economics Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and intera ...

, compensating variation (CV) is a measure of utility change introduced by

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). 'Compensating variation' refers to the amount of additional money an agent would need to reach their initial utility after a change in prices, a change in product quality, or the introduction of new products. Compensating variation can be used to find the effect of a price change on an agent's net welfare. CV reflects new prices and the old utility level. It is often written using an

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(p,u): :

CV = e(p_1, u_1) - e(p_1, u_0)

= w - e(p_1, u_0)

= e(p_0, u_0) - e(p_1, u_0)

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. 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. More intuitively, the equation can be written using the

value function The value function of an optimization problem gives the value attained by the objective function at a solution, while only depending on the parameters of the problem. In a controlled dynamical system, the value function represents the optimal payof ...

, v(p,w): :

v(p_1,w-CV)=u_0

e(p_1,v(p_1,w-CV))=e(p_1,u_0)

w-CV=e(p_1,u_0)

CV=w-e(p_1,u_0)

one of the equivalent definitions of the ''CV''. 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. The only practical change is that the sign of the CV is changed. This change of perspective often occurs in order to have the same sign of the

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 i ...

. Compensating variation is the metric behind Kaldor-Hicks efficiency; if the winners from a particular policy change can compensate the losers it is Kaldor-Hicks efficient, even if the compensation is not made.

(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. When the good is neither a

normal good In economics, a normal good is a type of a Good (economics), good which experiences an increase in demand due to an increase in income, unlike inferior goods, for which the opposite is observed. When there is an increase in a person's income, for ...

nor an

inferior good In economics, an inferior good is a good whose demand decreases when consumer income rises (or demand increases when consumer income decreases), unlike normal goods, for which the opposite is observed. Normal goods are those goods for which the d ...

, or when there are no income effects for the good (in particular when utility is

quasilinear Quasilinear may refer to: * Quasilinear function, a function that is both quasiconvex and quasiconcave * Quasilinear utility, an economic utility function linear in one argument * In complexity theory and mathematics, O(''n'' log ''n'') or some ...

), then EV (Equivalent variation) = CV (Compensating Variation) = ΔCS (Change in

Consumer Surplus In mainstream economics, economic surplus, also known as total welfare or total social welfare or Marshallian surplus (after Alfred Marshall), is either of two related quantities: * Consumer surplus, or consumers' surplus, is the monetary gain ...

)

References

* Hicks, J.R. ''Value and capital: An inquiry into some fundamental principles of economic theory,'' Oxford: Clarendon Press, 1939 * Brynjolfsson, E., Y. Hu, and M. Smith. "Consumer Surplus in the Digital Economy: Estimating the Value of Increased Product Variety at Online Booksellers," ''Management Science'': 49, No. 1, November, pp. 1580-1596. 2003. * Greenwood, J. and K.A. Kopecky. "Measuring the Welfare Gain from Personal Computers," ''Economic Inquiry'': 51, No. 1, pp. 336-347. 2013. Welfare economics

See also

References