LECTURE 8 GENERAL REFLECTIONS ON KEYNESIAN ECONOMICS. THE NUMERICAL VALUE OF THE MULTIPLIER JACOB T. SCHWARTZ EDITED BY KENNETH R. DRIESSEL Abstract. We discuss the significance of the Keynes Theorem and the heuristic model of the Keynesian economics. The multi- pliers are estimated by the statistical data. 1. Over-all Significance of the Keynes Theorem The Keynesian notions which we have approached through the sim- plified cycle-theory model of the last three lectures are so central to all current economic thinking that it is appropriate to dwell upon them, even if this requires us to interrupt our strictly mathematical develop- ment. To write total production − total industrial consumption of elements of(*) production = personal consumption + collective consumption + desired and executed investment + growth of inventories; is to write a tautology that follows from the definitions of the terms involved. But to supplement this tautology with the fact, taken from our cycle-theory model, that definite obstacles can exist to the growth of inventories (as also to the size of other categories of investment), is to make the basic step to the Keynesian theories. 2010 Mathematics Subject Classification. Primary 91B55; Secondary 91B82 . Key words and phrases. Keynesian Economics, Multiplier . 1 2 JACOB T. SCHWARTZ A succinct formulation of classical economics might be Consumption adjusts to the limits imposed by production; Keynesian economics on the contrary insists that Production adjusts to the limits imposed by consumption (and, of course, investment). The classical economics is then the economics of scarcity (no general overproduction of commodities possible), the Keynesian economics is the economics of affluence (general overproduction of commodities a recurrent phenomenon). There is, of course, something paradoxical in describing a recession or depression, which is a period of exceptional hardship and of production in amounts insufficient for general satisfac- tion, and hence is superficially a period of apparent underproduction, by the word \overproduction." That we do so, and that recessions appear in this way in our cycle-theory model, comes from the cir- cumstance that we have formulated our model in a labor-eliminated form; i.e., as a model involving material commodities only. To recon- struct the effect of wage-payments, we must unravel this mathematical simplification. Suppose, for the sake of simplicity, that we have only one single labor sector. Let πij be the extended input-output ma- trix, including the labor-input row and the input-to-labor column. Let ◦ πij denote the matrix with this row and column deleted. Thenπ ~ij ◦ −1 is the matrix πij + (1 − π00) πi0π0j; thus, in using the matrixπ ~ij, the commodities consumed by laborers out of wage payments accruing to the labor required to produce one unit of commodity i are being counted directly as a commodity input required to produce a unit of commodity i. The \consumption" (assumed constant) in our model is consequently nonwage-generated private consumption plus government consumption. Personal consumption, as it ordinarily figures in gross product tables, would then be the fixed autonomous consumption ej plus the wage-generated consumption n X −1 a(n) vi(1 − π00) πi0π0j: i=1 Calling this latter sum uj, we find personal consumption as ordinarily reckoned to be represented in our model by the expression ej + a(n)uj. 8. GENERAL REFLECTIONS ON KEYNESIAN ECONOMICS 3 The fluctuations of consumption during the cycle thus come from the fluctuations of a(n). The “affluence” aspect of a recession is visible to those whose consumption is relatively independent of production and forms a part of the terms e; a rather opposite aspect appears however to those whose consumption is directly dependent upon production and in our grossly simplified model forms part of the terms a(n)u. Demand, if expressed by persons in this later category, may constitute ineffective demand. With this understanding then of the meaning of the terms involved, we may state the Keynes relation (7.10) as n X (8.1)a ¯j − π~ija¯j = ej i=1 or with the inclusion of average investment n X (8.2)a ¯j − π~ija¯i =e ¯j + (investment)j i=1 the bars denoting time-averages. This equation, taken not as an average but as an indicator of the effect of one or another policy (ignoring dynamic complications), is the basis of many Keynesian policy recommendations. Thus, in order to avoid the stresses of recession, one can 1. Increase e, through \spend now" or \spend more" exhortations and programs, civil and military, and through unemployment relief, etc. 2. Increase investment by fast tax write-offs, guarantees against loss, public works programs, etc. 3. Increase the elements ofπ ~ij through wage increases of one or another sort. The difference between the Keynesian and the classical view is dra- matically evidenced by the familiar dispute over point 3 above. The classicist argues that wage cuts in depressions are prime means of bring- ing the depression to an end; the Keynesian considers that by reducing 4 JACOB T. SCHWARTZ the elementsπ ~ij in (8.1) (and perhaps, through reflex, reducing invest- ment) such an act will tend to make a depression worse. According to the Keynesian theory, the production levels are determined by solving the equations (8.2): (8.3a) a¯ = (1 − Π)~ −1(e¯ + investment); since (8.3b) (1 − Π)~ −1 = 1 + Π~ + Π~ 2 + Π~ 3 + ··· ; it is then plain that a¯ increases with Π,~ and hence with the wage level. This result is in direct contradiction to the non-Keynesian economic theory which makes the claim that the proper thing to do in time of depression is to cut wages. To illustrate the definiteness of the difference between Keynes and the classicists on this score, we quote such an opinion from the book of Mr. Henry Hazlitt: If I were put to it to name the most confused and fantastic chapter in the whole of the General Theory, the choice would be difficult. But I doubt that anyone could successfully challenge me if I named Chapter 19, on \Changes in Money-Wages." Its badness is after all not surprising. For it is here that Keynes sets out to challenge and deny what has become in the last two centuries the most strongly established principle in economics|to wit, that if the price of any commodity or service is kept too high (i.e., above the point of equilibrium) some of that commodity or service will remain unsold. This is true of eggs, cheese, cotton, Cadillacs, or labor. When wage rates are too high there will be unemployment. Reducing the myriad wage rates to their respective equilibrium points may not in itself be a sufficient step to the restoration of full employment (for there are other possible disequilibriums to be considered), but it is an absolutely necessary step. This is the elementary and inescapable truth that Keynes, with an incredible display of sophistry, irrelevance, and complicated obfuscation, tries to refute. The difference is evidently marked. We shall return in later lectures to this passage from Hazlitt. Let us only remark here that \classical" conclusions of this type are obtained by arguing that by driving down labor costs a larger total of labor will be used, essentially because man- ufacturers will use labor more freely. In our theory we have assumed fixed production coefficients, including the coefficients πi0: which is to 8. GENERAL REFLECTIONS ON KEYNESIAN ECONOMICS 5 say that the amount of labor is in proportion to production. Thus, we have assumed away Mr. Hazlitt's grounds of argument; the dif- fering conclusions of the present Keynesian theory and the classical non-Keynesian theory can be traced to differing fundamental assump- tions about the operation of an economy. We shall later put the two theories on common ground and be able to make a fairer comparison. We will see that by determining from actual statistics the extent to which production tends to use definite amounts of labor irrespective of wages paid, it is in principle possible to settle this dispute. 2. An Heuristic Model of the Keynesian Conclusions Certain significant features of classical economics appear vividly when presented in terms of a \Robinson Crusoe" model; in which Crusoe, faced with scarcities of almost everything, allocates his efforts to max- imize his satisfaction. It is instructive to set up a similar \Crusoe" picture of the central Keynesian phenomena. This may be done as follows. Crusoe has now occupied his desert island for many years, and, developing his own considerable initial endowments as an engi- neer, installed a complete variety of automatic machinery to supply all his needs. (Note the transition from scarcity to affluence.) It is then quite plain that the statistics for any typical activity of the automatic machinery, as e.g., electric power consumed, footpounds hoisted, etc., will be determined proportionately by Crusoe's desire to consume. If he lives frugally in a given month, the machinery will hardly turn; if he is possessed of a desire to construct a road, a palace, or what have you, the machinery will turn more vigorously. If included among the com- ponents of this machinery are found the humanoid robots beloved of science fiction, then the number of hours of labor performed by robots, their employment or unemployment, would be similarly proportional to Crusoe's desire to consume. Now if Crusoe's man Friday found himself classified among the robots, and paid at a fixed wage rate, he would of course prefer that Crusoe consume more rather than less, and might even try to insist, if he could, that Crusoe regularly engage in activities, wasteful for Crusoe, but sustaining for himself. Crusoe's affluence, if 6 JACOB T.