# On the Reason Why Keynes Brought Together All the Elements of His IS-LP(LM) Model in Chapter 21: He Had to Cover the Foundation Supplied by the D-Z Model of Chapter 20 First

26 Pages Posted: 22 Jan 2018

Date Written: January 10, 2018

### Abstract

Keynes carefully supplied a series of building blocks in the construction of his General Theory. Keynes’s Theory of Effective Demand consisted of two interrelated models. They are, first, the IS-LP(LM) model that determines the rate of interest and second, the D-Z model of expected aggregate demand (D) and expected aggregate supply (Z). Y, realized or actual aggregate demand, will be one of the set of all possible, expected D-Z (D=Z) outcomes that was introduced briefly in chapter 3 of the General Theory, where Keynes provided a brief outline of the theory he would fully develop in later chapters.

The IS-LP(LM) model is based on the Liquidity Preference Function, derived on page 199 of chapter 15 after being introduced in chapter 13 and 14, and the Consumption function and Investment Multiplier functions, derived from chapter 10 following his introductory analysis related to the Consumption function in chapters 8 and 9. The Investment function is analyzed as a function of rate of interest and expectations regarding expected future prices and profits in chapters 11 and 12. Chapters 16 and 17 generalize the Liquidity Preference analysis of chapter 15 to all assets. Keynes does not present his mathematical model of D and Z, which he briefly introduced in chapter 3, until chapter 20. This chapter 20 model supplies the aggregate production function, theory of the firm (purely competitive), analysis of expected prices and profits, multiple equilibria, and necessary and sufficient optimality conditions needed to obtain the crucial condition that the expected real wage equaled the marginal product of labor. Chapter 20 deals with the output and labor markets.

Keynes is now in position to bring together all of the elements of the IS-LP(LM) model in sections 4 and 5 of chapter 21 and then connect his results to chapter 20 by formally incorporating his money market analysis mathematically in section 6 of chapter 21. The Y variable has now explicitly been derived and supported with clear cut microeconomic foundations. Y appears in both the IS equation and LM equation. Both determine the rate of interest. The specific IS-LP(LM) equilibrium in (r, Y) space, of which there are many, since Keynes’s version of IS-LP(LM) incorporated expectations and uncertainty, will be in one to one correspondence with exactly one of the set of all possible D=Z outcomes specified by the Aggregate Supply Curve. The set or locus of all expected D=Z outcomes was derived in chapter 20 and called the Aggregate Supply Curve. D and Z were introduced in chapter 3.

Keynes is now finished with the presentation of the General Theory. He spends four additional pages of Section Four of chapter 21 discussing the possible deficiencies in his IS-LP(LM) model that are due to possible interactions with other relevant variables that were not formally specified in his IS-LP(LM) model, but which are included in the D-Z model. Chapters 4-7 are correctly described by Keynes as digressions from his structured approach that add nothing to the formal development of his general theory. Chapters 22-24 examine how the General theory can be implemented. The most important part of these chapters is on pages 377-379, where Keynes puts forth his proposal for a Keynesian – Neoclassical synthesis. This was ignored by all economists of the 1930’s-1940’s. Chapter 18 is a literary summary of the IS-LP(LM) model only that does not incorporate the technical details provided in chapter 20 and 21. The appendix to chapter 19, where Keynes compared his chapter 20 and 21 models to Pigou’s, makes it clear that Pigou, and Modigliani, had only one equilibrium in the output market. Chapters 2 and 19 deal with Pigou and the money wage issue and are not part of Keynes’s formal models.

The piece meal approach that economists take to reading Keynes’s GT is exemplified by Coddington’s 1976 Journal of Economic Literature article which provides a division of Keynesian readers into three different, conflicting categories, depending on the particular chapters picked from the GT by these readers which is being emphasized as providing the one, true message of the General Theory. Each category claims that Keynes’s “true” message can be found in the particular chapters that they have highlighted. The three Keynesian categories are Hydraulic, Fundamentalist, and Reconstituted Reductionist. In reality, Keynes, in the GT, is using all three of these characterizations of his work. For example, the labor market is in disequilibrium as determined by the output market, which is characterized as one of multiple equilibria. Keynes’s holistic approach can’t be broken up into different, disconnected parts if a reader is interested in understanding what Keynes really meant to say. What Keynes really meant to say is contained in all of the chapters in the General Theory.

**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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