In economics, compensating variation (CV) is a measure of utility change introduced by John Hicks (1939).
Compensating variation can be used to find the effect of a price change on an agent's net welfare.
The first equation can be interpreted as saying that, under the new price regime, the consumer would accept CV in exchange for allowing the change to occur.
Notice that in this second example the CV is computed from the point of view of the government, in this case the CV measures the tax (or if negative the subsidy) the government has to give to the consumer in order to let him reach his old utility with the new system of prices.
Equivalent variation (EV) is a closely related measure that uses old prices and the new utility level.
It measures the amount of money a consumer would pay to avoid a price change, before it happens.