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Labor Income Tax and Interest Income Tax
Exogenous Labor Supply
The theoretical literature on tax reform discusses a desirable tax system that assures the required revenue when multiple taxes are available. First, let us compare labor income tax and interest income tax with the equal revenue requirement.
Consider a simple two-period model. Let us denote the labor income tax rate by tw and the interest income tax rate by tr. The budget constraints of a representative consumer for each tax are written as
where c1 and c2 denote consumption in each period, Y is labor income, s is saving, and r is the rate of interest. Equations (9.1) and (9.2) include labor income tax, while Eqs. (9.3) and (9.4) include interest income tax. In this section, we assume that labor income Y is exogenously given. This is an important and crucial assumption. We also assume that the agent earns labor income only in period 1.
The present value budget constraint for each case is given as © Springer Science+Business Media Singapore 2017
T. Ihori, Principles of Public Finance, Springer Texts in Business and Economics, DOI 10.1007/978-981-10-2389-7_9
where Eq. (9.5) represents the labor income tax case and Eq. (9.6) the interest income tax case. In both equations, the left-hand side is the present value of consumption and the right-hand side is the present value of labor income. Labor income tax reduces disposable labor income, while interest income tax raises the relative price of future consumption.
In order to collect the same amount of tax revenue, which tax is relatively desirable for a household? Figure 9.1 explains this problem. The vertical axis is future consumption and the horizontal axis is present consumption. Point E is the initial equilibrium point before tax where the before-tax budget line is tangent to an indifference curve. Ew is the equilibrium point under labor income tax and Er is the equilibrium point under interest income tax. As shown in this figure, under the constraint of the same tax revenue, utility at Ew is always higher than utility at Er.
Let us explain this result in Fig. 9.1. The vertical (or horizontal) gap between line AB and line DF corresponds to tax revenue in terms of second (or first) period consumption. If the equilibrium point is on line DF, the government may collect the same amount of tax revenue in either case. Thus, we have to compare two points associated with labor income tax and interest income tax on line DF. With regard to tw, the relative price between c1 and c2 is not affected by tax; hence, the DF line is tangent to an indifference curve at Ew. In contrast, with regard to tr, the relative price between c1 and c2 is affected by tax; hence, line AB0, not AB, is tangent to an indifference curve at Er on line DF.
Thus, utility at Er is lower than utility at Ew. The optimal choice between c1 and c2 is distorted by interest income tax and creates an extra burden. This analysis suggests that labor income tax is better than interest income tax.
Fig. 9.1 Labor income tax and interest income tax
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