An Analysis of Keynes’s Straightforward, Easy to Follow, Alleged 'Infamous' Footnote 2 on pp. 55-56 of the General Theory - Is It Really that Difficult and Abominable?

Abstract

This note demonstrates that mathematical analysis in so called, alleged, Infamous footnote in General Theory is straightforward if reader possesses basic integration skills, understands Inverse Function Rule for unique functions, can follow Keynes's completely worked out microeconomic analysis in chapter 20 of GT of pure competition using standard marginal productivity analysis of one variable factor of production and one fixed factor of production at level of firm-industry, and understands that Keynes makes aggregation assumptions only about one variable input, labor, and one fixed input, capital (equipment). Keynes provides aggregation assumptions for no other variable input in General Theory. First, Infamous Footnote tells reader to set ΔZw /ΔN=ΔDw /ΔN and solve. Given that ΔZw /ΔN =1 and Dw =pwO, where O=Ψ(N), then ΔDw /ΔN= pw Ψ'(N). Keynes expected a reader to obtain 1=pw Ψ'(N) or w/p=Ψ'(N) so that the proceeds of marginal product is equal to marginal factor-cost at every point on aggregate supply curve. Second, slope of aggregate supply function, ΔZw /ΔN, where Zw =N Pw, is 1. Unfortunately,Keynes gives slope of inverse function, ΔN/ΔZw, where N=Zw –Pw ,which is equal to 1/w, in last line of footnote. This is Keynes’s only slip in this footnote and it is very minor.