Abstract
Much of the literature on an optimal taxation problem has adopted an objective of maximizing the sum of individual utilities. For instance, studies on an optimal direct tax consider the maximization of the sum of individual utilities consisting of their incomes with labor supplies, while studies on an indirect one examine that consisting of their consumption demanded. However, the studies have never seemed to put together optimal direct and indirect taxation in one model and analyze them with the other side when a total tax revenue is determined exogenously. In this paper, we consider such an imposition problem of both direct and indirect taxes in one model as done in the real society. In achieving its problem with the exogenous total amount of tax revenue, we find in a closed-form solution that the optimal proportion of the direct and the indirect tax revenue basically depends upon the pre-tax aggregate income, say Y as well as the double of the tax-excluded consumption expenditure, say 2C, or Y/2C. In the process of finding the above optimal direct/indirect tax ratio through a new law of equal marginal sacrifice, our model does not adopt the utilitarian objective. Instead, we try to maximize the sum of the market surpluses, not only in m markets of labor but also in n markets of goods. By focusing upon those m + n market surpluses, we can now include demand functions of labor and supply ones of goods, which have not yet been considered in the previous studies. Therefore, our model maybe more realistic than some others in order to show another optimal taxation without assumptions of fixed wages and prices as parameters like utilitarian maximization problems.
