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 ( $e(\cdot ,\cdot )$ ) as

$EV=e(p_{0},u_{1})-e(p_{0},u_{0})$

$=e(p_{0},u_{1})-w$

$=e(p_{0},u_{1})-e(p_{1},u_{1})$

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 indirect utility function ( $v(\cdot ,\cdot )$ ),

$v(p_{0},w+EV)=u_{1}$

This can be shown to be equivalent to the above by taking the expenditure function of both sides at $p_{0}$

$e(p_{0},v(p_{0},w+EV))=e(p_{0},u_{1})$

$w+EV=e(p_{0},u_{1})$

$EV=e(p_{0},u_{1})-w$

One of the three identical equations above.

Compensating variation (CV) is a closely related measure of welfare change.

References

Mas-olell, A., Whinston, M and Green, J. (1995) Microeconomic Theory, Oxford University Press, New York.
Greenwood, J. and K.A. Kopecky. "Measuring the Welfare Gain from Personal Computers," Economic Inquiry: 51, No. 1, pp. 336-347. 2013.

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