J M Keynes’s mathematical style: Very concise, precise, and exact

Abstract

Keynes's mathematical style, starting with his First Fellowship Dissertation in 1907 for Cambridge University, England, through his formulation of a linear, first order difference equation that incorporated the interaction of the Multiplier and Accelerator (called the Relation) for Harrod's use in his August,1938 correspondence with Harrod, and ending with his exchanges over probability and statistics with J. Tinbergen, an advocate of the Limiting Frequency Interpretation of Probability in 1939-40, was always very concise, precise and exact. Specifically, Keynes always provided the first steps in his mathematical analysis and the last step. However, he would rarely put in the intermediate steps. Keynes's view was that he always provided a clear, literary, prose explanation of his analysis that would allow any reader of his work to grasp the same basic, fundamental points that were being made in the mathematical analysis. A reader concentrating on Keynes's supplementary mathematical analysis would also grasp the basic fundamental point being made. The intermediate mathematical steps in a Keynesian analysis need to be formulated by working backwards from the final step by the reader. This is precisely what economists have failed to do. They have been unable to generate the intermediate steps that connect the first and last steps. For instance, the results that Keynes presented in the General Theory regarding his IS-LM (LP) and D-Z models were never correctly grasped by any mainstream economist in the 20 th and 21 st centuries because they were not able to reconstruct the mathematical analysis in chapters 20 and 21 of the General Theory. All current contributions to macroeconomic history and history of economic thought state that, at best, Keynes only had an intuitive, implicit understanding of the multiplier before 1931. Supposedly, Kahn used mathematical and logical analysis to derive the multiplier in his June, 1931 Economic Journal (EJ) article. He then taught Keynes the technical steps from his article. Therefore, it would have been impossible for Keynes to write the General Theory without Kahn's contribution and instruction. This paper shows that it was Keynes, not Kahn, who developed the mathematical and logical analysis of the multiplier in his A Treatise on Probability ten years before Kahn's article was published.