You may recall that I was rather critical of the Harvard economist Mankiw on this blog recently. In my piece I quoted Mankiw in a concessionary way, "it is also a standard result that in a competitive equilibrium, the factors of production are paid the value of their marginal product. That is, each person’s income reflects the value of what he contributed to society’s production of goods and services." I then argued, "Well, yes, this is true, and the theoretical work of "Gerard Debreu and Herbert Scarf" (1963) does allow one to see that "if the freedom to exit a society is taken as axiomatic, then the only permissible allocations of resources are the competitive market equilibria." I then went on to show why this provides no support for just-desert theory in the real world.
But as the distinguished mathematical economic theorist, M. Ali Khan (Johns Hopkins) (whose writings on the shared history of philosophy and economics are a must read to anybody serious about these matters) pointed out to me, "the Debreu-Scarf] theorem is false (first noticed explicitly by Foley of the New School) in the presence of public goods." (See Foley's piece here; see especially the conclusion. See also Muench 1972) Mankiw's whole appeal to Debreu/Scarf should be understood rhetorically (now in pejorative sense): cite some esoteric/technical literature in order to silence opponents and assume that the real experts are too polite to call you out (or maybe he misremembered from graduate school?)!
UPDATE: In an early version of this entry, I wrote "Since Mankiw's argument tendentiously ignores the contribution of public goods." Professor Mankiw kindly and correctly points out that he does discuss public goods in his piece. (In particular, to argue for progressive taxation and transfers to the poor.)
In fact, in his piece, Mankiw discusses Lindahl's work, so it all the more puzzling he chose to make his argument in terms of Debreu/Scarf.
Recent Comments