Signature
CV = e0_u0 - e1_u0; EV = e0_u1 - e1_u1
| Inputs | Definition | Unit |
|---|---|---|
e0_u0 | Minimum expenditure at the original prices to reach the original utility level, equal to income | currency per person |
e1_u0 | Minimum expenditure at the new prices to reach the original utility level | currency per person |
e0_u1 | Minimum expenditure at the original prices to reach the utility level achieved after the change | currency per person |
e1_u1 | Minimum expenditure at the new prices to reach the new utility level, equal to income | currency per person |
CV | Income that could be removed after the change leaving utility at its original level, positive for a gain | currency per person |
|---|---|---|
EV | Income that would give the same utility as the change at the original prices, positive for a gain | currency per person |
Function
Welfare change measurement and aggregation function
Converts each person's gain or loss from a change into money, with the compensating or equivalent variation or the consumer surplus approximation, and then ranks the change for society: by adding the money measures, as the Kaldor-Hicks potential compensation test does, or by combining individual outcomes with an explicit social welfare function that states how gains to one person are set against losses to another.
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Implementations
Excel
CV and EV from four expenditure values
With the four expenditure values in ExpOldPriceOldUtil, ExpNewPriceOldUtil, ExpOldPriceNewUtil and ExpNewPriceNewUtil, Excel returns CV and EV.
=ExpOldPriceOldUtil-ExpNewPriceOldUtil; =ExpOldPriceNewUtil-ExpNewPriceNewUtil
Assumptions
Income unchanged by the policy
Only prices change, so e0_u0 and e1_u1 both equal income. For a change in the quantity of a non-market good, such as a person's own health, the same logic applies with the expenditure function defined over that quantity.
Known preferences
The expenditure function comes from a specified utility function or an estimated demand system. Stated-preference surveys estimate CV or EV directly as willingness to pay or to accept, as set out on the willingness-to-pay page.
Worked examples
Halving the price of a health service with Cobb-Douglas preferences
A person with income 1,000 spends 20% of it on a health service whose price falls from 20 to 10. With Cobb-Douglas preferences the expenditure needed for the original utility falls to 870.55, and reaching the new utility at the old prices would cost 1,148.70. CV is 129.45 and EV 148.70; the consumer surplus from the demand curve, about 138.63, lies between them. The figures are illustrative.
e0_u0 = 1000; e1_u0 = 870.55; e0_u1 = 1148.70; e1_u1 = 1000; CV = 129.45; EV = 148.70
Doubling the price of the same service
Reversing the change, a price rise from 10 to 20, gives CV of minus 148.70 and EV of minus 129.45: the compensating variation of a loss equals minus the equivalent variation of the matching gain.
e0_u0 = 1000; e1_u0 = 1148.70; e0_u1 = 870.55; e1_u1 = 1000; CV = -148.70; EV = -129.45
Common errors
Using a stated willingness to accept as a compensating variation for a gain
For a gain, CV is the maximum willingness to pay and EV the minimum willingness to accept to forgo it. Mixing the two measures across gainers and losers in one comparison changes the result when income effects are large.
Assuming CV and EV are equal for health
The two coincide only without income effects. They differ most for goods with few substitutes, and a person's own health is one.
Sources
Expenditure function measures of welfare change
Mas-Colell A, Whinston MD, Green JR. Microeconomic Theory. New York: Oxford University Press; 1995. Section 3.I, Welfare evaluation of economic changes: equivalent and compensating variation defined with the expenditure function, and the area variation measure of consumer surplus.
Canonical Identity
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