Signature
NG = sum_(i=1)^n [N_i * CV_i]
| Inputs | Definition | Unit |
|---|---|---|
N_i | Number of people in group i, all affected alike | count of people |
CV_i | Compensating variation per person in group i: willingness to pay for a gain, or minus the compensation needed for a loss | currency per person |
NG | Sum over groups of the money gains minus the money losses | currency |
|---|
nNumber of groups affected, equal to the length of the N_i and CV_i lists (count)
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.
Try this function
Implementations
Excel
Aggregate net gain from group sizes and money measures
With group sizes in GroupSizes and money measures per person, negative for losers, in GainPerPerson, Excel returns the aggregate net gain; the second formula applies the Kaldor test.
=SUMPRODUCT(GroupSizes,GainPerPerson); =SUMPRODUCT(GroupSizes,GainPerPerson)>0
Assumptions
Equal weight on every unit of money
Each pound counts the same whoever gains or loses it. Because willingness to pay is bounded by income, the sum gives more weight to the preferences of people with more money unless distributional weights are applied.
Hypothetical compensation
Passing the test shows that compensation is possible, not that it is paid. Without payment the losers remain worse off.
Consistent ranking
Scitovsky showed that a change and its reversal can both pass the Kaldor test when the change alters the goods available. The double criterion requires that the change passes and its reversal fails.
Worked examples
Concentrating a specialist service
In the article's illustrative example, 1,000 people in Group A would each pay up to 300 pounds for the change and 1,000 people in Group B would each need 200 pounds in compensation. The aggregate net gain is 100,000 pounds, so the change passes the Kaldor test although it is not a Pareto improvement.
N_i = [1000,1000]; CV_i = [300,-200]; n = 2; NG = 100000
Larger losing group
If the outlying group had 1,600 members, each needing 200 pounds, the aggregate net gain would be minus 20,000 pounds and the change would fail the test.
N_i = [1000,1600]; CV_i = [300,-200]; n = 2; NG = -20000
Common errors
Reading a positive net gain as a Pareto improvement
A net gain of 100,000 pounds leaves 1,000 people worse off unless compensation is paid. The test shows potential, not actual, improvement.
Omitting the programme's resource cost
In applied cost-benefit analysis the opportunity cost of the resources used is a loss to someone and enters the sum. The worked example sets it aside only because every option costs the same.
Sources
Kaldor potential compensation criterion
Kaldor N. Welfare propositions of economics and interpersonal comparisons of utility. Economic Journal. 1939;49(195):549-552. A change is an improvement if those who gain could compensate those who lose and still be better off, whether or not compensation is paid.
Hicks on compensation and welfare economics
Hicks JR. The foundations of welfare economics. Economic Journal. 1939;49(196):696-712. Reforms judged by whether they would allow compensation of the losses and still show a net advantage.
Canonical Identity
Stable URI · Machine-readable · Resolvable · CC BY 4.0