Keynes’s IS-LM model in the General Theory, defined in (r,Y) space and contained in chapter 21 in Part IV on pp. 298-299 of the General Theory, was derived from the underlying D-Z model of Chapter 20 that incorporated expectations and uncertainty into the P(expected economic profits-Z) and p(expected economic prices-D)terms. Keynes explicitly derived Y from his Aggregate Supply Curve (ASC) analysis, which presented a locus of all possible expected D-Z intersections. The derivation of the ASC occurs two times in the General Theory. The first derivation is contained in ft. 2 of pp. 55-56 of the General Theory. The second derivation occurs in chapter 20 on p.283 in fts. 1 and 2 of the General Theory. Keynes then integrates the liquidity preference function formally into the D-Z model of chapter 20 on pp. 304-306 of chapter 21. Y is not derived from the IS curve a la Hicks, but from the D-Z model that incorporated long run concerns about future expected profits and the uncertainty of such profit.. Keynes then combined r, the nominal rate of interest, with the actual value of a particular D value that is actually realized, which is Y, where Y is nominal, actual, effective aggregate demand. The Harrod-Hicks-Lange-Modigliani -Hansen versions of IS-LM had no foundation in expectations and uncertainty, as they were based on perfect competition and risk. Only Champernowne, using an equivalent exposition to Keynes’s as presented in chapters 20 and 21 of the General Theory, combined and integrated expectations and uncertainty variables into his RES paper model by defining Q and Q’ variables, which were contained only in the three diagram-three equation Keynes model, but not in the three diagram-three equation neoclassical model. Champernowne correctly showed that if the Q and Q’ variables are removed from Keynes’s model, then one obtains the classical (neoclassical) model. For example, in the labor market, if Q and Q’ are present in the functions, then the first order condition for optimality becomes the marginal product of labor equals the EXPECTED real wage. If, on the other hand, there is no uncertainty about the future, then the first order condition for optimality becomes the neoclassical marginal product of labor equals the ACTUAL real wage. Therefore, if there is no uncertainty about future prices and profits, then chapter 20 of the General Theory drops out of consideration, since chapter 20 is Keynes’s more advanced mathematical modelling that Champernowne’s model provides in graphical form, which was based on Keynes’s original 1933 model, where Keynes used W=the state of the news to designate the impact of uncertainty about future levels of prices and profits on employment levels. Champernowne’s Q and Q’ variables are equivalent to Keynes’s early W variable, which Keynes replaced with uncertainty in the General Theory, where uncertainty was defined by Keynes as an inverse function of the evidential weight of the argument, V, where V=V(a/h) =w, where w is the weight of the evidence, from chapters 6 and 26 of Keynes’s A Treatise on Probabilit. Thus, Keynes’s W represented the change in w over time. If w increases, so that W represents an increase in positive evidence, then nervousness and uncertainty decreases. If w decreases, so that W represents a decrease in positive evidence and increase in negative evidence, then nervousness and uncertainty increase.The only IS-LM model that is consistent with Keynes’s chapter 21 model is Champernowne’s. Meade, while dealing with expectations, did not explicitly introduce uncertainty as done by Champernowne with his Q and Q’ variables.Thus, involuntary unemployment for Keynes and monetary unemployment for Champernowne have nothing to do with rigid or fixed money wages, as claimed by Hicks, Harrod, Lange, and Modigliani, but are due to the presence of uncertainty. The Harrod, Hicks, Lange and Modigliani models are mis-specified because they do not incorporate any possibility for uncertainty to exist
