Showing papers in "The Review of Economic Studies in 1971"

An Exploration in the Theory of Optimum Income Taxation

Abstract: 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 man's income (or, rather, his estimated income). One might obtain information about a man's 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 men's 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 year's income, with only limited possibilities of transferring one year's income to another for tax purposes. In an optimum system, one would no doubt wish …

A Non-cooperative Equilibrium for Supergames

Abstract: Presents a non-cooperative equilibrium concept, applicable to supergames, which fits John Nash's non-cooperative equilibrium and also has some features resembling the Nash cooperative solution. Description of an ordinary game; Definition and discussion of a non-cooperative equilibrium for supergames; Description of supergame and supergame strategies; Information on the Cournot strategy.

Choice Functions and Revealed Preference

Abstract: (1) Much of revealed preference theory has been concerned with choices restricted to certain distinguished subsets of alternatives, in particular to a class of convex polyhedra (e.g., " budget triangles " in the two commodity case). This restriction may have some rationale for analyzing the preferences of competitive consumers, but it makes the results unusable for other types of choices, e.g., of government bureaucracies, of voters, of consumers in an imperfect market. If the restriction is removed, the axiomatic structure of revealed preference theory changes radically. This axiomatic structure is studied in Sections 2-5. In Section 6 the rationale of restricting the domain of choice functions and that of rationality conditions is critically examined.

Differential Taxation, Public Goods, and Economic Efficiency

Abstract: (2) Differential factor taxes3 make the marginal rates of substitution of different factors in different industries different, and hence interfere with productive efficiency. Examples include the corporate income tax, which differentiates between capital used in the corporate and non-corporate sectors; the selective employment tax; and the differential treatment of gasoline used in road transportation and in agriculture.

Cournot Oligopoly and Competitive Behaviour

Abstract: This paper shows that the Cournot oligopoly model need not converge to perfect competition, regardless of the quasi-competitiveness of the model. Convergence takes place if, and only if, there are no scale economies. Without convergence, interest centres on the other properties of the Cournot model! It is shown, for example, that both quasicompetitiveness and stability may break down with large numbers of firms. But an example suggests that the numbers involved, though not impossible, might be higher than one could expect in practice. Throughout the analysis we examine the strong case in which all firms are identical. This strips away the non-essentials and considerably simplifies the analysis. Section II describes the model and demonstrates the uniqueness of the solution. Section III is devoted to the limiting behaviour of the Cournot model. Section IV examines the quasi-competitiveness and stability of the model. Section V offers an illustrative and suggestive example based on a general linear demand function and a general cubic cost function. Finally, Section VI makes some concluding remarks on the relation between numbers of firms and competitive behaviour.

A Tâtonnement Process for Public Goods

Abstract: In this paper, we discuss a procedure for choosing efficient output level for public goods. In section 1, we define the concepts of public goods. We introduce three assumptions. We then state the problem of finding a satisfactory procedure for guiding and financing the production of public goods. In section 2, we define our procedure, in the context of a partial equilibrium model, and prove a stability theorem. Section 3 is devoted to the important problem of incentives for correct revelation of preferences ; it is shown there that, at an equilibrium, our procedure provides proper incentives. A final section of concluding remarks points to various directions fo further research.

The Dynamic Effects of Fiscal Policy in an Economy with Foresight

Abstract: This paper presents the results of a study of several related dynamic fiscal problems in a simple economic model whose distinguishing feature is that the participants in the economy are assumed to make plans by looking into the future. The competitive equilibrium in the presence of a changing fiscal policy is calculated, and compared to the intertemporal equilibrium in the absence of any change. Throughout, we use the term equilibrium in its Walrasian sense, to indicate that all markets clear. In every case, we calculate the full general equilibrium in the economy, over all time periods and all markets. Part of the contribution of the paper, it is hoped, is in suggesting some methods for the characterization of intertemporal competitive equilibrium. Except for very general properties-existence of equilibrium and turnpike behaviour-this area of study has received very little attention in the literature. Since the actual calculation of the equilibrium is rather tediously algebraic, we have adopted the following organization: In part 1, we describe the model and indicate some of its properties. In part 2, we present, without proof, descriptions of the dynamic effects of a variety of fiscal policies. Finally, in part 3, we develop the analytic method applied in section 2. Four fiscal policies are treated: a recurrent head tax, a consumption tax, an interest tax, and an investment credit. In almost every case, there are important anticipatory effects on the economy in advance of the imposition of the policy. Generally, the anticipatory effects help to smooth the jolt caused by the policy. For example, savings gradually increase in anticipation of the head tax, enabling individuals to maintain a smooth level of consumption in spite of the tax, although eventually consumption must be reduced by the whole amount of the tax. Even when the policy change causes a jolt in the real flows of the economy, as in the case of the consumption tax, the anticipatory effect is in the opposite direction to the jolt. It is also instructive to note how the competitive price system acts to cushion the economy against the impact of a policy change. This is most strikingly illustrated in the case of the investment credit (defined as a negative excise tax on investment goods). In a partial equilibrium analysis ignoring the effect of the credit on interest rates, it appears that no rational entrepreneur would hold capital goods at the instant the credit became available. He could escape the capital loss induced by the credit, seemingly, by selling his capital goods just before the credit became available and buying them back an instant later. In fact, however, the simultaneous desire of all capital owners to sell and buy back causes a dramatic fall in the interest rate, exactly large enough to remove all the incentive to sell in the first place.

The Pasinetti Paradox in Neoclassical and More General Models: a Correction

Abstract: _S s _ ._ r*k* (k*) S1-Si f(k*) -r*k* I1(k*)9 i.e. the domain of the Pasinetti and Dual solutions in the extended case is dependent on the proportion of workers in each non-capitalist category and the savings propensities of all those categories, as well as on the maximum savings propensity of the capitalist class and the form of the production function. Thus we may note that the maximum extent of the Dual domain occurs when the inequality becomes sl ? oc(k*)sl, the Samuelson-Modigliani condition-when all workers have the same savings propensity (A1 = 1), whilst the minimum extent of the Dual domain occurs when large weight is accorded the worker categories who are minimal savers, when the inequality approaches sl ? scl.

The Structure of the Cost of Capital under Uncertainty

Abstract: In the analysis of models of competitive markets under uncertainty, different approaches can be distinguished. One approach, typically dealt with in welfare economics, is the specification of environmental conditions that are sufficient for the existence of equilibrium prices, with all the corollary implications for the efficiency of the competitive system. Prominent examples of this approach are the works of Arrow [2], Debreu [3] and Radner [12]. Another approach, typical to the analysis of capital markets, is concerned more with the structure of equilibrium prices, rather than their existence. Under this approach, basic interest lies in the implications of various given assumptions about the preferences of individuals (e.g. risk aversion) on the relationship between various properties of capital assets and their equilibrium prices, which are initially assumed to exist. Such studies extend from the classical investigations, such as Hicks [6] and Lutz [10], on the term to maturity of “riskless” capital assets, to recent ones concerned primarily with the issue of risk, such as Sharpe [13], Lintner [9], Hirshleifer [7,8] and others. 1 The present study represents an attempt at a slightly different approach. We postulate the existence of equilibrium prices for capital assets under uncertainty, and then proceed to analyze the properties implicit in their definition. It is shown that some results can be derived without recourse to the way individuals make decisions, their detailed preferences or their subjective assessments of probabilities. ∗ The author appreciates the must useful comments of two referees. 1 For example, see also Diamond [4], Green [5], and Myers [11] - all using the same ArrowDebreu framework of uncertainty used here.

On the Existence and Optimality of Competitive Equilibrium for a Slave Economy

Abstract: Author(s): Bergstrom, Ted | Abstract: A famous paper by Conrad and Meyer calculates that on the eve of the American Civil War, slave prices were about equal to the present values of the slaves' labor services. They argue that this is evidence for the proposition that ordinary economic forces, without political intervention were not likely to put an end to slavery.I wrote this paper when pretty much the only economics that I knew was 1) how to prove the existence of competitive general equilibrium. 2) how to calculate present values. So the paper does two things. It shows how to apply Arrow-Debreu type existence theory to an economy with slavery. (this involved some technical wrinkles that were not in the existing existence literature.) More importantly, it argues that the calculations of Conrad and Meyer showed only that capital markets for slaves were working pretty well, but were not direcly relevant to the question of whether slavery as an institution was economically viable. To answer the latter question, we need to calculate two things. 1) Does an infant slave have positive present value? [If not, reproduction would be discouraged.] 2) Would a freed adult slave, perhaps because of the better incentives and opportunities for free people, be able to earn more than enough on the labor market to repay his or her market price to a slaveowner. I investigate the latter two questions empirically. The answer to the first question is "Yes". Spotty evidence suggests that the answer to the second question was also often "Yes."

Weak Experimental Verification of the Expected Utility Hypothesis

Abstract: The five experiments described in this paper are the modest final product of an initially ambitious attempt to verify a theory of choice under uncertainty. Yaari [5] in 1965 reported the results of some experiments he had performed in which he attempted to show that the acceptance of unfair gambles is better explained by the assumption that gamblers are optimistic about the occurrence of low probability events, than by the assumption of increasing marginal utility of wealth as postulated by Friedman and Savage [1] and as demonstrated experimentally by Mosteller and Nogee [2]. The hypotheses I attempted to test in these five experiments all rest on the assumption that a subject faced with a choice under uncertainty will calculate the expected utility of each alternative, in the sense of von Neumann and Morgenstern [3], and will choose that alternative for which the expectation is greatest. In the first and second experiments I was testing a theory having to do with the formation, by the subject, of his beliefs as to the proper probabilities to use in the calculation. In the third I was interested in verifying Yaari's experimental findings, and in the fourth and fifth experiments I was trying merely to obtain very weak evidence to support the hypothesis that decisions are made under uncertainty so as to maximize expected utility.

An Exercise in the Theory of Heterogeneous Capital Accumulation

Abstract: C. CATON and K. SHELL University of Pennsylvania The basic result of Hahn's seminal contribution to the descriptive theory of hetero- geneous capital accumulation [2] is that the short-run-perfect-foresight balanced-growth equilibrium is a saddlepoint in the space of capital-labour ratios and capital goods prices. In the context of a special model, Shell and Stiglitz [5] show further that on paths not tending to balanced growth, price ratios become zero (or infinite) in finite time. If machines are freely disposable, asset markets cannot be in equilibrium on such " errant " trajectories. A recent paper by Atkinson [1] has pointed out some very special features of the Shell-Stiglitz technology, casting some doubt on the generality of the conclusions. In the present paper, we investigate the " Hahn problem " in the context of a more regular model of production, the " quarter-circle" technology employed by Samuelson in his study of joint production [4]. As in the previous studies, we find that the unique balanced-growth equilibrium is a saddlepoint, and on paths not tending to balanced growth the price ratio becomes zero or infinite in finite time. 1. THE MODEL As in [5], we study a one-sector, two-capital model in which a homogeneous output, Y, is produced by the cooperation of labour, L, machines of the first kind, K1, and machines of the second kind, K2. Assuming constant returns-to-scale and denoting quantities per unit labour by lower case letters, the production relation can be written as y = f(kl, k2). For ease of analysis we assume that the production function is linear in logarithms, so

An Investment Planning Process for an Economy with Increasing Returns

Abstract: In this paper, I propose a resource allocation (planning) process designed for an economy where increasing returns to scale prevail. The main feature of the process is to supplement the market mechanism by the central allocation of investment funds. It is well known that the unmodified market mechanism fails to solve optimal allocation problems, if non-decreasing returns to scale play a very important role in the economy. In order to meet the difficulty, Arrow and Hurwicz [1] introduced price speculation into a tatonnement process. Although locally convergent and informationally most efficient,2 their process is not entirely satisfactory especially from the motivational point of view. An alternative line of attack on optimization problems under non-decreasing returns may be found in rationalizing traditional planning methods of the central allocation of material quotas. This was first done by Kornai and Liptak [3] for the case of linear technologies. Later, in this Review, Heal [4] proposed a planning process based on essentially the same idea, but considerably generalized so as to cover non-convex technologies. In his process, each manager of a production process is instructed to report to the Central Planning Board (referred to as the CPB hereafter) the shadow prices of every input centrally allocated. In the light of this data, the CPB proposes a new allocation of inputs in which, by comparison with the previous one, resources have been shifted towards the uses where higher shadow prices are given. In this way, Heal has succeeded in defining a planning process with certain desirable properties, such as monotonicity and well-definedness3 in Malinvaud's sense [6], which the Arrow and Hurwicz process lacks. However, there are still some points to be improved on in this method:

Counter-examples to an Assertion concerning the Normal Distribution and a New Stochastic Price Fluctuation Model

Abstract: Consider the following assertion: If X1, ..., X, are random variables with finite second moments and if all non-trivial linear combinations a1X, +... + a,X, have the same distribution except for location and scale, then that distribution must be normal. True or false? The assertion would be true if any pair of the variables were assumed to be stochastically independent, but it is false in general, even for variables assumed to be uncorrelated. In Section I, we demonstrate that the assertion is false via counter-examples. A recent commentary in this Review by Borch [1], Feldstein [4], and Tobin [13] indicates that the truth of the above assertion has gone unquestioned by some eminent economic theorists. Nevertheless, the generality of Tobin's mean-variance approach to risk analysis is not much enhanced by our revelation; the numerous theoretical criticisms of the mean-variance approach (e.g. Borch [1] and Feldstein [4]) still obtain. As a practical matter, our counter-examples merely extend the class of approximating distributions available to portfolio analysts. A more intriguing ramification of our counter-examples is the possibility of a viable alternative to the stable Paretian model of stochastic price fluctuation [7], [8], [2], [3], [10]. The stable Paretian model follows from the assumption of independent stable increments in the log-price process. In Section II, we construct an alternative model with uncorrelated (but dependent) stable increments.