# Keynes’s IS-LM Model Was Not Meant to Be a Toy for Academic Economists to Play With or ‘Perform Their Accustomed Tricks’ (Hicks)

21 Pages Posted: 12 Jun 2018

Date Written: May 25, 2018

### Abstract

Hicks’s IS-LM model was a decidedly inferior version of Keynes’s original IS-LP(LM) model, which had been constructed by Keynes in chapters 15 and 21 of the General Theory after he had demonstrated graphically on pp.179-182 of the General Theory that it was mathematically impossible to derive the rate of interest from an IS equation only based on the demand for investment and the supply of savings. Keynes had clearly demonstrated that, just as there was a 2-equation missing from Pigou’s 1933 model in The Theory of Unemployment, there was also an equation missing that had not been specified by the neoclassical theory of the rate of interest. That missing equation was Keynes’s LP(LM) equation presented on Page 199 of the General Theory. Keynes’s major reason for writing the General Theory was to specify his IS-LP(LM), model.

However, underlying his IS-LP(LM) macro model was another model that contained Keynes’s supporting microeconomic foundations in the theory of the firm in which Keynes had incorporated uncertain expectations about prices and profits in a carefully developed mathematical analysis provided in chapters 20 and 21 of the General Theory. Keynes called this foundation his D-Z model of expected aggregate supply and expected aggregate demand. From the D-Z model’s set of possible and probable outcomes, only one actual realized result could occur. This result, derived from the Aggregate Supply Curve(ASC), which was a locus or set of all of the possible D-Z combinations, would provide the one Y value of Effective Demand that would be incorporated into the IS-LP(LM) model. Keynes’s IS-LP(LM) model incorporated price expectations. Prices were not fixed. The set of different expected prices was dealt with in the supporting D-Z model’s ASC by means of changing expectations.

Hicks’s inferior version of IS-LM removed the anchor of Keynes’s expected aggregate demand and supply analysis that had been provided in chapters 20 and 21 that supplied the foundation that incorporated an analysis of expectations. Keynes’s ASC specified a set of multiple equilibria that incorporated uncertainty about what the actual level of effective demand, Y, would be. Thus, Hicks, in direct contradiction with the conclusions stated in his June 1936 review in the Economic Journal, eliminated both expectations and uncertainty from Keynes’s theory. However, his equation system is correct, as is his elasticity analysis of both LM (Keynes’s LP) and IS.

Keynes and Knight are united in their understanding that assessments of probability in the real world are made based on weak evidence, whereas the 3-mathematical theory of probability advocated by Ramsey, Savage, and de Finetti in SEU theory requires strong evidence. This means that the probabilities, both Keynes’s “non-numerical “probabilities and Knight’s “estimates” will have to be interval-valued, involving both an upper probability and a lower probability. The probabilities will be indeterminate and/or imprecise, but rarely precise. The Keynes–Knight position is completely different from the Shackle–Robinson Davidson claim that there can never be any relevant evidence about the future so that all such decisions are based on the imaginations, fantasies, and dreams of decision makers.

**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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