Equivalent variation

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Equivalent variation (EV) is a measure of how much more money a consumer would pay before a price increase to avert the price increase. John Hicks (1939) is attributed with introducing the concept of compensating and equivalent variation.

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 () as

EV = e(p₀,u₁) − e(p₀,u₀)

= e(p₀,u₁) − w

= e(p₀,u₁) − e(p₁,u₁)

where w is the wealth level, p₀ and p₁ are the old and new prices respectively, and u₀ and u₁ are the old and new utility levels respectively.

[edit] Value function form

Equivalently, in terms of the value function (),

v(p₀,w + EV) = u₁

This can be shown to be equivalant to the above by taking the expenditure function of both sides at p₀

e(p₀,v(p₀,w + EV) = e(p₀,u₁)

w + EV = e(p₀,u₁)

EV = e(p₀,u₁) − w

One of the three identical equations above.

[edit] See also

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

[edit] References

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