IGNOU MEC 1 2012 - Derive the elasticity of substitution from the Cob-Douglas production

Question

Derive the elasticity of substitution from the Cob-Douglas production function q=f(K,L) = AK^aL^b.

25 Oct 2017

Answer :

Word Count : 324

The Cobb-Douglas production function is given by:

q=f(K,L) = AK^aL^b ,

where A, a and b are all positive constants.

Iso-quants resulting from the functional form have convex shape. The Cobb-Douglas function can exhibit any degree of returns scale depending on the values of a and b. Suppose all inputs were increased by a factor m. Then,

f(mK,mL) = A(mK)^a(mL)^b = Am^a+b K^aL^b (

= m^a+b f(K,L)

Hence,

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