by Michael Emmett Brady
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Product Description
The standard view of the economics profession is that Keynes was a brilliant, intuitive, non-rigorous innovator who was unable to apply formal mathematical analysis in his work. These essays show that Keynes backed up his "intuitions" with a rigorous mathematical and logical supporting analysis which has been overlooked by the economics profession for 70 years.The most likely reason that this occurred is that the ECONOMICS PROFESSION HAS ACCEPTED AS TRUE A NUMBER OF CANARDS CONCOCTED BY RICHARD KAHN,JOAN ROBINSON,AND AUSTIN ROBINSON that claimed that Keynes was a poor mathematician by 1927, who had never taken the 20 minutes that were necessary to master the theory of value(microeconomics).The result was that Keynes made all kinds of mathematical errors in his analysis of the aggregate supply function,Z,that his mentor,Richard Kahn,was not able to catch because Keynes had published the book prematurely. This is an abridged edition of my 2004 book,"Essays on J M Keynes and..."that concentrates on Keynes´s mathematical modeling of his theory of effective demand in chapters 20 and 21 of his General Theory(1936).I have added three new essays.The fundamental result of the book is to demonstrate mathematically that Keynes had a complete microeconomic foundation for his macroeconomic theory built on the theory of purely competitive firms.There are two different but complementary models in the GT.They are the Y-Multiplier model of chapter 10[Y=PO;Y=C+I=bY(or C=a+bY)+(1-b)Y],where Y is actual or realized nominal aggregate demand and P is the actual price level, and the expected D-Z model of chapters 3,20,and 21[D=pO and Z=wN+P],where p is the expected price,D is the expected,nominal aggregate demand, and P is the expected economic profit.This model is explicitly discussed by Keynes in straightforward English in chapter 3 and mathematically analyzed in chapters 20 and 21.Any reader who can integrate the derivatives presented by Keynes in ft.2,pp.55-56 or fts.1 and 2 on p.283 of the GT,can obtain this model.Keynes puts both of his models together to obtain his generalized version of classical and neoclassical theory,w/p=mpl/(mpc+mpi),where mpl is the marginal product of labor in the aggregate derived from an aggregated neoclassical production function(pp.283,285 of the GT),w/p is the expected real wage,mpc is the marginal propensity to spend on consumption goods,and mpi is the marginal propensity to spend on investment goods.If mpc+mpi=mpc+mps=1,where mps is the marginal propensity to save,Keynes´s general result simplifies to the standard neoclassical result that w/p=mpl defines a full employment equilibrium with only frictional and voluntary unemployment.On the other hand,if mpc+mpi<1,one of a number of possible unemployment equilibriums occurs which labor,in the aggregate,will be unable to eliminate because ,in this case ,the money wage must be increased,not decreased.Keynes is the first economist in history to analyze a set of stable,macroscopic, multiple equilibria.The technical result is discussed in literary fashion on pp.261-262 of the GT in chapter 19 for those 1930´s economists who lacked mathematical training in the differential and integral calculus.Keynes would be shocked to discover that the economics profession has,for the last 70 years contended either that (a)there is no mathematical model of Keynes´s theory in the GT that incorporates microeconomic foundations or(b)there is a model in the GT,but it is filled with all types of mathematical errors.Anyone trained in calculus at the lower division,undergraduate level can discover for himself that both (a) and (b) are false.
Average Customer Review:
1 of 4 people found the following review helpful:
The D-Z is Model Built On What Keynes Knew Were False Assumptions, 2008-03-11
Allow me to offer some reasons why economists have ignored the model contained in chapters 20-22 of The General Theory. I will hold back my own criticisms and focus on Keynes's qualifying statements.
Let's begin with a discussion of Keynes's initial assumptions. Brady fails to admit that these assumptions must be taken into consideration when questioning the validity of the theory: "Let us assume (to begin with) that the propensity to consume is given as well as the other factors which we have taken as given in chapter 18 above" (p. 281). Here are the assumptions that Keynes spells out in chapter 18: "it may be useful to make clear which elements in the economic system we usually take as given, which are the independent variables of our system and which are the dependent variables ... We take as given the existing skill and quantity of available labor, the existing quality and quantity of available equipment, the existing technique, the degree of competition, the tastes and habits of the consumer . . . the social structure including the forces . . . which determine the distribution of the national income. This does not mean that we assume these factors to be constant; but merely that, in this place and context, we are not considering or taking into account the effects and consequences of changes in them. Our independent variables are, in the first instance, the propensity to consume, the schedule of the marginal efficiency of capital, and the rate of interest ... Our dependent variables are the volume of employment and the national income measured in wage units (p. 245). Identifying such variables as independent or dependent is completely arbitrary and misleading. Keynes admits this later in the General Theory. Every factor in the economic system is dependent or, as Keynes later describes them, inter-dependent.
Keynes continues his discussion on his independent and dependent variables: "Thus we can sometimes regard our ultimate independent variables as consisting of (1) the three fundamental psychological factors, namely, the psychological propensity to consume, the psychological attitude to liquidity and the psychological expectation of the future yield from capital assets (2) the wage-unit as determined by the bargains reached between employers and employed, and (3) the quantity of money as determined by the action of the central bank ... if we take as given the factors specified above, these variables determine the national income and the quantity of employment" (p. 247). The first sentence of the next paragraph then reads: "The division of the determinants of the economic system into the two groups of given factors and independent variables is, of course, quite arbitrary from any absolute standpoint" (p. 247). Here Keynes agrees that identifying such variables as independent or dependent is completely arbitrary.
Keynes offers some uncharacteristically sound advice in chapter 21: "It is a great fault of symbolic pseudo-mathematical methods of formalizing a system of economic analysis, such as we shall set down in section VI of this chapter, that they expressly assume strict independence between the factors involved and lose all their cogency and authority if this hypothesis is disallowed ... Too large a proportion of recent 'mathematical' economics are mere concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols (p. 297-298)." This quotation should drive home the point I have tried to make above regarding the independency of certain variables. Brady is especially guilty of losing "lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols." Keynes has just admitted the model loses all validity if we admit for only an instant that these variables are not independent. Keynes has also admitted that the real world consists of interdependencies and hence D-Z model falls to the ground.
Keynes offers one last piece of evidence in section VI of Chapter 21 to support the conclusions reached above: "I do not myself attach much value to manipulations of this kind; and I would repeat the warning, which I have given above, that they involve just as much tacit assumption as to what variables are taken as independent (partial differentials being ignored throughout) as does ordinary discourse, whilst I doubt if they carry us any further than ordinary discourse can. Perhaps the best purpose served by writing them down is to exhibit the extreme complexity of the relationship between prices and the quantity of money, when we attempt to express it in a formal manner" (p. 305).
I will finish with a simple statement made by Keynes. Brady integrates the footnote found in section 1 of chapter 20 (p. 283). However, Keynes tells us in a footnote on the first page of section 1 of chapter 20: "Those who dislike algebra will lose little by omitting the first section of this chapter" (p. 280). Keynes included this comment because he doubted whether "they carry us any further than ordinary discourse".
I hope that I have demonstrated that a model is only as good as its initial assumptions. In this case the author has either accepted the initial assumptions without heeding Keynes's warnings or has forgotten the model's initial assumptions completely. None of Keynes's independent or dependent variables actually operate as such in the real world. Keynes admits this and does not try to convince us otherwise. Ignoring the significance of these assumptions allows Brady to advocate the total socialization of investment. Remember, when government controls investment they also control production. In short, Brady is advancing a model that Keynes admitted was built on false assumptions to advocate socialism.
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