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]
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.