# J.M. Keynes’s Criticisms, on Pages 275–276 and 297–298 of the General Theory, of the Marshallian, Neoclassical, Mathematical Approach to Partial Equilibrium (Ceteris Paribus) Analysis, Where Functions Have Only One Independent Variable Only: Keynes’s Application of Systems of Simultaneous Equations in the General Theory in Chapter 15 and the Appendix to Chapter 19 Was Keynes’s Breakthrough in Macroeconomics

26 Pages Posted: 11 Jul 2018 Last revised: 5 Nov 2019

Date Written: June 16, 2018

### Abstract

J.M. Keynes’s criticisms of the Marshallian, partial equilibrium (ceteris paribus) approach to mathematical modeling in the General Theory on pages 275- 276 and 297-298, where the mathematical modeling relies on functions with only one independent variable, has been completely misinterpreted by all macroeconomists for the 82 years as an attack on mathematical economics or formal analysis, in general. It is nothing of the sort. Given Keynes’s appreciation for the formal, mathematical work done of Frank Ramsey in 1927 and 1928 and by William Ernest Johnson in 1913 in a paper in the Economic Journal on mathematical methods in microeconomics, as well as Keynes appreciation of Ramsey’s betting quotients approach in 1930 as providing a stronger logical foundation for numerical probability, there is no objective support for the claims, made by Joan Robinson and many, many others, that Keynes was a partial equilibrium, Marshallian theorist, who would work only with mathematical functions that had only one independent variable, subject to ceteris paribus. Keynes’s modeling with simultaneous systems of mathematical equations in chapters 10, 15, 20, 21, and the appendix to chapter 19 of the General Theory demonstrates that Keynes’s critique was aimed primarily at A C Pigou’s 1933 The Theory of Unemployment, where Pigou’s mathematical analysis, while correct, could not deal with Keynes’s IS-(LM)LP analysis. Pigou’s entire framework was restricted to functions with only one independent variable, the real wage. This approach did not allow Pigou to consider the impact of the investment multiplier or the Liquidity Preference Function in his economic analysis since there was a missing equation in both the Pigouvian approach and a missing equation in the neoclassical theory of the rate of interest. Keynes’s Liquidity Preference Function provided the additional independent variables in an equation that had to be incorporated in the analysis in order to correct the misspecified Pigouvian and neoclassical models. Keynes’s General Theory provided the missing equations.

**Keywords:** IS-lM, iS-lP (lM), Reddaway, Champernowne, Keynes, Chapter 21, Chapter 15, Keynes's Views of Math

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

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