Professor Huntsman's paper is a welcome addition to the growing literature on portfolio theory. Traditional mean-variance analysis, in spite of its obvious simplicity and its ability to explain portfolio diversification, has come under increasing attack, both for the theoretical weaknesses underlying the technique and for its failure to recognize that investors manifestly prefer returns that are positively skewed to those that are not.

Estimation Problem, Cost allocation, Internal rate of return, Price-level Problem

In [2]Sethi and Thompson illustrated the applications of the maximum principle to solve simple dynamic cash balance problems. In Section IV of that paper, we introduced the idea of penalty function to solve the cash balance problem with bounded state variables arising out of disallowing overdrafts and short selling. This resulted in the adjoint equations containing terms in the state variables x(t) and y(t). We then stated the need for solving a two-point boundary value problem.

Pigou's parable of the belching factory imposing an externality on the neighboring laundry has elicited more controversy than one could have expected from such a simple situation. Ronald Coase claimed that the Pigouvian solution of taxes and subsidies was demonstrably inefficient while William Baumol recently defended Pigou by presenting a situation in which a tax placed upon the factory (without taxation or compensation to the laundry) optimizes resource allocation under pure competition. What if the externality affects the factory itself? Suppose the reduces the work efficiency of employees and causes ill health. It might be conjectured that nothing new is gained by adding the wrinkle of poisonous air which sickens factory workers, since the factory both generates the and is affected by it. By analogy, a city where everyone works in factories generating air pollution (which affects only the city) might be deemed consistent with Pareto optimality, presuming the factories compensate individuals for the air pollution with higher wages. 1 Similarly, recent policy discussions have advocated exporting air pollution by importing pollution-producing goods. Little concern has been given to the welfare implications since the republic of smoke would be experiencing the profit as well as the pollution from production. There are even proponents of the view that some regions of the United States ought to be kept quite clean, while others are allowed to become highlv polluted. Their reasoning is that

A "socioeconomic" definition of Pareto optimality, 305. — Can the income distribution be a public good?, 306. — The political economy of the model, 307. — Alternative approaches, 310.

T HE basic purpose of this paper is to show that an improved understanding of longswing mechanisms in economic-demographic interactions may be attained with cross-spectral analysis even though spectral analysis has, to date, cast only doubt on the existence of such long swings. The superiority of crossspectral analysis to simple estimation of power spectra stems from its emphasis upon examining relationships among economic and other variables (Granger, 1966). For exploration of the long-swing hypothesis, spectral analysis suffers from a further disadvantage its results are sensitive to the form of the data analyzed (levels, rates of growth, or deviations from trend), while cross-spectral analysis is not (see section II). Application of both spectral and cross-spectral analysis to economic and demographic data in Sweden, the United Kingdom, and the United States indicates (1) results of spectral analysis are generally similar across the three countries and negative with respect to the long swing hypothesis; and (2) cross-spectral analysis shows quite different long-swing mechanisms at work while giving some positive confirmation to the Easterlin model of long swings for the United States.

Journal Article Size Removes Inequity Get access Werner Hildenbrand, Werner Hildenbrand University of Bonn and CORE Search for other works by this author on: Oxford Academic Google Scholar Alan P. Kirman Alan P. Kirman CORE Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 40, Issue 3, July 1973, Pages 305–319, https://doi.org/10.2307/2296452 Published: 01 July 1973

E. Sieper, P. L. Swan; Monopoly and Competition in the Market for Durable Goods1, The Review of Economic Studies, Volume 40, Issue 3, 1 July 1973, Pages 33