Knowledge that Transforms

Following the lead of Markowitz,' the portfolio selection problem has usually taken the following form. An investor's utility for his portfolio is assumed to depend only on the mean and variance of its return over the following period. The investor has in mind means and variances for the returns on all the available securities. The problem is to determine the optimal proportions of these securities in his portfolio. Markowitz, himself, was largely concerned with calculating the dominant set of portfolios (i.e., those with minimum variance for given mean and maximum mean for given variance). Later Tobin 2 studied for two securities, one risky and the other riskless, how the optimal proportion of risky security would change with the mean and variance of its return. He also showed that the mean-variance approach of Markowitz would be consistent with the expected utility principle if the investor had a quadratic utility function or if he considered only a two parameter family of probability distributions. Recently Arrow 3 has reformulated the problem studied by Tobin. He lets the investor decide how to allocate a given amount of wealth between a risky and a riskless security so as to maximize his expected utility. Among other things he shows that the amount invested in the risky security will rise or fall with increasing wealth as minus U/U' (U being the investor's utility function) falls or rises with increasing wealth. In particular, for a quadratic U the amount invested in the risky security will necessarily decrease which is unrealistic. Thus, the mean-variance approach appears unduly restrictive for the portfolio problem, unless restrictions are placed on the form of the probability distribution. The restrictions require that the returns on the securities have a multivariate distribution such that a linear combination of the returns has a two parameter distribution. The multivariate normal is an important example of such a multivariate probability distribution. However, it may not be easy to find others when the returns are not independent. In this paper, the problem of portfolio selection is formulated so that it becomes formally identical to the traditional consumer theory for certain commodities. This permits all of the well-known results of this theory to be applied to the portfolio problem. It also permits the direct use of the traditional models for the price determination of certain commodities for determining the prices of securities. Investors are assumed to follow the expected utility principle and to form their own probability beliefs.

UBLIC education is a sector of government where a usable measure of output quality, the achievement score in basic subjects, has existed in refined form for some time. Given the well-known problems in measuring public service outputs, it is surprising that test scores have not been more widely used by economists in educational research. A recent study of school districts in New York State provides information highly useful for relating educational performance to per-pupil expenditure and size of administrative unit, while at the same time making possible a reasonable attempt to isolate the important influences of pupil intelligence and socio-economic background. This paper represents the results of a careful analysis of the New York State study. The findings have been somewhat surprising. Size of school district is negatively related to performance, if at all, and expenditure is related strongly to performance only in larger school districts. Performance in small school districts, here defined as those in which there are fewer than 2,000 pupils in average daily attendance, was found to be highly unpredictable. More detailed findings are presented below after a brief discussion of the data and the simple model of the educational process used as a framework for analysis.

JN recent years we have witnessed mounting controversy regarding balanced and unbalanced growth as competing policy objectives. Increasingly active theoretical discussions and political concern with this aspect of economic growth warrants a probe into the development experience of different countries. The virtual neglect, so far, of empirical investigation 1 into the nature and process of sectoral growth-rate dispersion can be partly explained by the paucity of relevant data and partly by the fact that precise operational concepts required for the study of the problem have not yet evolved. The purpose of this paper is to present sectoral growth-rate imbalances of different countries as related to the process of national overall development. Our concern will be with the dispersion of sectoral growth rates and their relation to the over-all growth rate on the one hand and to the level of national development on the other. For this purpose cross-sectional and time-series analyses have been used employing such data as are readily available. The various alternative versions of the doctrine of balanced growth (the uniformity concept of balance, the income elasticity concept of balance, etc.) are presented in section III and empirically tested. However, before embarking on this task, it is necessary to postulate the relationship between the over-all growth rate and the sectoral growth rate and specify precisely the nature of the variables entering into the postulated relationship. This is done in section II. Countries are classified according to their pattern of growth in section IV and the broad conclusions as to the relationship between the level of national development and sectoral are listed in section VI. It may be mentioned at the outset that the study is not meant to examine the causes of balanced and unbalanced growth. Sectoral or imbalance is taken as given. The affect of sectoral balance or on a country's over-all rate of growth is what is being investigated. In order to examine, with any thoroughness, the effects of variations in sectoral growth rates on the over-all growthrate, we must remove from consideration the causes of sectoral imbalance. It may also be mentioned that the present study does not take into account the affect of foreign trade on sectoral growth rates. Nurkse holds that

URING the past several years, substantial efforts seeking improvement in the design and economic evaluation of water resource (and other) public investments have been forthcoming.The issue in all of these analyses concerned both the nature of the appropriate investment criterion and the techniques for accurately estimating the parameters and variables which are its constituents.'While all of these contributions acknowledged the inadequacy or absence of market values in evaluating some benefits, generally all accepted the market prices of factors in computing the costs of project construction.2The primary rationale for this position rests on the proposition that, given full employment and factor markets which function as reasonably efficient allocative mechanisms, nominal factor prices reflect real cost and (social) worth.3However, even though most analysts have adopted the full-employment assumption in their own work, all have indicated the desirability of adjusting money costs so as to reflect more adequately true opportunity costs in a severe and widespread depression.4While the rationale for this position has varied among economists, essentially the same information is required to correct market costs, irrespective of viewpoint.For any particular project, knowledge is required of both the direct and indirect industrial and occupational demands imposed on the economy and the correspondence of the pattern of these demands with the pattern of unemployment and idle industrial capacity.Because of the magnitude of the empirical task of tracing these sectoral demands through several layers of transactions, appropriate cost adjustments have not, in practice, been made.Indeed, the impracticality of the empirical task may explain, as much as anything, the failure of the economics profession to choose the problem as a research undertaking.Recently, however, three basic empirical studies have been completed which enable the detailed tracing of public investment demands.In 1964, the Bureau of Labor Statistics released its study of the detailed on-site labor and materials reouirements of water resource