Find the elasticity of scale and the elasticity of substitution for the CES production function:11f(x₁, x₂) = (x³ + x2)³.Solution:We first calculate the marginal products:2fx₁= 3 +=x1fx1-+2210 - ² ( x² + x ) ( + x^²) = ( + + + + ² ) 15 ²0x²-2/3x₂+x2fxzElasticity of scale = _1₁_+_*__*(+)´<°¸«d«)*;»_f(x1,f(x1,‹2)²=-2/3r2/3 = TRS = t (where TRS = =t).⇒ r = t³/² ⇒ ln(r) = ln (t) and o =-2/3dln (r)dln (t)To get elasticity of substitution, we first need TRS and denote r =1x3 X1TMS - F (+4+2)0=fx₁fx₂21+ x²) x₂²MINx23-2/3(x²-2/322/32/3x1-2/3= r²/3x¹/3+1/3= 1.

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Find the elasticity of scale and the elasticity of substitution for the CES production function: 1 ƒ(x₁, x₂) = (x³ + x³)³. Solution: We first calculate the marginal products: 1 2 1 4. - ³ ( 4 + x² ) ( x ²) - ( 4² + x²) x, ** fx₁ -2/3 x1 2 1 - ³ (x ² + x²) * (1 x 5²³) = ( x² + x²) x² fx₂= 3 -2/3 x₂

Find the elasticity of scale and the elasticity of substitution for the CES production function: 1 ƒ(x₁, x₂) = (x³ + x³)³. Solution: We first calculate the marginal products: 1 2 1 4. - ³ ( 4 + x² ) ( x ²) - ( 4² + x²) x, ** fx₁ -2/3 x1 2 1 - ³ (x ² + x²) * (1 x 5²³) = ( x² + x²) x² fx₂= 3 -2/3 x₂

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.7P

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