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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). In Economics, elasticity is the ratio of the percent change in one variable to the percent change in another variable

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Mathematical definition

Let the utility over consumption be given by U(c1,c2). Then the elasticity of substitution is

E = \frac{d \ln (c_2/c_1) }{d \ln (MRS)} = \frac{d \ln (c_2/c_1) }{d \ln (U_{c_1}/U_{c_2})} = \frac{\frac{d (c_2/c_1) }{c_2/c_1}}{\frac{d (U_{c_1}/U_{c_2})}{U_{c_1}/U_{c_2}}}

where MRS is the marginal rate of substitution. In economics the marginal rate of substitution is the rate at which a consumer is ready to give up one good in exchange for another good while maintaining the same level of satisfaction

Similarly, if the production function is f(x1,x2) then the elasticity of substitution is

\sigma = \frac{d \ln (x_2/x_1) }{d \ln (TRS)} = \frac{d \ln (x_2/x_1) }{d \ln (\frac{df}{dx_1}/\frac{df}{dx_2})} = \frac{\frac{d (x_2/x_1) }{x_2/x_1}}{\frac{d (\frac{df}{dx_1}/\frac{df}{dx_2})}{\frac{df}{dx_1}/\frac{df}{dx_2}}}

where TRS is the technical rate of substitution. In Economics, the marginal rate of technical substitution ( MRTS) or the Technical Rate of Substitution ( TRS) is the amount by which the quantity

See also

References

External links

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