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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note by Samuelson, and also for an independent comment by W. M. Gorman which with characteristic modesty he has withdrawn from publication because its results were similar to Samuelson's. These admirable contributions do not call for extended comment on my part.'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

IN recent years there has been a good deal of discussion concerning the relationships among market structure, research and development, and the rate of technical change. Much of this discussion has focussed on the question of whether large firm size is a necessary condition before firms will engage in research, and whether research and development (R and D) is likely to grow more or less than in proportion to increases in firm size. A further set of questions deals with the relationship between research and the rate of technical change experienced by the firm. Can variation in the latter be explained largely by differences among firms in the size and character of their research programs? Are economies of scale in R and D likely to be present? What is the effect of firm size on the productivity of a research establishment? This paper provides an empirical analysis, concerned with these questions, of the experience of the United States pharmaceutical industry during the period between 1955 and 1960.

Richard S. Thorn, A Proposal to Remove Some Disequilibrating Movements in Official Holdings of Foreign Exchange: A Rejoinder, The Review of Economics and Statistics, Vol. 47, No. 3 (Aug., 1965), pp. 331-334

Journal Article Capital Longevity and Economic Growth Get access S. K. Bhattacharyya S. K. Bhattacharyya London School of Economics and Calcutta University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 32, Issue 1, January 1965, Pages 39–46, https://doi.org/10.2307/2296329 Published: 01 January 1965