6.1 Motivations and Objectives

This chapter begins by considering the problem of acquiring a certain amount of tax from the individuals in a society in conjunction with assigning a specific quantity of subsidy to the same set of individuals in an inequality-minimizing manner, where the tax and the subsidy sizes need not be the same (see Chakravarty and Sarkar, 2022). The tax-collection-subsidy provision scheme we are considering here can be viewed as follows: tax payments are made by the individuals to the government, and subsidy (benefit/transfer) payments are made from the government to the individuals. If the sizes of the total tax and total subsidy are the same, then Fei's (1981) inequality-minimizing solution for a balanced budget plan becomes a particular case of the tax-subsidy allocation program considered here. However, Fei's analysis has a limitation; it does not consider the practical problem where the before- and after-tax total incomes may differ. In general, total tax levied on a set of individuals is higher than the total transfer made to them. The administration may be required to make welfare payments on an absolute basis – for instance, when the individuals in a society get affected by some natural calamity such as cyclone and flood. It may become essential for the administration to spend money on an urgent basis for the maintenance or construction of a public good. All these expenditures are generally financed from the taxes raised from the individuals.