Equivalent variation

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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[edit]

Equivalently, in terms of the value 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.


  • Mas-Colell, A., Whinston, M and Green, J. (1995) Microeconomic Theory, Oxford University Press, New York.