The elasticity of substitution is given by the percentage change in the factor ratio over the percentage change in the TRS, with output held fixed.

Derivation[edit | edit source]

By definition,


An intuitive (albeit not rigorous) way to think of the second notation is to realize:



Combining both equations, we get


Note: The notation is unfortunate as it collides with the standard deviation but widely used (e.g. Varian (1994)). Be careful not to confuse both fundamentally different concepts.

Community content is available under CC-BY-SA unless otherwise noted.