Knowledge that Transforms

IN THIS paper we report the results of additional experiments with the short-run consumption function. In particular, in Section 2 we take up the problem of isolating expectation, inertia, and habit persistence effects and then go on in Section 3 to the problem of interpreting and estimating a real balance effect. As will be seen, the present work involves nonlinear relationships which have been estimated employing nonlinear techniques. Further, the problem of autocorrelation in distributed lag schemes is dealt with in a manner suggested by Fuller and Martin (1961). Aside from illustrating approaches to these methodological problems, the present study yields results on the role of liquid assets in determining consumption expenditures which, we believe, are of consequence with respect to establishing a direct influence of monetary variables on an expenditure relationship. This and other aspects of our study are discussed and summarized in Section 4.

IT IS GRATIFYING that my paper on Additive Preferences has been the occasion for the preceding note by Samuelson, and also for an independent comment by W. M. Gorman which with characteristic modesty he has withdrawn from publication because its results were similar to Samuelson's. These admirable contributions do not call for extended comment on my part.' I take the opportunity, however, to answer an open question raised by Samuelson.2 This question concerns the existence of a nontrivial self-dual preference ordering, that is a preference ordering with a direct utility function that can be written in the same mathematical form as the corresponding indirect utility function. Writing x for the vector of quantities and y for the vector of prices (each divided by income),3 while 4 and ,G, denote a direct and indirect utility function respectively, a preference ordering is self-dual if it has a +(x) that is the same kind of function of x as at least one jGr(y) is of y. If so, the demand functions x=f(y) and the inverse demand functions y=g(x) must also have the same form. More precisely, there must be a function F such that x=F(y, A) and y=F(x, B), where A and B are sets of m parameters;4 note that Fis a single function, not a class of functions involving arbitrary parameters. Substituting the expression for y into that for x we get the functional equation