How Keynes's Mathematical Analysis in Chapters 20 and 21 of the General Theory of His Elasticity Ew, Which Could Take on Any Values between ew =0 (Rigid, Given, Fixed, Constant, or Inflexible Money Wages) and ew =1 (Flexible Money Wages) Completely Destroys F. Modigliani's 1944 Econometrica Conclusion that Keynes's General Theory Category of Involuntary Unemployment Required Rigid Money Wages

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In 1944, Modigliani erroneously concluded that Hicks was the originator of the Keynesian IS-LM model. Modigliani then set about adding to Hick’s model missing labor market analysis, missing production function analysis, missing elasticity analysis, and missing theory of the firm, that were not contained in Hicks’s 1937 Econometrica paper, into his 1944 Econometrica paper. Unfortunately, Modigliani failed to realize that all of these missing elements were present and contained in Keynes’s chapters 20 and 21 of the General Theory. Keynes’s IS-LP(LM) model was specified by Keynes in section four of chapter 21 and is built upon the model in chapter 20. The missing labor market analysis, missing production function analysis, missing elasticity analysis, and missing theory of the firm, that were not contained in Hicks’s 1937 Econometrica paper, were all contained in chapter 20 of the General Theory. Modigliani’s critique, conclusion and results, therefore, can’t possibly apply to Keynes’s General Theory. They can only apply to Hicks’s 1937 inferior version of Keynes’s analysis. Hicks never covered chapters 20 and 21 of the General Theory. Neither did Modigliani. It is true that J Hicks’s 1937 version of Keynes’s 1936 IS-LP(LM) model was based on given (fixed) money wages. However, Keynes’s 1936 version is not based on this assumption, since money wages are completely flexible starting with chapter 19 of the General Theory. It is true that Keynes offered a simplified version of his Aggregate Supply Curve (ASC) analysis of chapter 20 on pp. 295-296 of chapter 21 of the General Theory that contained an infinitely elastic, horizontal segment of the ASC(ew=0), combined with a completely inelastic, vertical segment of the ASC that represented the case of rigid, given, fixed, constant or inflexible money wages. However, Keynes made it crystal clear that this was a special case. The major result of Modigliani’s 1944 paper in Econometrica, that Involuntary unemployment in Keynes’s General Theory is due to rigid money wages, is completely false. Modigliani’s major result, however, does apply to Hicks’s 1937 Econometrica paper, since Hicks assumed “…that w, the rate of money wages per head, can be taken as given.” (Hicks, 1937, p.148). Throughout his paper. Keynes deliberately defined his General Theory results in terms of wage units, so that the fixity or variability of money wages can have no impact and would not be an issue. All that happens is that the ASC is shifted up or down by changes in w. It in no way impacts Keynes’s analysis based on the existence of multiple equilibria imbedded in the ASC in the goods market. Finally, Modigliani’s entire paper is based on the assumption that there is only one equilibrium in the output market. Keynes’s multiple equilibria is what determines the amount of Involuntary Unemployment. This happens because it is the expectations of the employers, as regards what the expected real wage in the future will be, that determines the amount of employment (unemployment) in the labor market in the present, given the expectations holding in the output market. The history of Macroeconomics must be completely rewritten in order to correctly incorporate Keynes’s formal modeling in Chapters 20 and 21 of the General Theory.