On J. M. Keynes's 1936 Suggestion of a Keynes-Neoclassical Synthesis to Harrod and Hicks: Why It Fell on Deaf Ears

In 1936,Keynes suggested to both Hicks and Harrod that a synthesis between his mathematical model and the neoclassical model was possible. Keynes never received any written response from either Hicks or Harrod on his suggestion during his life time. It was left to Paul Samuelson to institute such a synthesis in 1955. Keynes’s model of his theory and the neoclassical limiting case is provided at the end of chapter 15 and in chapters 20 and 21 of the General Theory in his elasticity models. Elasticities with values such as ep=1, eo=0, e=1, ed=1, and ew=1 represent shapes and outcomes of the neoclassical limiting case. Values of ed and e less than 1 are Keynes’s general case. The elasticity of Keynes’s aggregate supply curve depends on the elasticities and slopes of Keynes’s aggregate supply function, Z, and Keynes’s aggregate demand function, D. Keynes used the first and second derivatives to show that Z MUST be a straight line, upward sloping curve, that D (and Y) MUST be concave curves and that the aggregate supply curve, or Z=D locus, MUST be a convex curve. This directly conflicts with Backhouse’s claims that Keynes never identified his General Theory functions as being curves, because, according to Backhouse, Keynes used the word curves only to refer to the classical(neoclassical) analysis. Of course, basic differential calculus covers the use of the first two derivatives for the purpose of fitting curves for specific functions. In fact, again contrary to Backhouse, Keynes does not work out any of his elasticity analysis in the footnotes in chapter 20. See Backhouse, 2010, p.140, footnote 11, p.146. The footnotes only give the final result. It requires an additional 20 pages of intermediate mathematical steps, graphs, and analysis to derive all of Keynes’s elasticity results on pp. 281-286 and pp. 304-306 of the General Theory. Harrod and Hicks did not respond to Keynes's offer because they could not follow Keynes’s specification of his more general results in Keynes’s elasticity analysis in chapters 20 and 21. Nor could they follow Keynes’s analysis in section IV of chapter 15.