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en:linear-production-function [2014/04/04 06:45] 200.123.218.241 |
en:linear-production-function [2018/08/10 11:12] (current) 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 | ||
| Line 29: | Line 34: | ||
| 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]] | ||