Journal Article The Pareto Distribution and the Cobb-Douglas Production Function in Activity Analysis Get access H. S. Houthakker H. S. Houthakker Stanford, California Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 23, Issue 1, 1955, Pages 27–31, https://doi.org/10.2307/2296148 Published: 01 April 1955

Compensated Changes in Quantities and Qualities Consumed Get access H. S. Houthakker H. S. Houthakker Cambridge Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 19, Issue 3, 1952, Pages 155–164, https://doi.org/10.2307/2296018 Published: 01 January 1952

Peak Loads and Efficient Pricing: Further Comment Get access H. S. Houthakker H. S. Houthakker Stanford University Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 72, Issue 3, August 1958, Pages 463–464, https://doi.org/10.2307/1882235 Published: 01 August 1958

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note by Samuelson, and also for an independent comment by W. M. Gorman which with characteristic modesty he has withdrawn from publication because its results were similar to Samuelson's. These admirable contributions do not call for extended comment on my part.'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

FEW DATES in the history of econometrics are more significant than 1857. In that year Ernst Engel (1821-1896) published a study on the conditions of production and consumption in the Kingdom of Saxony [6], in which he formulated an empirical law concerning the relation between income and expenditure on food. Engel's law, as it has since become known, states that the proportion of income spent on food declines as income rises. Its original statement was mainly based on an examination of about two hundred budgets of Belgian laborers collected by Ducp6tiaux. Since that date the law has been found to hold in many other budget surveys; similar laws have also been formulated for other items of expenditture. With the formulation of Engel's law an important branch of econometrics took its start, though it was not until our days that consumption research was placed on a sound theoretical and statistical basis. It is proper that in this centennial year econometricians should pay tribute tzo one of their most illustrious precursors. His successful attempt to derive meaningful regularities from seemingly arbitrary observations will always be an inspiring example to the profession, the more so because in his day economic theory and statistical techniques were of little assistance in such an attempt. There can, I think, be no more fitting tribute to this enlightened empiricist than a further inquiry into the subject to which he devoted much of his life's work. There is no need to go into details of Engel's analysis and of the developments that preceded it, for these matters have recently been discussed in the scholarly article by Stigler [13]. It should be enough to note that Engel was mainly influenced by two of his older contemporaries. One was the French engineer Fred6ric Le Play, who had collected budgets from households all over Europe, mostly, it seems, from humanitarian interest. Engel had been Le Play's student at the Ecole des Mines in Paris. The other main influence was the Belgian statistician Qu6telet, who was a firm propoinent of the idea that human characteristics, at least in the average, were governed by laws as definiite as those which govern

(e) Net interest paid by government. The national income net interest total comprises total interest accruing to United States persons and governments less the total interest paid by United States governments to persons, governments, and businesses. The personal income interest total is obtained by adding to the national figure the excess of interest payments by governments over their interest receipts. Thus it measures total interest paid to United States persons.3 The share of the national total attributable to any one state is extremely difficult, if not impossible, to estimate by direct means, if this were desired. But allocation can be made more easily, although the method rests upon the same sort of fundamental and hazardous assumptions as in the case of allocating corporate income. Figures are availalble from the Department of Commerce of private interest received by residents of Texas and the United States. The Texas state income component of United States net interest paid by governments was obtained by applying the ratio obtained from the private interest figures to the United States net government interest total. The assumption here, of course, is that Texas residents' entitlement to a share of the national total of net government interest was the same as their entitlement to a share of the national total of private interest, as reflected in the payments actually made or imputed. The method also, as in the corporate income case, has the merit of conforming to the conceptual framework which emphasizes the wherereceived measure. TABLE 4.-GOVERNMENT AND BUSINESS TRANSFER PAYMENTS, TEXAS, I950-58 ($ million)