Question

Consider a production function: Q = LK^2, which has corresponding marginal products, MP_L = K^2 and MP_K = 2LK. Show that the elasticity of substitution for this production function is exactly equal to 1, no matter what the values of K and L are.

Name: consider a production function qlk2 which has corresponding marginal products mplk2 and mpk2lk show that the elasticity of substitution for this production function is exactly equal to 1 n 66672
Uploaded: 2023-03-03T19:22:05-08:00
Duration: 2 min 8 s
Channel: Andrew Davis
Description: consider a production function qlk2 which has corresponding marginal products mplk2 and mpk2lk show that the elasticity of substitution for this production function is exactly equal to 1 n 66672

          Consider a production function: Q = LK^2, which has corresponding marginal products, MP_L = K^2 and MP_K = 2LK. Show that the elasticity of substitution for this production function is exactly equal to 1, no matter what the values of K and L are.

Added by Juan Jos- S.

Principles of Economics

Gregory Mankiw 8th Edition

Instant Answer

Solved by Expert Andrew Davis

03/03/2023

Step 1

The formula for σ is given by: σ = (d(ln(K/L)) / d(ln(MP_L/MP_K))) Now, let's find the natural logarithm of the ratio of marginal products: ln(MP_L/MP_K) = ln(K^2 / (2LK)) = ln(K^2) - ln(2LK) Now, let's differentiate this expression with respect to Show more…

Show all steps

Thanks for your feedback!

Consider a production function: Q = LK^2, which has corresponding marginal products, MP_L = K^2 and MP_K = 2LK. Show that the elasticity of substitution for this production function is exactly equal to 1, no matter what the values of K and L are.