On Professor Neisser on Magnification

Abstract

an essential part of the theory and study of competition and monopoly. Second, in any industry or other meaningful group, the number of firms, an essential magnitude in Mr. Prais's system, is usually un-knowable with any precision.4 It follows that average size or growth rate is equally unknowable. In any case, Mr. Prais's definition of concentration, as he points out, is a member of the same family as the Gini coefficient (op. cit., 268), or what I called Lorenz-type concentration, and that type has been rejected implicitly by other students, and explicitly by me, again, not for reasons of internal consistency, but of relevance to economic analysis. Mr. Prais's system has the immense advantage (and prestige) of being an extension of the classical statistical system, with all the logical symmetry and practical aids this would imply since it is a sum of squares, for example, it is additive, and significance tests are directly applicable. By comparison, the concentration ratio is a very clumsy and imperfect sort of expedient; the nearest approach to a general theory is in a brilliant paper by Jiirg Niehans.5 It would be incorrect, however, to leave the reader with the impression that Mr. Prais's system is of no interest or use. First, it may be applicable to non-economic problems, or to economic data which neither of us has investigated. Second, we should be interested in differential growth rates as such. Stephen Hymer and Peter Pashigian presented a paper, Firm Size and Differential Growth Rates, to the I958 meetings of the Econometric Society; although they did not have occasion to use measures of Mr. Prais's type, it is conceivable that others could. Finally, it is not only helpful but essential to conceive of the operations of any industry as a general system of random influences which will cause firms to gain or lose position or market share. Tendencies toward greater or lesser concentration, or toward no change, must be fitted into or superimposed upon such a general framework, or else we hail every passing leaf as evidence of the prevailing wind. I do not think Mr. Prais's definition of concentration is of any help in this task, but this is perhaps secondary; it should stimulate thinking toward incorporating the notion of a statistical system into the analysis of industry situations. 4 Ibid., and see the chapter on The Business Population in the forthcoming revision of Historical Statistics of the United States. 5 Jiirg Niehans, Eine Messziffer fur Betriebsgrossen, Zeitschrift fur die Gesamte Staatswissenschaft, iII (I955), 529-42. It is to appear in English in a forthcoming issue of International Economic Papers.