Definitions

# Equivalent variation

Equivalent variation (EV) is a measure of how much more money a consumer would pay before a price increase to avert the price increase. Because the meaning of "equivalent" may be unclear, it is also called extortionary variation. John Hicks (1939) is attributed with introducing the concept of compensating and equivalent variation.

It is a useful tool when the present prices are the best place to make a comparison.

The value of the equivalent variation is given in terms of the expenditure function ($e\left(cdot,cdot\right)$) as

$EV = e\left(p_0, u_1\right) - e\left(p_0, u_0\right)$

$= e\left(p_0, u_1\right) - w$

$= e\left(p_0, u_1\right) - e\left(p_1, u_1\right)$

where $w$ is the wealth level, $p_0$ and $p_1$ are the old and new prices respectively, and $u_0$ and $u_1$ are the old and new utility levels respectively.

## Value function form

Equivalently, in terms of the value function ($v\left(cdot,cdot\right)$),

$v\left(p_0,w+EV\right) = u_1$

This can be shown to be equivalent to the above by taking the expenditure function of both sides at $p_0$

$e\left(p_0,v\left(p_0,w+EV\right) = e\left(p_0,u_1\right)$

$w+EV = e\left(p_0,u_1\right)$

$EV = e\left(p_0,u_1\right) -w$

One of the three identical equations above.