Involuntary Unemployment: The Elusive Quest for a Theory (ISBN 0415407109)

De Vroey skips the mathematical modeling in chs.10,20,and21:
Michel De Vroey(V)arrives at the following conclusion in his book on Keynes's theory of effective demand and involuntary unemployment:"...Two main lines of argumentation are developed by Keynes.The first concerns the working of the labour market.Keynes claims...that wage-earners are unable to fix the market-clearing real wage in spite of their ability to fix the nominal wage...Keynes's second line of argumentation consists of claiming that involuntary unemployment is caused by a deficiency in effective demand.After an in-depth examination of these two claims,I come to the conclusion that neither of them stands up....In sum,no valid explanation of involuntary unemployment remains after Keynes'reasoning errors have been straightened out".(De Vroey,2004,p.5).Further sections of the book examine how the involuntary unemployment concept was used,first, in combination with IS-LM models by Keynesian economists(Hicks,Hansen,Tobin ,Klein,and Modigliani),second,by the original disequilibrium Keynesians(Patinkin,Clower,and Leijonhufvud)and their successors(Barro,Grossman,Dreze,Benassy,and Malinvaud),third,the Friedman-Lucas(F-L) critique of the concept of involuntary unemployment,fourth,New Keynesian counter arguments to F-L based on implicit contracts theory,menu cost models ,efficiency wage models,insider-outsider theory ,coordination failures and imperfect competition.V essentially ignores the nonsymmetric,incomplete,and imperfect information approach of Stiglitz which,while inferior to Keynes's own c coefficient model in chapter 26 of the A Treatise on Probability(1921) that Keynes used informally on pp.239-241 of The General Theory(1936),comes closest to Keynes's approach.V summarizes in his last chapter by essentially repeating the conclusion quoted above from his introductory chapter. V spends all of the second part of his book supposedly analyzing Keynes's analysis of his concept of involuntary unemployment as it was developed within the framework of his theory of effective demand.Unfortunately,V completely fails to consider the mathematical models presented by Keynes in chapter 10(the Y-multiplier model of actual aggregate demand where Y=C+I),chapters 20 and 21(the D-Z model consisting of a)D=f(N)=pO,the expected aggregate demand function,where p is an expected price and O=F(N)is an aggregate production function, defined as such on p.283 of the GT,(b)Z=g(N)=P +wN,the expected aggregate supply function,where P is future,expected profit,w is the money wage,either fixed or variable, and N is the aggregate amount of employment,(c)the aggregate supply curve, D=Z,which is a locus of the set of all possible expected price-profit combinations,a different possible employment level corresponding to each member of the set.The aggregate supply curve,D=Z, automatically specifies a set of stable multiple equilibria,all of which satisfy the necessary first order and sufficient second order conditions for a profit maximum derived from an optimization problem.Only one of the elements of this set will represent a full employment equilibrium.All of the other feasible points represent unemployment equilibriums,which Keynes designated as representing involuntary unemployment.In 1940,Keynes expanded his model' s range of application informally so as to incorporate points of overemployment in his How to Pay for the War.)and the appendix to chapter 19,where Keynes compared his model,theory,and results to the model,theory,and results derived by A C Pigou in Part II,chapters 8-10,pp.86-102,of The Theory of Unemployment(1933).Instead,V studies chapters 2,3,and 19 of the GT while ignoring chapters 10,20,21,and the appendix to chapter 19 of the same book.V's approach to "reading" the GT is based on five canards passed down to historians of economic thought and academic specialists in economic thought.The first canard is the claim made by Richard Kahn to Robert Skidelsky,who accepted it at face value,that Keynes was a poor mathematician by 1927.The second canard is the claim made by Joan Robinson that Gerald Shove told her that Keynes had never taken the twenty minutes necessary to master the theory of value.Naturally, Kahn(along with A.Robinson) claimed that Shove told him the same thing.The third canard was Dennis Robertson's claim,made in a 1955 article(with an error filled appendix by Harry Johnson) in the Economic Journal that was part of an error filled exchange over the meaning of Keynes's aggregate supply function between Robertson, De Jong and Ralph Hawtrey ,that pages 24-30 of the GT(chapter 3) contains the important theoretical core that is central to an understanding of Keynes's theory of effective demand,despite Keynes's own assessment that chapter 3 was merely an introductory guide or outline of his theory that might be unintelligible until later chapters filled in all the missing analysis.The fourth canard was Johnson's claim that Z=pO(instead of the correct D=pO).The fifth canard was that,according to Robertson,D=C+I(instead of the correct Y=C+I).A mathematically literate reader of this review,who can differentiate and integrate, can easily duplicate any and all of the mathematical results obtained by Keynes in chapters 20 and 21.The major result is that the optimality condition for the labor market,making the standard assumption of decreasing returns to labor in the short run ,is determined in the commodity(output)market by the condition that w/p=mpl/(mpc+mpi),as opposed to the classical and neoclassical result that equilibrium in the labor market is determined independently of the commodity market by the condition w/p=mpl,where mpl is the marginal product of labor,mpc is the marginal propensity to spend on consumption goods andmpi the marginal propensity to spend on investmant goods.Only in the special case where mpc+mpi =1 will the neoclassical result(no involuntary unemployment)hold.I am now able to show why Keynes's two lines of argumentation are correct and why De Vroey and a host of other economists,who have accepted one or more of the five canards listed above,are incorrect in their reasoning.First,it is impossible for labor,in the aggregate ,to lower their money wage,w,as long as mpc+mpi<1.Second,there is a deficiency of aggregate demand by definition as long as mpc+mpi<1.There is nothing wrong with Keynes's reasoning,which follows strictly from a mathematical analysis of an aggregated economy operating under conditions of pure competition(KEYNES,1936)or free competition(PIGOU,1933).As pointed out by Keynes in the appendix to chapter 19 of the GT,the neoclassical analysis is missing an equation.That missing equation is the Y-multiplier model of chapter 10 of the GT.Of course,one can simply assume that mpc+mpi =1,just as the economist,who was taking a cruise with a physicist and a chemist and ends up on a deserted island after their ship sinks, assumes a can opener.