# Keynes’s IS-LM(LP) Model Was Complementary with Keynes’s Aggregate Demand(D)-Aggregate Supply(Z) Model: They Were Never Rival Models

33 Pages Posted: 29 Oct 2018

Date Written: October 5, 2018

### Abstract

The current belief among economists that Keynes’s IS-LM (LP)and D-Z models represented rival “interpretations,” as regards Keynes’s mathematical modeling of the General Theory, is incorrect. Keynes used the D-Z model, first introduced as a brief outline in Chapter 3 of the General Theory and then developed mathematically in chapters 20 and 21 of the General Theory, to derive the Y=C I variable, actual aggregate Income or Effective Demand. Y was then combined with r, the nominal long run rate of interest, to determine (r,Y) space in which Keynes demonstrated, in chapter 21 of the General Theory, that his downward sloping IS curve and upward sloping LP curve, both brought together in section four of chapter 21, determined the rate of interest in (r,Y) space.

Keynes dealt with expectations , uncertainty, and liquidity factors in the D-Z model of chapters 20 and 21. Keynes’s Y=C I model does not deal at all with uncertainty or expectations. The purpose of the D-Z model was to deal explicitly with both uncertainty and expectations. One Y value will be selected from the set of possible, expected D values. This Y value is then combined with r, the nominal long run rate of interest, to analyze the IS-LM(LP) model in (r,Y) space in the General Theory.Thus, Keynes specifically developed the D-Z model to deal with the variable W that he had originally defined as a major, independent variable in his original IS-LM(LP) model of December 4,1933, that he presented in his student lectures that were attended by Reddaway and Champernowne. Champernowne was the only reviewer of the General Theory who incorporated variables, that he called Q and Q′, that dealt with Keynes’s W variable, which represented the state of the news, which represented the change in the weight of the evidence variable that Keynes used to define uncertainty on page 148 of the General Theory in chapter 12 in a footnote.

Keynes, however, realized that his original December 4th,1933 model and the mid -1934 draft copy of the General Theory IS-LM(LP) model, with confidence now replacing the state of the news, was mathematically intractable and incapable of further development. It was a tremendous conceptual breakthrough because it had allowed Keynes to incorporate his Logical Theory of Probability approach from the A Treatise on Probability,1921,into the General Theory, a point that has only been recognized by one economist, H. Townshend, in 1937-38. However, Keynes could make no further technical progress until he had digested the mathematical models developed by Pigou in his July 1933,The Theory of Unemployment. Keynes was able to modify Pigou’s “concoction” by combining a version of Pigou’s 1933 model of chapters 8-10 of part II with expectations and uncertainty to produce the D-Z model worked out by Keynes in chapters 20 and 21.

Keynes, therefore, split his original IS-LM(LP) model of December,1933 into two parts, the revised IS-LM(LP) model of chapter 21 and the D-Z model of chapters 20 and 21. No reviewer or reader of the General Theory, except H. Townshend again, recognized, to some degree, the relative importance of the D-Z model. The Post Keynesian attempt to eliminate the IS-LM(LP) model and replace it only with Keynes’s D-Z model was an intellectual catastrophe directly linked to Robertson’s mathematically confused exposition contained in his November,1936 Quarterly Journal of Economics article.This article also provides all the support that Paul Samuelson would have needed to show how poorly trained in the use of mathematics 1930’s economists were.

**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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