Elasticity of complementarity
# Elasticity of complementarity

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 $f(x_{1},x_{2})$ then the elasticity of complementarity is defined as

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

The inverse of elasticity of complementarity is elasticity of substitution.

