Given $ Y=f(K,L;\sigma) $, the effect on labor from a change in the price of capital can be gauged through a substitution effect and a scale effect: \begin{align*} \frac{\partial L}{\partial r} & =\underset{Sub}{\underbrace{\left. \frac{\partial L^{c}}{\partial r}\right\vert _{Y}}}% +\underset{Scale}{\underbrace{\frac{\partial L^{c}}{\partial Y}\frac{\partial Y}{\partial r}}}\\ \\ & =SH_{_{Labor}}\left( \sigma+\eta\right) \end{align*} where $L^c$ is the conditional demand (the smooth movement along the isoquant).

This can then - as far as I can see - be also expressed as the sum of the factor substitution elasticity and the firm's elasticity of demand, weighted by the labor cost share.

But are $\eta$ and $\sigma$ independent of one another? If a firm can readily substitute factors in response to factor price changes, this will presumably impact its price elasticity of demand. Any thoughts?



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.