Nonlinear tax function
Book III introduced the Bentham tax function Bentham[y] = r (y - x) with exemption x and marginal rate r. This function is linear but already results into nonproportional taxes. Governments in practice have nonlinear tax schemes that give stronger nonproportionality, reflecting political views on the redistribution of income.
Strong nonproportionality has a special effect. Since taxes in the 1960s were more nonproportional than nowadays, the tax structure combined with the lognormal shape of the employment function, and generated strong nonlinear effects and a strong upswing of the CWIRU in the early phase of stagflation.
It is useful to introduce a flexible tax function with one more parameter than Bentham’s function to incorporate some curvature. This new function allows us to give concrete examples whenever nonlinearity is useful. For clarity, it appears that this function can approximate the actual Dutch tax situation. The tax function is:
(y > x)
with y the tax base and x the exemption or threshold, r the marginal rate in the limit when y goes to infinity, and c a curvature parameter. The ordered set of parameters is q = (r, x, c). [94] We do not use Greek symbols for these parameters since we will regard them as key strategic variables. If governments would use this function for practical tax collection, they might note (1) that exemption would be determined by subsistence, (2) that r would follow from the limit marginal rate for the highest incomes, (3) so that curvature c would follow from required total revenue and the income distribution. Use of this function thus both allows for a decent degree of nonproportionality and would reduce much of political debate about positioning of tax brackets and rates.
A person’s average tax is:
