Let us take the example of a doubling of income. Point A is an arbitrary point on the employment density. We scale the density so that A also lies on the tax function (H). For that arbitrary income at A we determine the average tax as a ray through A and the origin. Now, if all incomes double, then the employment frequency density shifts, and A becomes 2A. If tax parameters x and c double too, then the tax function becomes (2H). At 2A the individual pays tax C, which is the same average tax as in A (vide the straight line through origin, A and C).
Off balanced growth
Income growth means a shift of the employment density or the earnings distribution. Earlier we looked at income distributions for Holland 1950 and 1988, and the reader may now better understand why. The Dutch distributions could be approximated by lognormal distributions, but the mean, variance and the size of the labour force changed. Taxes also have been indexed on inflation instead of income. So we may surmise that there was no balanced growth.
How do agents react when there is no balanced growth ? Indexation to national income can be said to be “neutral to the income change”. The tax choices facing an individual, whose income grows as national income, are constant. The utility reaction thus depends on the change of income itself. It may be that an individual, whose income might grow as fast as national income, decides to grow differently, either more or less, depending upon his leisure-income utility. Since the context is that all individuals are adjusting, this may be reformulated as that individuals are determining their place within the income distribution.
Our analysis thus suggests that tax incentives primarily affect decisions about one’s place in the income density. Any individual change that differs from the national average can be interpreted, or defined, as the individual decision to accept another place in the income distribution. It would be interesting to reinterprete economic models on growth in these terms, and see whether elegant regularities can be found or constructed. However, it leads too far to really look into this matter, since it is not our proper subject.
We conclude that indexation and expectations about the growth of national income (relevant for indexation) lead to other results than the conventional view on marginal rates.
30. Dynamic curvature of the tax wedge
Introduction
The tax wedge at the minimum is caused by differential indexation, and makes for a higher gross minimum wage. This has been clarified above. A second point is curvature. Due to curvature, the wedge comes close to its limit value for already low levels of productivity growth. Thus, the negative effects of the wedge occur primarily at the onset of economic growth, and are less noticeable when stagnation has already set in. This already has been indicated above, but the argument can be developed by giving formulas and plots. Especially, it are the plots that may help us to understand that the major distortionary effects took place in the 1960s and 1970s. People looking only at the events in the 1990s are less likely to see the root of the problem.