Equivalent variation (EV) is a

measure Measure may refer to: * Measurement, the assignment of a number to a characteristic of an object or event Law * Ballot measure, proposed legislation in the United States * Church of England Measure, legislation of the Church of England * Mea ...

economic welfare The welfare definition of economics is an attempt by Alfred Marshall, a pioneer of neoclassical economics, to redefine his field of study. This definition expands the field of economic science to a larger study of humanity. Specifically, Marshall's ...

changes associated with changes in prices.

John Hicks Sir John Richards Hicks (8 April 1904 – 20 May 1989) was a British economist. He is considered one of the most important and influential economists of the twentieth century. The most familiar of his many contributions in the field of economic ...

(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 In microeconomics, the expenditure function gives the minimum amount of money an individual needs to spend to achieve some level of utility, given a utility function and the prices of the available goods. Formally, if there is a utility function u ...

(

e(\cdot,\cdot)

) as

EV = e(p_0, u_1) - e(p_0, u_0)

= e(p_0, u_1) - w

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. Furthermore, if the wealth level does not change,

e(p_0,u_0)=w=e(p_1,u_1)

since under both old and new utility levels and prices, a consumer exhausts their Budget Constraint by

Walras's law Walras's law is a principle in general equilibrium theory asserting that budget constraints imply that the ''values'' of excess demand (or, conversely, excess market supplies) must sum to zero regardless of whether the prices are general equilibr ...

, so

EV = e(p_0, u_1) - e(p_1, u_1)

However, the last equality only holds in the case where the wealth level of a consumer does not change and is thus only a special (albeit very useful and widely used) case of the definition of Equivalent Variation. It fails to hold e.g. when we consider an endowment economy, in which the wealth level is not exogenously given by but endogenous to the price.

Value function form

Equivalently, in terms of the

indirect utility function __NOTOC__ In economics, a consumer's indirect utility function v(p, w) gives the consumer's maximal attainable utility when faced with a vector p of goods prices and an amount of income w. It reflects both the consumer's preferences and market con ...

(

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 In economics, compensating variation (CV) is a measure of utility change introduced by John Hicks (1939). 'Compensating variation' refers to the amount of additional money an agent would need to reach their initial utility after a change in prices, ...

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

References

* Mas-Colell, 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. Welfare economics {{econ-stub