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?
12 Pages Posted: 23 Sep 2010
Date Written: September 23, 2010
This note demonstrates that the mathematical analysis in the so called, alleged, "Infamous" footnote in the General Theory is straightforward if the reader possesses basic integration skills, understands the Inverse Function Rule for unique functions, can follow Keynes's completely worked out microeconomic analysis in chapter 20 of the GT of pure competition using the standard marginal productivity analysis of one variable factor of production and one fixed factor of production at the level of the 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 the General Theory. First, the "Infamous" Footnote tells the 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 the marginal product is equal to the marginal factor-cost at every point on the aggregate supply curve". Second, the slope of the aggregate supply function, ΔZw /ΔN, where Zw =N Pw, is 1. Unfortunately,Keynes gives the slope of the inverse function, ΔN/ΔZw, where N=Zw –Pw ,which is equal to 1/w, in the last line of the footnote. This is Keynes’s only slip in this footnote and it is very minor.
Keywords: Keynes, integration, inverse function rule
JEL Classification: B23, B41, E12
Suggested Citation: Suggested Citation