Robert Dorfman

Personal probabilities of probabilities

By definition, the subjective probability distribution of a random event is revealed by the (‘rational’) subjects choice between bets — a view expressed by F. Ramsey, B. De Finetti, L. J. Savage and traceable to E. Borel and, it can be argued, to T. Bayes. Since hypotheses are not observable events, no bet can be made, and paid off, on a hypothesis. The subjective probability distribution of hypotheses (or of a parameter, as in the current ‘Bayesian’ statistical literature) is therefore a figure of speech, an ‘as if’, justifiable in the limit. Given a long sequence of previous observations, the subjective posterior probabilities of events still to be observed are derived by using a mathematical expression that would approximate the subjective probability distribution of hypotheses, if these could be bet on. This position was taken by most, but not all, respondents to a ‘Round Robin’ initiated by J. Marschak after M. H. De-Groots talk on Stopping Rules presented at the UCLA Interdisciplinary Colloquium on Mathematics in Behavioral Sciences. Other participants: K. Borch, H. Chernoif, R. Dorfman, W. Edwards, T. S. Ferguson, G. Graves, K. Miyasawa, P. Randolph, L. J. Savage, R. Schlaifer, R. L. Winkler. Attention is also drawn to K. Borchs article in this issue.

Waiting and the Period of Production

They also serve who only stand and wait. — Milton Statement of the problems, 351. — Bohm-Bawerks analysis, 352. — Interest in a two-sector economy, 355. — Digression on waiting, 359. — Calculation of the period of production, 362. — Necessity of positive rate of interest, 364. — Sketch of more complicated models, 365. — Conclusions, 367. — Mathematical appendix, 367; the bathtub theorem, 367; solution of the Solow two-sector model, 368; direct calculation of the period of investment of waiting, 370.

Regional Allocation of Investment: Comment

Mr. Rahman is concerned with planning investment in an underdeveloped country so as to maintain a reasonable balance among the rates of progress in different regions of the country. The importance of this problem does not require discussion. But, as Rahman notes, it is strongly analogous to another, more pervasive problem, the allocation of investment among different industrial sectors of an underdeveloped country so as to attain a maximum over-all rate of growth in a specified planning period. In this version of the problem the rates of progress of the different sectors need not be kept in balance if doing so interferes with the basic goal, namely attaining maximal wealth at the end of the planning period. It is therefore somewhat simpler than the regional allocation problem and since it has some interesting implications of its own, it will be discussed in this note. Let the length of the planning period be T. Let Kit be the capital stock, measured in appropriate physical units (for example, number of looms, nameplate capacity of generators, and so on), in sector i at date t (t = 0, 1,..., T). Let ca be the value assigned by the planning commission to a unit of capital in sector i at the terminal date, T. These valuation numbers, ci, are entirely arbitrary. They might approximate the income-producing potential of capital in various sectors; they might, if industrial employment is an important national goal, approximate the employment opportunities per unit of capital; they might be simply unity for sectors deemed desirable and zero for others. Whatever they are, we take it that the objective of the plan is to maximize the value of capital at the terminal date, namely W = UCXKIT. Investment in each year is to be financed out of saving or reinvestible surplus, computed as follows. Each unit of capital in sector i contributes vi per year to the total value added in the economy. This contribution can be divided (for example) into three parts: wages equal to nmwj, where nm is employment per unit of capital and wj is the wage rate in sector i; rentier and interest payments equal to ri per unit of capital; and profits equal to vi niwi ri. Differing proportions of these three streams of income are reinvestible, so the total reinvestible surplus per unit of capital in the ith sector is

Forty Years of Cost-Benefit Analysis

This year is a triple anniversary. With great fanfare the United States is celebrating the 200th anniversary of its Declaration of Independence. With considerable solemnity but less fanfare economists all over the world are celebratinglhe 200th anniversary of The Wealth of Nations. And with almost no fanfare whatsoever benefit-cost analysts are celebrating the 40th anniversary of their craft, which had its official inception in the Flood Control Act of 1936.1

On optimal congestion

Abstract A number of classic papers conclude that if a congestible facility is the property of a profit maximizing entrepreneur, he will impose a charge for use that induces the socially optimal level of use and congestion. All these papers happen to deal with a special case in which that conclusion holds, but it is not true in general. In general, the socially optimal level of use of a congestible facility is the level at which the marginal cost of providing the service is equal to the sum of the decreases in the users willingnesses to pay for a unit of service when the level of congestion is optimal, and need not coincide with the level resulting from a profit-maximizing charge. This sum is derived from the integral under a fictitious demand curve constructed by imagining that the level of congestion is the same (and optimal) at all levels of the use-charge.

Protecting the global environment: An immodest proposal

Abstract As the other essays in this symposium note, the threats to the global environment are an aggravated instance of the Prisoners Dilemma game. On the assumption that one nations environmental behavior does not affect the behaviors of other nations, each nation serves its interests best by continuing to abuse the environment, no matter what other nations do. As a result, the benign global environment is doomed unless the nations of the world, or most of them, learn how to restrain each others environmentally destructive activities. The experience of the thinning of the ozone layer and the signing of the Montreal Protocol in response shows that the countries can cooperate when the conditions are right, and indicates the conditions that are required.

Austrian and American Capital Theories: A Contrast of Cultures

Controversies about capital, its role in the economy, and its claims for reward are still very much with us. Though the exchanges are often heated, all the contestants are descended from either of two monumental works of about a century ago: Eugen von Bohm-Bawerks Positive Theory of Capital (1889) and Irving Fishers The Rate of Interest (1907). This essay inquires: in what respects are these two theories the same? In what respects do they differ? And why?

Modernizing Böhm-Bawerk's Theory of Interest

In 1690, John Locke proclaimed, “Whatsoever [anyone]; removes out of the State that Nature hath provided … hath mixed his Labour with, and joyned to it something that is his own, and thereby makes it his Property .” Ever since this dictum was pronounced philosophers, economists, and, especially, capital theorists have been embarrassed by the virtually universal disregard of it in practice. At the very inception of economic theorizing, Ricardo declared that explaining the division of the national income into wages, rents, and interest was “the principal problem in Political Economy.” He proposed an ingenious explanation, but was far from settling the matter. Some fifty years later, Marx, building on Ricardos concept of value, brought the debate to a sharp focus; after him, it became largely an argument between Marxists and everyone else. Put starkly, Marx defined the value of any good or service to be the amount of labor required to produce it. Since a worker and his family can be supported for a year by the product of a good deal less than a full years labor, this definition implies a gap between the value of a years labor and the value of its products. Owners of land and capital are only too glad to close the gap by claiming the “surplus value.” Marxs diagnosis of the nature and origin of surplus value became the focus of discussions of the distribution of income for most of the following century.

In appreciation of Wassily Leontief

Abstract Virtually single-handedly, Wassily Leontief conceived, invented, and applied input-output analysis, one of the twentieth centurys major advances in economics. In so doing, he overcame daunting obstacles, including lack of data and the fact that when he undertook his project computing machines able to perform the necessary computations did not exist. He was driven by his life-long conviction that economic analysis requires concrete, verifiable numbers rather than algebraic formulas, no matter how elegant.

Social Decisions without Social Preferences

One of the most sacred foundations of economic reasoning is that decisions are a reflection and implementation of preferences. Consumers ’ decisions reveal ‘revealed preference ’. Business decisions are intended to maximise profits because businessmen prefer higher profits to lower. All decisions are intended to obtain the more preferred in lieu of the less preferred.