{{htmlmetatags>
metatag-description=(Linear Production Function: definition, examples and formula)
metatag-title=(Linear Production Function: Definition and Explanation [and formula])
}}

====== Linear Production Function ======

The linear [[en:production-function|production function]] describes a linear relationship between the inputs and the output.

For example:

Q = aL

Q = aL + bK

Chart:

{{:en:linear-production-function-1.png|}}

===== Returns to scale =====


The linear production function has constant [[returns to scale]].

**Proof**:\\
Y = aK + bL\\
Y’ = a (cK) + b (cL)\\
= c (aK + bL)\\
= c Y

===== Elasticity of substitution =====


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]]