On a Difficulty in Welfare Economics: Numeraire Illusion in the Marshall-Pigou-Kaldor-Hicks Methodology

The Kaldor-Hicks criterion (potential Pareto improvement) and the careful treatment of consumer and seller surpluses have fostered a modern revival of an older Marshall-Pigou tradition of welfare economics. That tradition was based on the parsing of a potential change into a change in the size of some "social pie" measured in money (e.g., Pigou's "national dividend") and a change in the distribution of the pie. By characterizing an increase in the size of the pie (i.e., a Kaldor-Hicks improvement) as an "increase in efficiency," this modernized Marshall-PigouKaldor-Hicks (MPKH) tradition seeks to transcend the strictures of the Paretian treatment of efficiency (which would require actual compensation of the losers so that the whole change was a Pareto improvement). Economists can then with clear professional conscience make the policy recommendation for the increase in efficiency and put to one side the question of compensating the losers as a separate question of equity. However, this whole efficiencyequity analysis turns out to be vulnerable to a simple redescription of exactly the same total change using reversed numeraires. Then the "efficiency" change and the "equity" change reverse themselves so the "policy recommendation" would reverse itself as well. The flaw is the "numeraire illusion" involved in concluding that transfers in the numeraire (e.g., the compensation) do not increase value since they make no change in the size of the pie as measured by the same numeraire. Changes in a yardstick will never be revealed by that yardstick—but are revealed by switching to a different yardstick (or numeraire). This result undercuts the major applications of the MPKH methodology in the standard Chicago school ("social wealth" maximization) of law-and-economics, costbenefit analysis, policy analysis, and related parts of applied welfare economics.