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 en:elasticity-of-production [2017/08/31 14:48]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] Both sides previous revision Previous revision 2019/02/06 07:52 federico [Elasticity of Production] 2019/02/06 07:52 federico [Elasticity of Production] 2019/02/06 07:51 federico [Elasticity of Production] 2018/07/22 09:51 federico 2018/04/19 11:00 [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 15:02 federico 2017/08/31 14:57 federico 2017/08/31 14:53 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:52 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:52 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:51 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:51 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:50 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:49 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:48 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:48 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:46 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:46 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:39 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:39 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:38 federico 2017/08/31 14:36 federico 2017/08/18 20:07 federico 2017/08/18 20:06 federico 2017/08/18 20:05 federico created Next revision Previous revision 2019/02/06 07:52 federico [Elasticity of Production] 2019/02/06 07:52 federico [Elasticity of Production] 2019/02/06 07:51 federico [Elasticity of Production] 2018/07/22 09:51 federico 2018/04/19 11:00 [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 15:02 federico 2017/08/31 14:57 federico 2017/08/31 14:53 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:52 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:52 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:51 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:51 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:50 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:49 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:48 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:48 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:46 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:46 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:39 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:39 federico [Example: Elasticity of Production of a Cobb Douglas Production Function] 2017/08/31 14:38 federico 2017/08/31 14:36 federico 2017/08/18 20:07 federico 2017/08/18 20:06 federico 2017/08/18 20:05 federico created Line 1: Line 1: ====== 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: Line 9: Line 11: **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 ===== Line 28: Line 34: ==== 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 ​ K<​sup>​α​ + + 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: + + $$\frac {\frac{\partial Q}{Q}} {\frac{\partial K}{K}} = \frac {\frac{\partial Q}{\partial K}} {\frac{Q}{K}} = \frac { α A L ^{β} K^{α-1} }{ \frac {A L^β K^α}{K} }$$ - Q(L,K) = A Lβ ​Kα​ + = \frac { α A L ^{β} K^{α} K^{-1} }{ \frac {A L^β K^α}{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: + = \frac { \frac {α A L ^{β} K^{α}}{K} }{ \frac {A L^β K^α}{K} } - (∂Q/Q) / (∂K/​K) ​= (∂Q/∂K) / (Q/K) = = [ Aα L<​sup>​β​ K<​sup>​α-1​ ] / [ A L<​sup>​β​ K<​sup>​α​ ] + ​= \frac { \frac {α Q}{K} }{ \frac {Q}{K} } - + $$= α$$ - \frac {\frac{\partial Q}{Q}} {\frac{\partial K}{K}} + - = \frac {\frac{\partial Q}{\partial K}} {\frac{Q}{K}} + - = \frac { Aβ L ^{β-1} K^α }{ A L^β K^α } + - + - + [[production-function-example]] - \frac {\frac{\partial Q}{Q}} {\frac{\partial K}{K}} + - = \frac {\frac{\partial Q}{\partial K}} {\frac{Q}{K}} + - = \frac { β A L ^(β-1) K^α }{ A L^β K^α } + - +