title: Elasticity of complementarity
text: # 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.
  
  