Some Analytics of Income Tax/Transfer Systems

Although there has been a great deal of discussion of the relative merits of alternative income maintenance schemes, the precise relationships between benefit levels and tax rates required are not usually examined in detail. The purpose of the present article is, therefore, to provide comparable results for a number of systems so that the “trade‐offs” involved can easily be examined and compared. The majority of results are quite general, and do not depend on the form of the distribution of gross income, but in common with other analyses it has not been possible to allow for incentive effects. Some of the schemes have been examined elsewhere, but the results presented below provide a much more unified and simplified set of comparisions. While fairly simple results may be obtained for the relationships between taxes and benefits, it is much more difficult to provide convenient expressions for the dispersion of post‐transfer income. However, a method of calculating the coefficient of variation of post‐transfer income is presented in the final section of this article.