看不了图片内容的话这是打字版:
The CES (Constant Elasticity of Substitution) utility function is given
by u(x1, x2) = (x1^ρ + x2^ρ)^(1/ρ), where 0≠ ρ<1. It can be easily verified this utility
function is strictly monotonic increasing and strictly concave. Since preferences are
invariant with respect to monotonic transforms of utility, we could just as well choose
u(x1, x2) = 1/ρ ln(x1^ρ + x2^ρ).
This is easiest to see using the marginal rate of substitution
MRS = − (x1/ x2)^ρ−1 :
If ρ = 1, we have u(x1, x2) = x1 + x2;
求助下两种情况的具体推导:
If ρ = 0, we have u(x1, x2) is the Cobb-Douglas utility function.
If ρ = −∞, u(x1, x2) = min{x1,x2}
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