On J. M. Keynes's Use of Multiple Equilibrium (Not Partial Equilibrium) Modeling in the General Theory in 1936: The Aggregate Supply Curve

Abstract

G L S Shackle and Joan Robinson both adopted the Neoclassical position that there could only be one theoretical equilibrium position in either the short run or long run. They combined this supposition with their own redefinition of the concept of uncertainty to mean complete, total, fundamental and radical uncertainty or ignorance of the future. They then claimed that it was impossible to use formal mathematical models in macroeconomics that incorporated the concept of equilibrium if there was complete and total uncertainty of the future. Pace Shackle and Robinson, Keynes never defined uncertainty as Ignorance. Keynes recognized that it was mainly only investment projects in long lived, fixed, durable, capital, producer goods that faced the problem of ignorance. Keynes explicitly dealt with this issue in his two 1937 contributions to the Quarterly Journal of Economics and the Eugenics Review if one was dealing with decision problems dealing with the very distant future. An example of such a decision problem would be deciding to invest in a new technology today, given the great uncertainty generated by technological change, advance and innovation, plus the constant threat of technological obsolescence. In general, Keynes dealt with uncertainty as a range. Ignorance was one extreme. This was done by Keynes in the A Treatise on Probability through the use of his logical relation V, where the evidential weight of the argument is defined by V(a/h) = degree w, where 0≤w≤1 and w measures the degree of the completeness of the relevant information, knowledge, data or evidence. Keynes then defined uncertainty, U, to be an inverse function of w in the General Theory in chapter 12 on page 148. Again, Keynes never defined uncertainty as ignorance. It is Shackle and Robinson who claimed that uncertainty meant ignorance. Keynes introduced multiple equilibria into macroeconomics with his creation of the Aggregate Supply Curve, a locus of all D=Z intersections. Uncertainty is thus dealt with by multiple equilibria. There is no evidence that either Shackle or Robinson ever grasped any of Keynes’s theoretical advances In their lifetimes. The belief that Keynes’s approach in the GT was a multiple equilibrium one is correct. However, economists do not understand how Keynes carried out his modeling of multiple equilibria because they have not been able to follow Keynes’s mathematical exposition in Chapters 20 and 21 of the GT. Keynes’s ASC represents a locus of a set of multiple equilibria, where D=Z, in chapter 20. Out of this set, one actual Y value will be realized. This Y value is then combined with r,the rate of interest, to model his IS-LP(LM) model in chapter 21 of the GT. Keynes, as pointed out by Townshend and confirmed by Keynes in the Townshend–Keynes exchanges, made it crystal clear that his Liquidity Preference (LP) equation, specified on page 199 of the GT, in his IS-LP(LM) model, is directly based on his analysis in his A Treatise on Probability of non numerical (interval valued ) probabilities and weight of the evidence, w. This is not surprising at all since Keynes explicitly defined uncertainty(not radical uncertainty) as an inverse function of the weight of the evidence, w, on page 148 of chapter 12 of the GT and explicitly redirected Townshend to his footnote on p.148 (Keynes also asked Townshend to reread page 240 of the GT) explicitly linking uncertainty to the concept of weight. Hence, there is no need to develop from scratch mathematical models of complexity to understand Keynes’s mathematical modeling in the A Treatise on Probability and General Theory.