Definition & Reality in the General Theory of Political Economy

by Thomas Cool

= M {1 - r (M - P x[0]) / (M + P c[0])}

These equations define J as an implicit function of rsi. We also see that P falls away in the right hand side:

B = P rsi B[0] = M {1 - r (M - P x[0]) / (M + P c[0]) }

rsi B[0] = J M[0] {1 - r (M[0] - x[0] / J) / ( M[0] + c[0] / J) }

As rsi and J go to infinity, then rsi B[0] ~ J M[0] (1 - r). We had B[0] > (1 - r) M[0]. Thus J > rsi.

(2) We secondly prove that J > rwi in the limit. With limit ratio R:

using the fact that the denominator equals F defined above. We want to prove that R > 1. Note, then, that M[0] < W[0], and that, due to the progressive character of the tax, the ratio of net income to total income must be higher at subsistence than at the average level, so that: