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.

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