James A. Mirrlees

An Exploration in the Theory of Optimum Income Taxation

you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We enable the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org. 1. INTRODUCTION One would suppose that in any economic system where equality is valued, progressive income taxation would be an important instrument of policy. Even in a highly socialist economy, where all who work are employed by the State, the shadow price of highly skilled labour should surely be considerably greater than the disposable income actually available to the labourer. In Western Europe and America, tax rates on both high and low incomes are widely and lengthily discussed3: but there is virtually no relevant economic theory to appeal to, despite the importance of the tax. Redistributive progressive taxation is usually related to a mans income (or, rather, his estimated income). One might obtain information about a mans income-earning potential from his apparent I.Q., the number of his degrees, his address, age or colour: but the natural, and one would suppose the most reliable, indicator of his income-earning potential is his income. As a result of using mens economic performance as evidence of their economic potentialities, complete equality of social marginal utilities of income ceases to be desirable, for the tax system that would bring about that result would completely discourage unpleasant work. The questions therefore arise what principles should govern an optimum income tax; what such a tax schedule would look like; and what degree of inequality would remain once it was established. The problem seems to be a rather difficult one even in the simplest cases. In this paper, I make the following simplifying assumptions: (1) Intertemporal problems are ignored. It is usual to levy income tax upon each years income, with only limited possibilities of transferring one years income to another for tax purposes. In an optimum system, one would no doubt wish …

The Optimal Structure of Incentives and Authority Within an Organization

Two kinds of models for a productive organization are presented. In the first, both production and rewards are based on the performance of individuals, which is perfectly observed. Their abilities are not observable. Despite this, theorems are proved giving strong grounds for the equality of wages and marginal products unless there is monopsony in the labor market. This latter case is also discussed. The second model, which focuses on the imperfect observation of performance, allows interesting deductions about optimal payment schedules and organizational structure.

The Theory of Moral Hazard and Unobservable Behaviour: Part I

Principal-agent models are studied, in which outcomes conditional on the agents action are uncertain, and the agents behaviour therefore unobservable. For a model with bounded agents utility, conditions are given under which the first-best equilibrium can be approximated arbitrarily closely by contracts relating payment to observable outcomes. For general models, it is shown that the solution may not always be obtained by using the agents first-order conditions as constraint. General conditions of Lagrangean type are given for problems in which contracts are finite-dimensional.

Optimal Tax Theory: A Synthesis

Abstract Necessary conditions for optimal taxation are derived (i) when taxes are constrained to be linear, (ii) when the form of taxation is unconstrained, (iii) when some commodities are subject to nonlinear taxation, the remainder to proportional taxation. Among the results obtained are several that help to determine upon which commodities the tax system ought to bear most heavily. In particular, a criterion for the effect of commodity taxes in the presence of an optimal income tax is found. The paper concludes with a general principle of simple form for optimal economic policies of all kinds.

A Model of Social Insurance With Variable Retirement

Abstract Models are studied, in which ability to supply labour is affected by a random variable (health) not observable by government. When ill-health strikes, the consumer must retire, but he may choose to retire in any case. Optimal social insurance policies are found for one-period, two- period, and continuous-time models. It is found that, under plausible conditions, at the optimums consumers are indifferent whether to work or not, but do work when able. Insurance contributions decrease with age, and insurance benefits increase with age of retirement. It is desirable to prevent private saving. Some comments on the U.S. Social Security system are added.

A New Model of Economic Growth

The purpose of this paper is to present a “Keynesian” model of economic growth which is an amended version of previous attempts put forward by one of the authors in three former publications.1 This new theory differs from earlier theories mainly in the following respects: (1) it gives more explicit recognition to the fact that technical progress is infused into the economic system through the creation of new equipment, which depends on current (gross) investment expenditure. Hence the “technical progress function” has been re-defined so as to exhibit a relationship between the rate of change of gross (fixed) investment per operative and the rate of increase in labour productivity on newly installed equipment; (2) it takes explicit account of obsolescence, caused by the fact that the profitability of plant and equipment of any particular “ vintage ” must continually diminish in time owing to the competition of equipment of superior efficiency installed at subsequent dates; and it assumes that this continuing obsolescence is broadly foreseen by entrepreneurs who take it into account in framing their investment decision. The model also assumes that, irrespective of whether plant and equipment has a finite physical life-time or not, its operative life-time is determined by a complex of economic factors which govern the rate of obsolescence, and not by physical wear and tear; (3) in accordance with this, the behavioural assumptions concerning the investors’ attitudes to uncertainty in connection with investment decisions and which arc set out below, differ in important respects from those made in the earlier models; (4) account is also taken, in the present model, of the fact that some proportion of the existing stock of equipment disappears each year through physical causes—accidents, fire, explosions, etc.—and this gives rise to some “ radioactive ” physical depreciation in addition to obsolescence; (5) since, under continuous technical progress and obsolescence, there is no way of measuring the “ stock of capital ” (measurement in terms of the historical cost of the surviving capital equipment is irrelevant; in terms of historical cost less accrued “ obsolescence ” is question-begging, since the allowance for obsolescence, unlike the charge for physical wear and tear etc., depends on the share of profits, the rate of growth, etc., and cannot therefore be determined independently of all other relations), the model avoids the notion of a quantity of capital, and its corollary, the rate of capital accumulation, as variables of the system; it operates solely with the value of current gross investment (gross (fixed) capital expenditure per unit of time) and its rate of change in time. The macro-economic notions of income, income per head, etc., on the the other hand are retained.

Evaluating Economics Research in Europe: An Introduction

This paper introduces a symposium of EEA-funded studies that evaluate economics research in Europe. The paper considers some general issues in evaluations, paying special attention to the problem of selecting journal weights, and notes some special features of the individual studies. Despite their very different approaches, the same group of institutions tend to appear at the top of all lists, though individual ranks are sensitive to the choice of more or less elitist journal weights. All the studies show that the gap between economics research in Europe and the United States is narrowing, but remains very wide. (JEL: A10, J44)

Migration and optimal income taxes.

Abstract The issue addressed in this paper is the optimal taxation of incomes earned in the home economy, and of incomes earned abroad, when people can migrate. As a preliminary, the optimal taxation of home incomes when there is migration and no taxation of foreign incomes, is discussed. Then in a more general setting, we deal with optimal taxation of different kinds of labour when another kind of labour is not taxable, and show how this bears on the taxation of foreign incomes. The last sections of the paper analyse a simple model in which people choose between taxable labour at home, taxable labour abroad, and untaxable labour. A condition is found implying that the optimal tax on foreign income is higher than on the home income of a person of equal utility.

Payroll-Tax Financed Social Insurance with Variable Retirement

The optimal relationship between retirement benefits and retirement age is derived. The model assumes ex ante identical workers, zero-one labor supply, no private savings, wages and payroll taxes constant over life, random onset of an inability to work, and the impossibility of distinguishing those unable to work from those choosing retirement. This formulation is meant to capture some issues for retirement programs where governments commonly do not measure disability, e.g., ages 65-70. With intertemporally additive preferences, optimal benefits rise with the age of retirement, but more slowly than would be actuarially fair. A nonadditive example is also considered.

On Producer Taxation

1. Dasgupta and Stiglitz [1] have recently discussed the optimum taxation of profits accruing to firms under diminishing returns to scale, and the implications for optimum commodity taxation and public production. Their main theorem asserts that, when the rents of different producers can be taxed at different rates, production efficiency is desirable. In the analysis of commodity taxation and public production by Diamond and myself [2] it was assumed that constant returns prevailed in the private sector, and we had supposed that productive efficiency would not usually be desirable when this assumption was violated. It may therefore be interesting to see how the new result can be obtained by the methods of our paper. In this way, I hope that it may be easier to understand the reason for their result. It also appears that one, possibly important, modification must be made in it. The final theorem has a quite unusual form.