# How J M Keynes Split His Original IS-LP(LM) Model of His Student Lectures of December, 1933 and His Mid-1934 Draft Copy of the General Theory into Two Separate Models in 1936: The Revised IS-LP(LM) Model of Chapter 21 and the Expected D-Z Model of Chapter 20 in the General Theory

31 Pages Posted: 27 Jul 2018 Last revised: 13 Feb 2020

Date Written: July 7, 2018

### Abstract

In late 1933, Keynes was facing a serious problem. The problem was how to integrate his A treatise on probability, 1921 work on expectations, interval valued probability, and the weight of the evidence, V(a/h) =w, 0≤w≤1, into his IS-LP(LM) model.

Keynes’s first attempt was to integrate W, the State of the News, where W = the change in w, the weight of the evidence, over time. However, this was unsatisfactory because this did not correctly integrate expectations into the definitions of the Y, C, and I variables, which were actual, realized values. In mid-1934, Keynes eliminate W and incorporated E, where E was now defined as the “state of long-term expectation (or confidence).” This also did not work because E could not be integrated into the definitions of the Y, C, and I variables, since the model dealt with the actual, realized values of the Y, C, and I variables.

Keynes needed another, separate model dealing only with expectations and uncertainty from which the actual, realized results could be derived. However, by mid-1934, Keynes had finally mastered Pigou’s July 1933, The Theory of Unemployment mathematical model. Keynes now saw how he could adapt Pigou’s microanalysis into the expected D-Z model of the General Theory. By 1936, Keynes could analyze his Y=C plus I as the actual, realized result, which he uses in his IS and LP(LM) equations, where Y is actual Aggregate demand (Effective Demand) while expectations and confidence are now integrated completely into a new model, the D=Z model, where Expected Aggregate Demand is D=D1 plus D2, and Expected Aggregate Supply is Z=Z1 plus Z2. The one, actual, Y value is then derived from the set of all, expected, D=Z values, which integrate a set of different degrees of probability and definiteness(weight) into them. Expectations and Confidence are now dealt with by the D=Z model that supports the IS equation. Keynes integrates these same concerns into the LP(LM) model by explicitly defining the liquidity preference function to be a function of uncertainty, where uncertainty is an inverse function of the weight of the evidence, w. Y appears in both the IS and LP(LM) equations and is completely supported by a micro foundation resting on Keynes’s analysis of D and Z in chapters 20 and 21, which supplies the D=Z locus, called by Keynes the Aggregate Supply Curve, which provides the set of multiple macro equilibria.

The misbelief, that Keynes eliminated from the GT his December,1933 IS-LP(LM) model and his mid 1934 draft copy of the GT, a misbelief shared by, for instance, both Dimand (2007, pp.86-87) and Skidelsky (1992, p.616), as well as all other economists who have written on Keynes, has led to another misbelief, that Keynes did this because he was a Marshallian, who followed Marshall’s advise to burn the mathematics after a researcher had checked to make sure that the literary prose that took its place was correct. Of course, Keynes himself refuted this ‘interpretation' in the appendix to chapter 19 and chapter 21 of the GT by pointing out that the Marshallian, Partial Equilibrium approach, the approach used by Pigou in TTOU (1933) ,could not possibly take into account the repercussions between the independent variables because “The pitfalls of a pseudo-mathematical method, which can make no progress except by making everything a function of a single variable and assuming that all the partial differentials vanish, could not be better illustrated.” (Keynes, 1936, pp.275-276) and “It is a great fault of symbolic pseudo-mathematical methods of formalising a system of economic analysis, such as we shall set down in section vi of this chapter, that they expressly assume strict independence between the factors involved and lose all their cogency and authority if this hypothesis is disallowed…” (Keynes,1936, p.297-298).

Keynes’s IS-LP(LM) model on pp.298-299 of the GT, could, of course, account for some of these interdependencies. Keynes, on pp.299-303 of the GT, also discussed some of the deficiencies in his IS-LP(LM) model.

Keynes required the two interconnected models, IS-LP(LM) and D-Z, in order to deal with macro feedbacks between independent variables, as well as incorporate uncertainty and expectations. Hicks’s error was to remove the uncertainty and expectations factors. This left Hicks’s inferior variation of IS-LM open to attack from the Post Keynesian and Neo–Keynesian schools of thought. Hicks’s misguided attempt to fix the error he had made in 1937 in Econometrica in a 1981 issue of the Journal of Post Keynesian Economics fixed nothing, since readers of the 1981 article were misled into believing that Hicks had rejected the entire apparatus. All Hicks did was to admit that uncertainty and expectations needed to have been in the IS-LM model, as originally specified by Keynes in 1936 in pp.298-299 of the GT.He never showed how Keynes did this with a D-Z result determining a specific Y result,which Keynes then combined with r, the rate of interest,to create the IS-LM model.

**Keywords:** IS-LM, IS-LP(LM), Skidelsky, Dimand, Keynes, Chapter 21, Chapter 20, Keynes's IS-LP And D-Z Models

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

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