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A Life-Cycle Model of the Linear Income Tax

Review of Economic Studies 1980 47(4), 777
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.

Uzawa's Preference Axioms: A Comment

Review of Economic Studies 1980 47(3), 641
Much attention in the theory of revealed preference has been devoted to the problem of demand functions generated from continuous utility functions. First Samuelson (1938), the originator of the theory of revealed preference, presented assumptions for P2+. Later Houthakker (1950) developed this model of consumer's behaviour for the n-dimensional case. A gap in Houthakker's proof has been recently closed by B. Stigum (1973). Uzawa (1960) presented a different version of Houthakker's theorem. His conditions AI-AIV and the Strong Axiom of Revealed Preference establish the existence of an upper semicontinuous utility function generating the given demand function. Uzawa's query whether these conditions guarantee the existence of a continuous utility function was answered in the negative by a counterexample of Hurwicz and Richter (1971). At approximately the same time E. Gordon (1971) published an article in the Review of Economic Studies where he tried to demonstrate that the axioms AI-AIV and the Strong Axiom do imply the existence of a continuous utility function. Unfortunately the proof of his Proposition 3 (p. 327) contains an error which led to this wrong conclusion. The purpose of this paper is to correct Gordon's theorem by adding conditions which are essentially due to Stigum. We will see that supporting hyperplanes play an important part in the method of the proof. The correction of Gordon's proof, based on results of Uzawa, turns out to be another method to prove Houthakker's theorem.

Target Controllability

Review of Economic Studies 1980 47(2), 451
Journal Article Target Controllability Get access Alfred L. Norman, Alfred L. Norman Board of Governors of the Federal Reserve System, Washington, and University of Texas at Austin Search for other works by this author on: Oxford Academic Google Scholar Woo S. Jung Woo S. Jung Vanderbilt University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 47, Issue 2, January 1980, Pages 451–457, https://doi.org/10.2307/2297004 Published: 01 January 1980 Article history Received: 01 January 1977 Accepted: 01 November 1978 Published: 01 January 1980

Employment and Dividend Policy of the Firm under Risk

Review of Economic Studies 1980 47(3), 503
Journal Article Employment and Dividend Policy of the Firm under Risk Get access Pierre Dehez Pierre Dehez Centre for Operations Research and Econometrics Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 47, Issue 3, April 1980, Pages 503–511, https://doi.org/10.2307/2297301 Published: 01 April 1980 Article history Received: 01 November 1978 Accepted: 01 August 1979 Published: 01 April 1980

Uncertain Lifetime, Imperfect Insurance Markets and the Valuation of Pension Wealth

Review of Economic Studies 1980 47(3), 587
In most of the developed countries provision is now made, by either the state or a private institution, for individuals to provide for themselves a retirement income which is a return on the accumulated value of regular payments made during the working life. Given that for many individuals the discounted present value of expected pension rights is one of the most important components of personal wealth it would seem desirable to include an estimate of the former in any measure of the latter. This will require the discounting of anticipated future payments and receipts at an appropriate rate. In the absence of uncertainty and with perfect capital markets anticipated future payments and receipts would be discounted at the prevailing rate of interest on financial assets. Where the individual's lifetime is of uncertain length but there exist perfect insurance markets of the type considered by Yaari (1965) the appropriate rate of discount would be the actuarially fair rate of interest prevailing on insurance notes. Now whilst the individual is uncertain as to how long he will live it is not the case that individuals are observed trading in actuarially fair insurance notes as suggested by the Yaari model. The aim of this paper is to try and obtain some insight into the appropriate rate of discount to be used in the valuation of pension wealth when insurance markets are less perfect than those described by Yaari.