Money-metrics in local welfare analysis: Pareto improvements and equity considerations

We identify local Pareto improvements from a valuation equilibrium, and extend the results of Hirshleifer, Arrow-Lind, Milleron, and Radner on the evaluation of small projects to behavioral or nonstandard choice models. We use the sign of directional derivative of the sum of McKenzie-Samuelson money metrics to evaluate small projects, but, rather than assume its differentiability, furnish preference conditions that guarantee it. Our methods yield, as an unintended consequence, (i) a refutation of Samuelson's (1974) conjecture that the money metric is locally concave in a neighborhood of a demand point, thereby settling an issue open for five decades; and (ii) a substantive extension of the 1988 Blackorby-Donaldson theorem that the money metric is concave in consumption only if preferences are quasihomothetic. We explain some equity implications of our local-welfare result, and as part of the rehabilitation of money metrics, suggest a case for using a second-order approximation to a money metric for local welfare. We illustrate when our results hold and don't hold with several non-standard choice models.