# On the Importance of Pigou's Mathematical Model in Part II of His 1933 The Theory of Unemployment to the Development of Keynes's IS-LP(LM) Model in the General Theory: Keynes Had No Mathematical Model Supporting His Y=C plus I Model Until He Integrated an Improved Version of Pigou's Model into the D-Z Model of Chapter 20 of the General Theory

22 Pages Posted: 7 Mar 2018

Date Written: February 28, 2018

### Abstract

Keynes created, developed, taught and applied his version of the IS-LM model,which he called the IS-LP model, between Dec. 1933 and February,1936 when the General Theory appeared in print. However, before Pigou’s July,1933 book came out, Keynes had no worked out D-Z model to support the derivation of his Y=C I model that lay at the heart of his IS-LP(LM) model. Keynes needed to support the Y model, introduced on page 63 of the General Theory along with the IS condition and analyzed more explicitly in chapter 10 of the General Theory, with an explicit microeconomic foundation in the theory of the firm, production function, labor market, incorporation of profit and price expectations, and marginal analysis. Pigou’s 1933 The Theory of Unemployment showed Keynes exactly what to do and how to proceed. Keynes’s D-Z model is an improved version of Pigou’s model in chapters 8-10 of Part II of Pigou’s book, as acknowledged by Keynes in his appendix to chapter 19 of the general Theory and to H. Townshend in correspondence.

Keynes’s introductory, original IS-LP(LM), presented on December 4,1933 at his student lectures and published in the 1934 draft of the General Theory, incorporated a Y variable at the macroeconomic level that had no corresponding microeconomic foundations or incorporation of price and profit expectations.Keynes’s final presentation of his IS-LP(LM) model in chapter 21 rests on a technical elasticity analysis that is based on the D-Z analysis of chapter 20,which is the chapter where Keynes developed his Pigou–like “concoctions” that he had alluded to in the appendix to chapter 19 and in his correspondence with Townshend into the mathematical foundations for the General Theory.

Keynes was stuck in late 1933 with an IS-LP(LM) model without any micro foundations. Exactly the same issue had occurred in his 1930 A Treatise on Money.

Keynes adapted Pigou’s mathematical analysis and modeling techniques,presented in his 1933 The Theory of Unemployment, to provide him with the needed tools so that he could provide his main General Theory model, ther IS-LP(LM) model, with exactly the precise mathematical foundation in microtheory he needed to finish writing the General Theory.

The conclusion reached is that Keynes could not have finished writing the General Theory by 1936 if Pigou had not published his 1933 The Theory of Unemployment in July,1933 first. Pigou never at any point in his lifetime sought to point out in print that Keynes’s chapters 20 and 21 analysis,as well as the analysis presented in footnote two on pages 55-56 of the General Theory, were very similar to his own original presentation of a macro model in July, 1933.

**Keywords:** IS-LM, IS-LP(LM), J. Robinson, R. Kahn, Keynes, mathematical illiteracy, A. Robinson, Y=C I, D-Z model

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

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