# Harrod, Keynes and the Missing Equation (Liquidity Preference Equation) from the Neoclassical Theory of the Rate of Interest: '…Has to Be Determined by Some New Equation Not Provided for in the Classical System. Thus the Way is Clear for a Radical Reconstruction. Your New Equation is the Liquidity Preference Schedule…'. (Harrod, 1973, CWJMK, Vol. 13, p.556).

24 Pages Posted: 18 Aug 2018 Last revised: 28 Sep 2018

Date Written: August 5, 2018

### Abstract

In the post script of his letter of August 30th,1935 to Keynes, contained on page 556, CWJMK, Volume 13, Harrod completely and totally capitulated to Keynes: “…has to be determined by some new equation not provided for in the classical system. Thus the way is clear for a radical reconstruction. Your new equation is the liquidity preference schedule…”. (Harrod, 1973, CWJMK, Vol. 13, p.556). Although Harrod capitulated to Keynes, he nevertheless attempted to defend a micro, partial equilibrium approach to theory at the macro level. Harrod’s constant error throughout this correspondence (CWJMK, Volume 13, pp.526-563) with Keynes was his attempt to maintain the applicability of a neoclassical, micro based, economic, Marshallian, partial equilibrium, ceteris paribus model, based on functions that had only one independent variable, at the macro level.

Of course, Keynes rejected Harrod’s 1935 Marshallian, partial equilibrium macro approach, just as he had rejected Pigou’s 1933 Marshallian, partial equilibrium, macro approach in The Theory of Unemployment in the appendix to chapter 19 of the General Theory. Keynes presented, for the first time in history, a macro model based on a set of three simultaneous, mathematical equations that captured many of the feedback and interdependencies that would occur at the macro level. It is unfortunate that Harrod decided not to incorporate this admission in his 1951 biography of Keynes and his 1937 Econometrica paper in which he is basically restating Keynes’s 1936 IS-LP(LM) model presented on pages 298-299 of the General Theory. The fact that Harrod acknowledged that Keynes’s system of three simultaneous equations model was a ‘radical reconstruction’ of neoclassical theory, mentioned also in the body of Harrod’s letter, has two major results.

First, Harrod’s admission completely destroys the Joan Robinson-Post Keynesian-Neo-Keynesian claim that there was no IS-LP(LM) model in the General Theory. Second, it completely destroys the claim that the IS-LM model was a neoclassical model invented by Hicks in 1937 in order to make sense of Keynes’s strictly, literary prose presentation in the General Theory. This was followed by Modigliani in 1944. He assumed that Hicks’s paper was the correct way in which to explain Keynes’s supposed ,literary prose only, exposition that was done without any mathematical analysis. This is obviously false if one has access to the August-September, 1935, Harrod-Keynes correspondence. What has not been explained is why Harrod’s August,1935 postscript to his letter of August 30th has not been analyzed by any economist, historian, or philosopher of social science since 1973, when this material became available in Volume 13 of the CWJMK.

**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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