A loglinear tax and transfer function: majority voting and optimal rates

This paper explores the use of a loglinear tax and transfer function, displaying increasing marginal and average tax rates along with a means-tested transfer payment. The two parameters are a break-even income threshold, where the average tax rate is zero, and a tax parameter equivalent to the marginal tax rate at the break-even income level. When combined with Cobb-Douglas utility, the resulting labour supply is fixed and independent of the individual’s wage rate. For an additive social welfare function involving the sum of logarithms of (indirect) utilities, a convenient expression is available for the optimal tax rate in a framework in which individuals differ only in the wage rate they face. It is shown that a unique optimal rate exists, which depends on the preference for consumption and the inequality of wage rates. This coincides with the majority voting equilibrium rate. As with the linear tax function, higher inequality is associated with choice of a higher tax rate.