Wednesday, September 25, 2013

S. Abu Turab Rizvi, Not Steve Keen

Notice the point about the need in neoclassical theory to assume that preferences satisfy Gorman's assumptions of identical and homothetic (non-varying with income) preferences:

"Extensions of the basic arbitrariness results to configurations of preferences and endowments which are in no way 'pathological', and are in fact more and more restrictive, indicate the robustness of S[onnenschein-]M[antel-]D[ebreu] theory.

For instance, an assumption which is often made to improve the chances of meaningful aggregation is that of homothetic preferences, which yields linear Engel curves and so no complicated income effects at the level of the individual. However, with only a slight strengthening of the requirements of Debreu's theorem, Mantel (1976) showed that the assumption of homotheticity does not remove the arbitrariness of A[ggregate] E[xcess] D[emand functions].

Moreover, the possibility that consumers have to be very different, or that unusual endowment effects need to take place, in order for SMD-type results to hold was refuted by Kirman and Koch (1986): even supposing consumers to have identical preferences and collinear endowments does not remove the arbitrariness of the AEDs. Of course, if preferences are simultaneously identical and homothetic, AED is a proportional magnification of individual excess demand (Gorman, 1953; Nataf, 1953) and the whole economy behaves as if it were an individual (obeying the Weak Axiom of Revealed Preference in the aggregate), but this is an extremely special situation. The Mantel and Kirman-Koch theorems effectively countered the criticism of SMD theory raised by Deaton by showing that the primitives can be arrayed in ways which on the face of it are very congenial towards generating well-behaved results, yet the arbitrariness property of AEDs remains." -- S. Abu Turab Rizvi, "The Microfoundations Project in General Equilibrium Theory", Cambridge Journal of Economics, V. 18 (1994): p. 362.

In short, neoclassical economists have proved (by contradiction, in some sense) that neoclassical microeconomics is not even wrong and that methodological individualism has failed.

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