Kahn’s Mathematical Style, in His June, 1931 Multiplier Article in the Economic Journal, Is Identical to Keynes’ Style of Presenting Mathematical Results Starting in 1921 in the A Treatise on Probability

The manner in which R. Kahn presented his mathematical results on the multiplier in the Economic Journal of June, 1931, is identical to the style of presenting mathematical results used by Keynes to present his mathematical analysis starting with the A Treatise on Probability in 1921. Keynes’s style was to present only the initial statement of the problem and the main, final results. Keynes assumed that the mathematically interested reader would have sufficient training to be able to work backwards from the final result that he had given to the intermediate steps. A mathematically trained reader would finally arrive at the initial conditions that had been set up to specify what the problem was.

This style is in contrast to all of the other presentations made by Kahn, who would incorporate intermediate steps.

The only conclusion which is possible is that Keynes, who was the editor of the EJ and probably the referee of Kahn’s paper, showed Kahn his analysis from the A Treatise on Probability in 1921 dealing with the problem of taking the limit of a geometrical series of declining, infinite numbers, so as to arrive at a finite sum for the series. The only difference between Kahn and Keynes is that Kahn uses the variable k, whereas Keynes used the variable q. Nowhere in his 1931 article does Kahn present any technical explanation of how he arrives at the limit value or provide any of the needed, intermediate steps required in order to arrive at the finite answer.