The Personal Income Tax and Family Labor Supply

Abstract

The traditional theory of family labor supply based on utility maximization subject to a budget constraint implies that there is a reduced form relationship between hours supplied by family members and the market wages of individual workers and family nonlabor income. Using this theory, and assuming that families do not regard taxes as payment for collective goods, Kosters [11] has analyzed effects of the personal income tax on family labor supply by converting the tax into a change in wage rates at the marginal tax rate. This technique is appropriate for a proportional tax but not for a progressive income tax in which average and marginal rates diverge. Using other approaches to the determination of labor supply behavior, Hall [7] and Wales [12] have developed appropriate procedures for dealing with the effects of a personal income tax. Hall develops a model in which labor supply is a function of primary and secondary worker wages and family wh le income, where whole income is the sum of non-labor income and family earnings calculated under the assumption that ach wo ker is employed full time. Hall adjusts for the presence of the personal income tax by interpreting the tax as a combined wage tax at the marginal tax rate and lump sum tax reducing whole income. The lump sum tax is equal to the total tax that would be paid if gross income were equal to whole come nd if the prevailing marginal tax rate remained constant for all higher levels of income. Following Cooper [5], Wales [12] handles a progressive income tax by maximizing n explicit utility function for a single worker family subject to a budget constraint that includes the tax schedule. He rejects the reduced form estimation apoach because it is not clear how the afterax wage rate and the gross wage rate would be incorporated in an ad hoc reduced form regression analysis. The purpose of this paper is to present the generalized analysis of reduced form labor supply functions in the presence of a progressive income tax. We demonstrate that within