The Applied Mathematics of J.M. Keynes' Theory of Effective Demand in the General Theory

About the Book

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 within the context of the D,Z model.This model is explicitly discussed by Keynes in straightforward English in chapter 3 and mathematically analyzed in chapters 20 and 21 in terms of elasticities so that a reader of the GT can compare Keynes´s elasticities with Pigou´s elasticities from Pigou´s 1933 book,The Theory of Unemployment.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,any one of a number of different possible unemployment equilibriums occurs which labor,in the aggregate,will be unable to eliminate because ,in all cases ,the money wage must be increased,not decreased.This result is further generalized in chapter 21 where Keynes explicitly adds the money market and bond market implicitly.The optimality condition becomes w/p= mpl/e,where e = the elasticity (dp/dM)/(p/M).If e=1,the neoclassical result holds.On the other hand,if e<1,involuntary unemployment results .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

About the Author

Michael Emmett Brady received his Ph.D. degree in Economics from the University of California. He received his B.A. and M.A. degrees from California State University as well as completing all requirements for a B.A. in Mathematics. He has done graduate level work in mathematics