en:elasticity-of-production

This shows you the differences between two versions of the page.

Both sides previous revision Previous revision Next revision | Previous revision | ||

en:elasticity-of-production [2017/08/31 14:46] 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] |
||
---|---|---|---|

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</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: | ||

+ | | ||

+ | \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} | ||

+ | | ||

+ | \begin{equation} = \frac { α A L ^{β} K^{α} K^{-1} }{ \frac {A L^β K^α}{K} } \end{equation} | ||

- | Q(L,K) = A L<sup>β</sup> K<sup>α</sup> | + | \begin{equation} = \frac { \frac {α A L ^{β} K^{α}}{K} }{ \frac {A L^β K^α}{K} } \end{equation} |

- | 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 {α Q}{K} }{ \frac {Q}{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} = α \end{equation} |

- | \begin{equation} | + | [[production-function-example]] |

- | \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 } | + | |

- | \end{equation} | + |

en/elasticity-of-production.1504205160.txt.gz · Last modified: 2017/08/31 14:46 by federico