Public Good Provision: Lindahl Tax, Income Tax, Commodity Tax, and Poll Tax, A Simulation I

There are two traditions in the argument on taxation. On the one hand, the argument on taxation is constructed in such a way that which taxation is desirable in order to impose a tax, income tax, commodity tax or poll tax, without paying any attention on why the tax is necessary. In the partial equilibrium framework, the lump-sum tax, such as poll tax, is regarded as the best. On the other hand, it is also a tradition to assert that government imposes a tax in order to provide public goods. This paper integrates the above two traditions by constructing a primitive general equilibrium (GE) model which incorporates a public good, asking which taxation is desirable in order to impose tax, income tax, commodity tax, or poll tax to optimally provide the public good. Formally, in Part I, we start with utilizing the Lindahl mechanism to compute a Pareto-optimal public good level under a specification of the parameters on production and utility functions. The burden-sharing in this Lindahl mechanism may be regarded as a tax on the society members, while utilizing pseudo-market mechanism. We call it Lindahl tax. Next, we compute the rate of income tax in order to sustain the optimal public good level, and compare the Lindahl tax and income tax. We proceed to the computation of the rate of (proportional) commodity tax in order to sustain the optimal public good level, and compare the Lindahl tax, income tax and commodity tax. Finally we proceed to the comparison between the Lindahl tax, income tax, commodity tax and poll tax under the specification of the model. In Part II, selecting the parameters randomly, we examine the robustness of the conclusion in Part I. Production functions are assumed as the Cobb-Douglass type while the utility function as the CES type with k the substitution parameter. It was shown for a specified case that when 0<k<1, there exists no general equilibrium for the poll tax case, while the income tax (and proportional commodity tax) is more desirable than the Lindahl tax not only from the fairness viewpoint but also from the utilitarian efficiency viewpoint under some specification of parameters. It was also shown for another specified case that even when 0<k<1, there exists general equilibrium for the poll tax case, and the income tax and the commodity tax is more desirable than the Lindahl tax, while the comparison between the poll taxation and other taxations are impossible from the above mentioned two viewpoints. Finally, specifying parameters on production and utility functions and initial endowments randomly, this paper showed that when 0<k<1, the income tax (and proportional commodity tax) is more desirable than the Lindahl tax from the fairness and efficiency viewpoints with high possibility of non-existence for poll tax general equilibrium. However, when k<0, specifying parameters on production and utility functions and initial endowments randomly, this paper showed that the Lindahl tax is more desirable than the income tax (and proportional commodity tax) from the fairness and efficiency viewpoints with high possibility of existence for poll tax although the comparison between the poll tax and other taxes are impossible from the two viewpoints. Thus, this paper showed that the comparison completely depends on the substitution parameter of the CES utility function.