Compensating variation
Encyclopedia
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 its initial utility after a change in prices, or 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
, e(p,u):
where
is the wealth level, 
and 
are the old and new prices respectively, and 
and 
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, v(p,w):
one of the equivalent definitions of the CV.
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.
Equivalent variation
(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 normal nor inferior, or when there are no income effects for the good, then EV (Equivalent variation
) = CV (Compensating Variation) = CS (Consumer Surplus)
.
The compensating variation resulting from the introduction of this new product is
Assuming no income effect
and no sales of the product prior to introduction 
, this simplifies to
For no income effect but previous products on the market at a different price,
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
, compensating variation (CV) is a measure of utility change introduced by John Hicks
John Hicks
Sir John Richard Hicks was a British economist and one of the most important and influential economists of the twentieth century. The most familiar of his many contributions in the field of economics were his statement of consumer demand theory in microeconomics, and the IS/LM model , which...
(1939). 'Compensating variation' refers to the amount of additional money an agent would need to reach its initial utility after a change in prices, or 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
Expenditure function
In microeconomics, the expenditure function describes the minimum amount of money an individual needs to achieve some level of utility, given a utility function and prices....
, e(p,u):
where
is the wealth level, and are the old and new prices respectively, and and 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, v(p,w):
one of the equivalent definitions of the CV.
Compensating variation is the metric behind Kaldor-Hicks efficiency
Kaldor-Hicks efficiency
Kaldor–Hicks efficiency, named for Nicholas Kaldor and John Hicks, also known as Kaldor–Hicks criterion, is a measure of economic efficiency that captures some of the intuitive appeal of Pareto efficiency, but has less stringent criteria and is hence applicable to more circumstances...
; if the winners from a particular policy change can compensate the losers it is Kaldor-Hicks efficient, even if the compensation is not made.
Equivalent variation
Equivalent variation
Equivalent variation is a measure of how much more money a consumer would pay before a price increase to avert the price increase. Because the meaning of "equivalent" may be unclear, it is also called extortionary variation...
(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 normal nor inferior, or when there are no income effects for the good, then EV (Equivalent variation
Equivalent variation
Equivalent variation is a measure of how much more money a consumer would pay before a price increase to avert the price increase. Because the meaning of "equivalent" may be unclear, it is also called extortionary variation...
) = CV (Compensating Variation) = CS (Consumer Surplus)
Example of Adding a New Product
Assume a log-linear demand function for a product given by.The compensating variation resulting from the introduction of this new product is
Assuming no income effect
and no sales of the product prior to introduction , this simplifies toFor no income effect but previous products on the market at a different price,