(B + gp + q) / ((1+Z) W - gs - B u + q).
Let us consider a numerical example. Suppose that gn = gs = q = 0 and that prices are equal. Suppose also that AWTR = TAX/WT = 0.30. We also take the Bentham tax T[y] = Bentham[y] = 0.5 (y - B). Let us consider the path that subsistence is half of average income, i.e. B/W = ½, and then compute the various ratios. Then:
· Indexation on gross average income gives B / W = 0.5.
· Indexation on net average income gives B / Net[W] = B / (2B - 0.5 B) = 0.66.
· Then T[W] / W = 0.5 (W - ½ W) / W = 0.25, and Z
0.30 - 0.25 = 0.05.
· Since gn = gs = 0, g = gp, and AWTR = (gp + b) / W = gp/W + ½ u = 0.30. If we assume full employment u = 0.02, then gp/W = 0.29.
· Then RIR = (B / W + gp /W) / ((1 + Z) - 0.01) = (½ + 0.29) / 1.04 = 0.76.