# The Labor Market Analysis in Lange’s 1938 Economica Article, Modigliani’s 1944 Econometrica Article, and Klein’s 1946 Book, the Keynesian Revolution, Are All Equivalent to Keynes’s Special Case of a Completely Elastic, Horizontal Aggregate Supply Curve for Labor Based on Rigid Money Wages (Ew =0) in Section III of Chapter 21 of the General Theory in 1936: Keynes’s General Case, That Considered Both Rigid and Flexible Money Wages (0≤ ew≤1) Mathematically in Chapters 20 and 21 of the General Theory, Was Overlooked by Lange, Modigliani and Klein

29 Pages Posted: 2 Jul 2019

Date Written: July 2, 2019

### Abstract

Work done by Lange (1938), Modigliani (1944), and Klein (1946), that aimed at providing a microeconomic foundation in the aggregate Labor market for the IS-LM model of Hicks’s 1937 Econometrica article, completely overlooked the fact that Keynes had already provided exactly such a mathematical model of the microeconomic foundations of the labor market for Keynes’s IS-LM model of Section Four of Chapter 21 in chapter 20 of the General Theory. Keynes provided simplifying assumptions in chapter 21's Section III of the General Theory that are identical to the completely elastic (horizontal) range of the Labor supply curve based on the assumption of rigid money wages based on the special assumption that ew=0.

However, Keynes also provided analysis that covered the general case where 0≤ew≤1 in chapters 20 and 21 of the General Theory. Involuntary unemployment arises in both cases because Keynes’s necessary, first order condition for optimality is NOT the one used by Lange, Modigliani, and Klein, which was that the actual real wage equals the marginal product of labor, but that the expected real wage equals the marginal produce of labor, which introduces a set of multiple equilibria into the labor market analysis specifying Keynes’s Aggregate Supply Curve, a set of equilibria where D=Z. The analysis of Lange, Modigliani,and Klein only specifies one out of the total number of possible multiple equilibria much like Pigou did in his 1933 The Theory of Unemployment.

Solow’s (2005) interesting summary of events that happened in the late 1930’s-1940’s demonstrates that the work of Lange, Modigliani, and Klein completely overlooked Keynes’s mathematical modeling techniques that were presented in the appendix to chapter 19,chapter 20,and chapter 21. Keynes’s mathematical models were presented in the form of elasticity analysis was presented as elasticity analysis.

The point of Keynes’s appendix to Chapter 19 appendix is that Pigou has an inferior version of Keynes’s D-Z analysis without any IS-LM model. Pigou’s model is based on only one optimal equilibrium condition, that the actual real wage equals the marginal product of labor. It is impossible for Pigou to specify a rate of interest that would have allowed Pigou to incorporate an mec analysis of how shifts in the IS curve, due to changing expectations of fixed capital goods, leads to changes in aggregate Investment through the investment multiplier, thereby causing changes in employment that are completely independent of the money wage rate.

**Keywords:** IS-LM, IS-LP(LM), Keynes, chapter 21, chapter 20, Klein, Lange, Modigliani

**JEL Classification:** B10, B12, B14, B16, B20, B22

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