Money Metric, Consumer Surplus and Welfare Measurement

The paper provides a rigorous derivation of the "welfare triangle approximation" (WTA), which is at the center of cost benefit analysis. The result is generalized by showing that the WTA is one of two dual expressions, one of which approximates the change in real consumption, the other the change in the cost-of-living. The result is based on a correction of a proof attempted by Hicks. Many other derivations are also given, each based on a different definition of the theoretical functions to be approximated. The final result is the following: Each of the empirical variations corresponds to a range of theoretical variations. The edges of the range are theoretical Laspeyres and Paasche variations which are approximated linearly; the interior region of the range is approximated quadratically; the center of the range is replicated exactly by the empirical measures