It must be noted that y[0] depends upon y, so that f may take continuous values. ATRwi[f, rwi] expresses that if we have a value of y, then we could interprete this as deriving from various combinations of f and rwi as long as rwi x[0] / f = y. The dynamic ATRwi[f, rwi] thus seems no different from the static ATR[y]. The complication however comes from subsistence. We cannot regard M as a normal case of y = P rwi y[0].
Denote the average tax at the minimum wage as, ATR M [rwi]. We will use the suffix ‘M’ in general to signify this dynamic point of view. [99]
In Book III we derived the real subsistence index rsi for the Bentham function when x = P x[0], so that B = rsi P B[0].
(13.3d)
Then:
M = B + Bentham[M]
M = (B - r x) / (1 - r)