The Qualitative Content of Maximizing Models

Abstract

It seems unfortunately to be the case that the general qualitative content of maximizing models is small, if not trivial. By ‘general’ here is meant explicitly ‘knowing or assuming no more than that sufficient conditions for an extreme solution are satisfied’.² This is enough, as Samuelson showed,³ to prove the basic theorem of conjugate pairs; but, unfortunately, the case of conjugate pairs appears to be the only case in which an unambiguous qualitative prediction can be obtained, and yet not be empirically a very important case. A good deal of attention has been given in recent years to cases that are not conjugate pairs; and surprise and disappointment are often expressed at the discovery that the conventional — or ‘general’ — allowance of qualitative information is not sufficient for an unambiguously signed prediction to be obtained. Thus one object of this paper is to gather together some of these cases, and to show that the reason for the lack of qualitative content is the same, that the theorem of conjugate pairs cannot be used, while another object is to set out systematically what can be got from the theorem, and to offer some assessment.

I owe an enormous long-term debt to my colleagues in the Staff Seminar on Methodology, Measurement, and Testing in Economics at the London School of Economics, and to Kelvin Lancaster in particular. My immediate debt is to Hugh W. Folk, with whom I have had the privilege of discussing each stage during the writing of this paper. I am also grateful to him and to Dipak Banerjee, Peter B. Kenen, and Sidney Winter for comments on an earlier draft.