| The public sector has a substantial influence on economic activity. A major part of what government does is redistributive in nature and intent. The purpose of this thesis is to study the redistribution of labor incomes in an economy where agents have different productivities, based on Foley's (1967) concept of fairness as no-envy (or envy-freeness) and its alternatives. An allocation is envy-free if nobody envies the consumption-labor bundle of any other agent. Previous works showed that the class of fair allocations that are implementable by income and commodity taxation is quite limited. After a historical overview of the developments that have led to this thesis in Chapter 1, in Chapter 2, we examine the implementability of fair allocations by a tax schedule that depends on labor supply and gross income (( y, l)-implementability). We first show that in any economy, every envy-free allocation is (y, l)-implementable. On the other hand, whereas we already know that no-envy may be incompatible with first-best Pareto efficiency, alternative equity concepts which circumvent this first-best equity-efficiency trade-off meet the obstacle of tax implementability even when labor supply is observable. In Chapters 3 and 4, we examine the optimal redistribution issue based on an envy measure by Chaudhuri (1986) and Diamantaras and Thomson (1990), under the assumption that neither ability nor labor supply is observable. An allocation is λ-equitable if no agent envies a proportion λ of any other agent's bundle. In Chapter 3, we study the allocations that maximize λ among the second-best Pareto efficient allocations. We first consider linear commodity taxes and linear income taxation. We show that the consistency between envy reduction and enhancement of the low ability's utility depends on (1) the income elasticity of leisure, and (2) the degree of preference and skill differences. We next consider an environment where non-linear income tax is feasible. In the standard two-class economy with identical preferences, under normality of consumption and leisure, envy is minimized at the leximin allocation. In a many-person economy, it is possible to order the class of second-best Pareto efficient allocations graded by progressivity in the sense of Hemming and Keen (1983), with respect to the intensity of envy. When the income elasticity of leisure is equal to or greater than unity, envy is minimized in the most progressive tax system. However, we can find an economy where envy is not minimized at the leximin allocation when we allow double-crossing of the tax schedules. In Chapter 4, we examine the optimal nonlinear income taxation problem based on λ-equitability. We study the properties of Pareto undominated allocations for various λ-equitability requirements. When there is one output, the marginal income tax rate can increase in income only if the income elasticity of leisure is greater than unity. In a multi-commodity model with commodity taxes, the goods preferred by the low skilled agent and/or those with high Hicksian elasticities are taxed more heavily. When preferences exhibit quasi-linearity in leisure, we can show that the introduction of a binding λ-equitability constraint increases the marginal income tax rates of the entire population. |
