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.

References

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