Question
Asked May 14, 2019

Derive the elasticity of substitution for the Cobb-Douglas production Fonction.

f(L,K) = ALαKβ

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Step 1

Elasticity of substitution measures the responsiveness of change in MRTS (Marginal Rate of Technical Substitution) to input ratio (K/L).

MRTS (Marginal Rate of Technical Substitution) measures the rate at which one factor can be substituted for another to yield the same level of output. MRTS is the slope of isoquant.

We are given the Cobb-Douglas production function as follows:

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Step 2

The formula for calculating elasticity of substitution (σ) is as follows:

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Step 3

The MRTS for the given Cobb-Douglas produc...

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