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en:linear-production-function [2014/04/04 06:44] 200.123.218.241 created |
en:linear-production-function [2018/08/10 11:12] federico |
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+ | {{htmlmetatags> | ||
+ | metatag-description=(Linear Production Function: definition, examples and formula) | ||
+ | metatag-title=(Linear Production Function: Definition and Explanation [and formula]) | ||
+ | }} | ||
+ | |||
====== Linear Production Function ====== | ====== Linear Production Function ====== | ||
- | The linear production function describes a linear relationship between the inputs and the ooutput. | + | The linear [[en:production-function|production function]] describes a linear relationship between the inputs and the output. |
For example: | For example: | ||
Line 16: | Line 21: | ||
- | The linear production function has constant returns to scale. | + | The linear production function has constant [[returns to scale]]. |
- | Proof: | + | **Proof**:\\ |
- | Y = aK + bL | + | Y = aK + bL\\ |
- | Y’ = a (cK) + b (cL) | + | Y’ = a (cK) + b (cL)\\ |
- | = c (aK + bL) | + | = c (aK + bL)\\ |
= c Y | = c Y | ||
- | ==== Elasticity of substitution ==== | + | ===== Elasticity of substitution ===== |
The elasticity of substitution is ∞. | The elasticity of substitution is ∞. | ||
+ | Proof: | ||
+ | |||
+ | The [[elasticity of substitution]] is the change in K/L divided the change in the MTRS, when K/L changes. | ||
+ | |||
+ | The MTRS is constant. The change in the MTRS is always 0. | ||
+ | |||
+ | By definition, the numerator is not 0. | ||
+ | |||
+ | The elasticity of substitution is ∞. | ||
+ | [[Proof of The Law of Cosines]] |