On the Conflict Between Kahn’s 1936 Reply to Neisser, That ‘My Own Ideas Were Largely Derived From Mr. Keynes’, and Kahn’s Critical Assessment of Keynes’s Math Skills in R. Skidelsky (1992)

Abstract

The claim made to Robert Skidelsky by Richard Kahn, published in Skidelsky’s 1992 second volume of his autobiography of Keynes, that “…he recalled Keynes himself as being a poor mathematician by 1927…”, is in direct conflict with Kahn’s 1936 reply to Neisser, that My own ideas were largely derived from Mr. Keynes.” An examination of the mathematical analysis on page 183 of Kahn’s June, 1931, Economic Journal article on the employment multiplier shows that the mathematical style in Kahn’s article is identical to Keynes’s mathematical style of stating the problem and then giving the final result, but in which none of the intermediate steps in the mathematical analysis are provided. Kahn’s answer on page 183 of his article in 1931, which was the result of finding the finite limiting value of a geometrical, declining, infinite series of numbers, is identical to the answer presented by Keynes on page 315 in footnote 1 in chapter 26 of Keynes’s 1921 A Treatise on Probability except for notation. One need only replace Keynes’s q variable with Kahn’s k variable to get the answer provided by Kahn on page 183 of his 1931 article. Nowhere in Kahn’s article is there any explanation or discussion of what he is doing mathematically or technically that allows him to derive the finite limiting value. There are no intermediate steps provided anywhere in the article by Kahn. There is no discussion of the words “geometrical”, ”infinite series ”, ”declining”, or “limit” in the article. All Kahn does is present the initial problem and then present the answer, which is identical to Keynes’s style. Given Keynes’s worked out multiplier analysis, used by Keynes in a speech in May, 1929, the evidence is overwhelming that Keynes showed Kahn, sometime before June, 1931, how his employment multiplier problem was mathematically identical to Keynes’s A Treatise on Probability problem on page 315 in footnote 1 of chapter 26. Given this, then it is clear why Kahn stated in 1936 that My own ideas were largely derived from Mr. Keynes. Historians of economic thought and economic historians have all overlooked Keynes mathematical analysis of the theoretical and mathematical foundations for the multiplier provided in the A Treatise on Probability. For instance, Paul Samuelson missed a golden opportunity in his 1977 Journal of Economic Literature to show that Keynes had already developed the logical and mathematical technique needed to generate the multiplier, but Samuelson overlooked Keynes’s technical analysis in his work on Keynes’s risk analysis in chapter 26 of the A Treatise on Probability. The real unanswered question is why, after nine decades, no economist has yet recognized that it was Keynes who showed Kahn how to apply the technical tools to derive the multiplier concept and not the other way around.