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en:linear-production-function

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Linear Production Function

The linear production function describes a linear relationship between the inputs and the output.

For example:

Q = aL

Q = aL + bK

Chart:

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.

The MTRS is constant. The change in the MTRS is always 0.

The numerator is not 0.

The elasticity of substitution is ∞.

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en/linear-production-function.1396611265.txt.gz · Last modified: 2015/03/26 11:48 (external edit)