Elasticity of substitution

Elasticity of substitution is the elasticity of the ratio of two inputs to a production (or utility) function with respect to the ratio of their marginal products (or utilities).

Mathematical definition

Let the utility over consumption be given by

U(c_1,c_2,c_3,...)

Then the intertemporal elasticity of substitution between dates $i$ and $j$ is

E = \frac{d \ln (c_i/c_j) }{d \ln (U_{c_i}/U_{c_j})}

= \frac{\frac{d (c_i/c_j) }{c_i/c_j}}{\frac{d (U_{c_i}/U_{c_j})}{U_{c_i}/U_{c_j}}}

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Mathematical definition

See also