Definition
Equivalent Variation (EV): consider a change (increase) in price decreases the utility of consumer. EV is evaluated as "how much money would have to be taken from the consumer before the price change to leave him as well off as he would be after the price change"
Interpretation: EV can be defined as the measurement of the maximum amount of income that the consumer is willing to pay to avoid the price change.
Possible EV indicates welfare gain, negative EV indicates welfare loss.
See also:
Calculation of equivalent variation
(1) From utility function and budget constraint, calculate the demand of each commodity x = F(p, w), also calculate the indirect utility function u(p, w)
(2) calculate the demand of each commodity with new price p', and calculate the utility level after price change u'
(3) let u' = u(p, w*), solve for w'', then EV = w* - w
Linearization of EV
Take total differentiating, we have:
Note: here "d" refers to change, it may not be the "tiny change" we used to think.