Equivalent variation

Equivalent variation (EV) is a measure of economic welfare changes associated with changes in prices. John Hicks (1939) is attributed with introducing the concept of compensating and equivalent variation. 
The equivalent variation is the change in wealth, at current prices, that would have the same effect on consumer welfare as would the change in prices, with income unchanged. 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 (formula_1) as
formula_2
formula_3
where formula_4 is the wealth level, formula_5 and formula_6 are the old and new prices respectively, and formula_7 and formula_8 are the old and new utility levels respectively.
Furthermore, if the wealth level does not change, formula_9 since under both old and new utility levels and prices, a consumer exhausts their Budget Constraint by Walras's law, so
formula_10
However, the last equality only holds in the case where the wealth level of a consumer does not change and is thus only a special (albeit very useful and widely used) case of the definition of Equivalent Variation.
Value function form.
Equivalently, in terms of the indirect utility function (formula_11),
formula_12
This can be shown to be equivalent to the above by taking the expenditure function of both sides at formula_5
formula_14
formula_15
formula_16
One of the three identical equations above.
Compensating variation (CV) is a closely related measure of welfare change.