Consider the utility function $u \left( x _ { 1 } , x _ { 2 } \right) = \left( \alpha x _ { 1 } ^ { - \rho } + ( 1 - \alpha ) x _ { 2 } ^ { - \rho } \right) ^ { - 1 / \rho }$ .If $\rho = 0$ ,the elasticity of substitution is equal to 1.
The elasticity of substitution for CES utility functions is $\frac { 1 } { 1 + \rho }$ .

Question

Consider the utility function $u \left( x _ { 1 } , x _ { 2 } \right) = \left( \alpha x _ { 1 } ^ { - \rho } + ( 1 - \alpha ) x _ { 2 } ^ { - \rho } \right) ^ { - 1 / \rho }$ .If $\rho  = 0$ ,the elasticity of substitution is equal to 1.
The elasticity of substitution for CES utility functions is $\frac { 1 } { 1 + \rho }$ .

Quizplus · Accepted Answer

The Answer of Consider the utility function $u \left( x _ { 1 } , x _ { 2 } \right) = \left( \alpha x _ { 1 } ^ { - \rho } + ( 1 - \alpha ) x _ { 2 } ^ { - \rho } \right) ^ { - 1 / \rho }$ .If $\rho  = 0$ ,the elasticity of substitution is equal to 1.
The elasticity of substitution for CES utility functions is $\frac { 1 } { 1 + \rho }$ .

Consider the Utility Function u(x1,x2)=(αx1−ρ+(1−α)x2−ρ)−1/ρu \left( x _ { 1 } , x _ { 2 } \right) = \left( \alpha x _ { 1 } ^ { - \rho } + ( 1 - \alpha ) x _ { 2 } ^ { - \rho } \right) ^ { - 1 / \rho }u(x1​,x2​)=(αx1−ρ​+(1−α)x2−ρ​)−1/ρ

Consider the Utility Function $u \left( x _ { 1 } , x _ { 2 } \right) = \left( \alpha x _ { 1 } ^ { - \rho } + ( 1 - \alpha ) x _ { 2 } ^ { - \rho } \right) ^ { - 1 / \rho }$