AN APPROXIMATION FOR THE OPTIMAL LINEAR INCOME TAX RATE

This paper derives a convenient method of calculating an approximation to the optimal tax rate in a linear income tax structure. Individuals are assumed to have Cobb-Douglas preferences and the wage rate distribution is lognormal. First, the optimal tax rate is shown, for a general form of social welfare function, to be the smallest root of a quadratic equation involving a welfare-weighted average wage rate. Second, an approximation to this average is derived for an isoelastic social welfare function. This average depends on the degree of inequality aversion of the welfare function and the coefficient on consumption in individuals' utility functions. Calculations show that the method performs well in comparison with standard simulation methods of computing the optimal tax rate.