Budget Size Effects on the Optimal Linear Income Tax

Abstract

This study examines the effects of the government budget on the optimal linear income tax. The size of government spending is a popular political topic. Some politicians argue for a decrease in the government's role as a purchaser of goods and services. Others see the necessity for an expanding role. In this study the income tax function must collect a fixed sum of revenues for nontransfer expenditures. By altering the size of this fixed sum we discover the budget size effects on the optimal tax function. To summarize, we use an individualistic social welfare function developed by Atkinson to determine the optimal tax function. Cobb-Douglas and CES utility functions are used to describe people's preferences between consumption and leisure. We approximate the U.S. distribution of skills with two different skill distributions consisting of five or six representative skill divisions. Our simulations are carried out using data for 1975 from the 1976 Current Population Survey. We prove several general results for the simple additive welfare function and the maximin welfare function, but in most instances we rely on simulations to ascertain the direction of change in the tax rate and guarantee and, also, to determine the size of these changes. Generally, we find that an increase in the government budget raises the marginal tax rate and lowers the guarantee of the optimal linear income tax. In a few simulations, however, where additional workers enter the labor force, the optimal tax rate falls.