frac {\frac{\partial Q}{\partial K}} {\frac{Q}{K}} = \frac { α A L ^{β} K^{α-1} }{ \frac {A L^β K^α}{K} } \end{equation}
  
-(∂Q/Q) / (∂K/​K) ​(∂Q/∂K) / (Q/K) = = [ Aα L<sup>β</​sup> ​K<sup>α-1</​sup>​ ] / [ A L<sup>β</​sup> ​K<sup>α</​sup>​ ]+\begin{equation} ​\frac { α A L ^{βK^{α} K^{-1} }{ \frac {A L^β K^α}{K} } \end{equation}
  
-\begin{equation} +\begin{equation} ​\frac { \frac {α A L ^{β} K^{α}}{K} }{ \frac {A L^β K^α}{K} ​\end{equation}
-\frac {\frac{\partial Q}{Q}} {\frac{\partial ​K}{K}} +
-= \frac {\frac{\partial Q}{\partial ​K}} {\frac{Q}{K}} +
-= \frac { α A L ^{βK^{α-1} }{ A L^β K^α } +
-\end{equation}+
  
-\begin{equation} +\begin{equation} = \frac { \frac {α Q}{K} }{ \frac {Q}{K} \end{equation}
-= \frac { α A L ^{β} K^{α} K^{-1} }{ A L^β K^α } +
-\end{equation}+
  
 +\begin{equation} = α \end{equation}
  
 +[[production-function-example]]
en/elasticity-of-production.1504205406.txt.gz · Last modified: 2017/08/31 14:50 by federico