1. Deference to the reader calls for a blueprint of the article's contents. Its contributions are of two distinct varieties. The first and prime contribution consists in the extension of existing analyses for finite numbers of commodities to the case of infinitely many. Hotelling and others have emphasized the desirability of stating the results of entrepreneurial and consumer demand theories for infinite numbers of goods. Apart from its utility in treating commodity groups embracing large, though not necessarily infinite, numbers of items, the economic properties of which shade from one member to the next, the extension is stamped with true intellectual concinnity. The finite theories are contained, as very special cases, in the infinite analyses. A more distinctly economic flavor breathes from the second species of offering. It includes propositions and economic tools novel even to the finite analyses. The theorem that an entrepreneur's derived demand functions for factors of production are stable in the sense of Hicks' extension of the classical definition is an example.' Evolution of the inverse utility function (more properly functional), described in ?2, is another. Unlike its counterpart, the inverse utility function is a function of prices. Economically, it is the negative of the maximum utility attainable by the consumer, income specified, when a stated price regime prevails in the competitive market. Noteworthy operational properties characterize the inverse utility function. Designate the consumer's budgetary limitation, prices constant and quantities varying, direct. Term it inverse when quantities remain constant and prices vary. Maximization of the utility function subject to the direct budgetary limitation results in individual consumer demand functions. Maxi-

(1) MR. HAAVELMO' contends that the variate difference method is not applicable to certain dynamic economic schemes, as, e.g., the cobweb theorem. It never has been claimed that this is the case, and the author has pointed out very carefully in his monograph2 that the variate difference method deals only with superimposed random variation. A more extensive discussion of the general problem of the role of errors in economics is to be found in a short article published in the Quarterly Journal.3 The view is put forward there that some types of errors have a deep-rooted influence on economic developments, and this is in agreement with Mr. Haavelmo's statements. Dynamic schemes, like the one of Frisch and the ideas indicated in Haavelmo's article have to be dealt with by other methods. These problems are probably closely related to a study of serial correlation. The author has indicated some possible methods of analysis in an appendix of his monograph4 and even put forward tentatively an exact test of significance for serial correlation based upon the method of selection. (2) The author has indicated5 that he does not consider the method of selection an entirely satisfactory test of significance for the equality of the variances of two consecutive series of differences. It is of course very true that the test is not efficient since it utilizes only a certain percentage of the total data available. The fundamental hypothesis tested is the equality of the variances of two consecutive difference series. The case that the variance of the higher difference series is larger and not smaller than the variance of the lower difference series can arise (a) because they are really equal and appear different because of chance fluctuations, (b) because the variances form an increasing instead of a decreasing series and the whole method is not applicable. For this reason it seems that we have to consider not only the upper but also the lower tail of the distribution in testing the hypothesis that the variances of two consecutive difference series are equal and appear different only because of random fluctuations.