Knowledge that Transforms

AT least since Mandeville's Fable of the Bees (I728), there have been underconsumptionists who have ascribed trade depressions to deficiency in consumption expenditures.' Underconsumptionist thought may further be subdivided into two schools. Monetary underconsumptionism, which does not concern us here, blames underconsumption upon flaws in the processes of creation and circulation of money and credit. Social Credit movement in Great Britain and the Greenback movement in the United States may serve as illustrations. Since Marx and Rodbertus, however, the deficiency of consumption expenditures (and purchasing power) has been ascribed more commonly to maldistribution of real income. This we shall call maldistributionist or real underconsumption. During prosperity, income is concentrated in the higher brackets, where a large fraction is saved. If the savings are hoarded, there arises an immediate deficiency in consumption. If the savings are invested, the deficiency is only postponed until the day when additional consumption goods are produced because of the new investment, and come on to market without additional purchasing power to absorb them. Such, in briefest outline, is the position of the late John A. Hobson, the leading English-language representative of real underconsumptionism in the twentieth century.2 In this view, the principal means to prevent and to remedy depressions is substantial redistribution of income in the direction of greater eaualitv. In addition to Rodbertus, Marx, Hobson, and other leaders of the economic underworld, Keynes has given this position an indirect accolade in the General Theory,3 and it has been adopted by a substantial fraction of the neo-Keynesian school. Virtually all of the discussion, however, has been carried on in a quantitative semi-vacuum, which is to say, without any precise ideas as to the quantitative importance of possible income redistributions. It was of course recognized from the outset that personal savings rise faster than personal income, or in current jargon, that individuals' average propensities to save rise with their incomes. What was not recognized, however, was that for redistribution problems the relative marginal propensities to save of different income classes were likewise important, since redistribution involves shifts between income classes at the margin. To cite an extreme case, if all individuals' marginal propensities to save were identical, equalization of incomes would have no effect whatever on aggregate consumption and saving, however great might be the disparities in average propensities between rich and poor.4 Keynes himself, it would appear, was guilty of some inconsistency on this subject. He considered his consumption function relatively stable (which presumably means stable with respect to changes in income distribution), and at the same time he advocated income equalization in the interest of increased aggregate consumption. One of the first studies to apply modern aggregative analysis in estimating the quantitative effect of income redistribution on aggregate consumption was carried out by Harold Lubell at the Board of Governors of the Federal Reserve System.5 His study, which has been un* This study was financed by a grant from the Social Science Research Committee of the University of Wisconsin. 1 Harry G. Johnson cites the French Physiocrat Boisguillebert a century earlier as maintaining that trade would be more active if taxation fell on the rich than if it fell on the poor, which comes closer than Mandeville to a maldistributionist position. The Macro-Economics of Income Redistribution, in Alan T. Peacock (ed.), Income Redistribution and Social Policy (London, I954), p. I9. 2 For a full presentation of Hobson's views, see Erwin E. Nemmers, Hobson and Underconsumption (unpublished Ph.D. dissertation, Wisconsin, I953). We have called Hobson a twentieth-century writer, :but the initial presentations of his views appeared before the turn of the century. 'Keynes, General Theory, pp. 369-74. ' average propensities are important in this case only if ioo per cent of one individual's income is being taken away, or in a case where income is being given to individuals who had none before. 5 Harold Lubell, Effects of Income Redistribution on Consumers' Expenditures, American Economic Review, xxxvii (March 1947), 157-70, corrected in part, ibid., xxxvii (December 1947), 930. Lubell results appear to have furnished statistical

THE purpose of this paper is to analyze the formal structure of the matrix as an accounting tool (I to 7), to review actual inputoutput matrices under the aspect of their formal structure (8), and finally to construct an income-product matrix (g to I 2 ). i. A matrix, as used in macro-accounting, is a form of presentation of accounting material. It is distinguished from other forms of presentation mainly by four technical features: economy in figures, consolidation of interaccount flows, absence of narrations, and specific grouping of the accounting material. The economy in figures is obtained by making one figure serve two purposes simultaneously. According to the direction in which it is read, either vertically or horizontally, a figure is either a debit entry or a credit entry. This feature has the advantage that the number of figures required to communicate a given volume of information is in a matrix roughly one-half of that required in any other form of accounting statement. On the other hand, difficulties arise if the volume of information becomes large. The usual device of making statements manageable in size, which is to relegate part of the information to subsidiary schedules, is not available in the case of a matrix, because, in consequence of the double purpose served by each figure, figures cannot be taken out of the context within the matrix. A matrix grows therefore in direct proportion to the volume of information and, after a certain point, becomes an unwieldy instrument. The second feature is the necessity of consolidating inter-account flows. Transactions affecting any two accounts have to be contracted into two figures, because the framework of a matrix has only two places available for the record of flows affecting two accounts. One is the place of intersection of the row representing the credit entries to the first account with the column representing the debit entries to the second account; in this place, the flows from the first to the second account are recorded. The other place is the intersection of the row of the second account with the column of the first account, which is the place for the flows from the second to the first account. The matrix thus allows an expression of the direction in which transactions flow between any two accounts. But no more. If the transactions between two accounts are for instance composed of a number of heterogeneous flows and that occurs quite regularly in macro-accounting the social accountant faces an inconvenient choice. One alternative is to consolidate different transactions among the same transactors. This entails a loss of information or even of meaning, though the macro-accountant may help himself to some extent by cumbersome devices such as double rows 1 or footnotes. The other alternative is to split one transactor into as many accounts as different intertransactor-relations are to be recorded. This entails a loss of institutional or other transactor unity. In any case, the number of meaningful flows between two transactors which can be shown in a matrix is technically limited by the number of available accounts. The third feature of a matrix is the absence of what accountants call narration, that is a short explanation of the meaning of an entry. An economy in text is thus added to the economy in figures, making the matrix a still more concise form of presentation. Without the guidance of narrations, the reader of a matrix can derive the meaning of an entry solely from the captions of the row and column at whose intersection the figure stands. In this way, captions in a matrix are charged with two functions. They have to describe not only the account as a point of reference, but also the kind of transactions entered in the account. To call a personal account by the name of the transactor, or the impersonal account by the subject-matter assembled in it, is not sufficient. A way must also be found to describe the transactions entered in the account; otherwise

IT all began when that Schumpeterian innovator, John Maynard Keynes, introduced into a model the idea that savings and investment are brought to equality not (merely) by changes in the rate of interest but by changes in the level of income. Business cycle theorists -some of them -had assumed for decades that fluctuations in the rate of capital formation caused fluctuations in the level of income. But because the then foundations of economic theory included the axiom that the flow of saving and that of investment are brought to equality by the interest mechanism, without aid from change in the income level, cycle theorists were inhibited from pursuing the implications of their assumption, and schizophrenia divided cycle theory from the central body of economic theory. So it was not until Keynes broke the cake of custom and elevated the determinants of saving to a new importance that the search for knowledge of those determinants began. In a limited sense this statement is incorrect, for studies of the relationship between family income and components of family expenditure go back a century. But these were not directed toward an understanding of the determinants of aggregate consumer expenditure in an economy, and so at least in purpose they are not forerunners of the studies discussed here. Not many topics in the history of the development of economic theory have occasioned more discussion within a period of some two decades than has the form of the consumption function since the publication of the General Theory in I936. The discussion continues, among other places, in many of the papers in Savings in the Modern Economy,* the point of departure for this essay. And the end is not yet. On the contrary, the present state of the discussion invites further research. This is natural. The maturation period of an idea is often longer than that of a man.