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Elasticity of complementarity

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Elasticity of complementarity (Hamermesh, 1993) is the percentage responsiveness of relative factor prices to a 1 percent change in relative inputs.

Mathematical definition

Given the production function f ( x 1 , x 2 ) {\displaystyle f(x_{1},x_{2})} then the elasticity of complementarity is defined as

c = d ln ⁡ ( d f d x 1 / d f d x 2 ) d ln ⁡ ( x 2 / x 1 ) = d ( d f d x 1 / d f d x 2 ) d f d x 1 / d f d x 2 d ( x 2 / x 1 ) x 2 / x 1 . {\displaystyle c={\frac {d\ln \left(\displaystyle {\frac {df}{dx_{1}}}/\displaystyle {\frac {df}{dx_{2}}}\right)}{d\ln(x_{2}/x_{1})}}={\frac {\displaystyle {\frac {d({\frac {df}{dx_{1}}}/{\frac {df}{dx_{2}}})}{{\frac {df}{dx_{1}}}/{\frac {df}{dx_{2}}}}}}{\displaystyle {\frac {d(x_{2}/x_{1})}{x_{2}/x_{1}}}}}.}

The inverse of elasticity of complementarity is elasticity of substitution.

References

  • Hamermesh, Daniel S., Labor Demand, Princeton University Press, Princeton NJ, 1993, ISBN 0-691-02587-8


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