A Life-Cycle Model of the Linear Income Tax

Abstract

Although an income tax is often a government's most important instrument for raising revenue and redistributing income, its potential usefulness for either of these purposes is limited by its negative impact on work incentives. The implications of the incentive effect have been studied by examining optimal tax structures under a variety of assumptions about preferences, the distribution of wage rates, and the form of the social welfare function. Much of this work has been done using models that include interpersonal variation in ability (wage rates), but in which no saving or dissaving occurs, i.e. in which the consumption of each individual is exactly equal to his labour income net of taxes within the time period (Mirrlees (1971), Sheshinski (1972a), (1972b), Atkinson (1973a), (1973b), Phelps (1973), Cooter and Helpman (1974), Itsumi (1974), Sadka (1976)). While the latter assumption might be innocuous if wage rates were approximately constant over an individual's lifetime, so that there was little incentive to borrow or save, or if capital markets were non-existent, so that borrowing and saving were impossible, wage profiles are in fact quite steep and most individuals make use of (admittedly imperfect) capital markets. Multiperiod models incorporating consumption-saving decisions have been used to study the effects on capital accumulation of wage, interest, capital gains, and other taxes, but even those models that include variation in ability have in general assumed that labour is supplied at a constant rate over the individual's working years (Ordover and Phelps (1975), Sheshinski (1976), Feldstein (1974)). A life-cycle model of individual behaviour that includes both labour supply and consumption decisions is used below. Although a general equilibrium framework is used, for simplicity real capital is ignored; labour is the only factor of production and government debt is the only asset available to savers. Only steady states and only linear tax schedules are considered, and the utilitarian social welfare function is used throughout. First, the conditions under which the life-cycle model reduces to the one-period case are derived, as well as the conditions under which the first-best tax policies for the two are identical. Next it is shown that if all individuals are identical, the optimal policy consists of lump-sum taxes together with an interest rate equal to the rate of pure time preference. The non-optimality of the biological interest rate proposed by Samuelson (1958) in his Exact Consumption-Loan Model is discussed. Finally, an upper bound on the optimal marginal tax rate is derived. This bound depends on the elasticity of total labour supply and on the elasticity of demand for debt.