The analysis of reswitching of techniques enables us to show that if stationary states are compared, low rates of interest do not necessarily go together with a high consumption per head. If a stationary state with a high rate of interest gives way to one with a low rate of interest, the corresponding switch need not necessarily be from a technique with a low consumption per head to one with a high consumption per head. It may also be from a technique with a high to one with a low consumption per head. What has not been sufficiently emphasized in the literature, however, is that whether the former or the latter is the case may depend not only on which technique replaces which but also on what is the pattern of consumption. M. Bruno, E. Burmeister, and E. Sheshinski assert I that this is not so. They argue that the hyperplanes representing the opportunity sets of consumption for the techniques which are optimal at different rates of interest never intersect, and that whatever the pattern of consumption the respective point on one hyperplane must always be above, or always below, that on the other plane. The purpose of the present note is to show by means of a numerical example that this assertion is not correct. Consider a circulating-capital model with a generalized Leontief technology. There is no joint production in it; the same goods may be used either as inputs or as consumer goods; alternative methods of production are available for each of them; and labor is the only primary factor of production. Let wages be paid at the end of the period, and all other inputs at the beginning of it. The technique actually used is then that which minimizes prices subject to the constraint that at the given wage and the given rate of interest no production processes are run at a loss. This means that if a is the optimal technique, the vector of prices may be written as (A) pa(r) =wao[I(l+r)a]'where w is the wage, r is the rate of interest, a is the matrix of input coefficients for technique a, and ao is the corresponding vector of labor coefficients. The consumption hyperplane is then L=wao [I-a] -lCa=Pa(O)Ca

The economic setting, 71. — The human capital model, 73. — Factors inhibiting human capital development, 79. — Secular trends in the parameters, 80. — Conclusions, 83.

[This paper begins by formulating a finite horizon linear programming model for economic development. The formulation allows for heterogeneous capital goods and for nonnegativity constraints upon investment in each sector. It is then proved that a certain set of conditions are sufficient to ensure that an optimal solution to this T period, finite horizon plan will also coincide with an optimal solution during the first T periods of an infinite horizon plan. Among the restrictive conditions imposed to prove this sufficiency theorem are the following: gradualist consumption paths, no primary factors that cannot themselves be produced within the economy, a Leontief technology, and a characterization of the optimal finite horizon solution as one in which the terminal investment and output levels are positive. An illustrative numerical example is provided.]

[Production correspondences are defined and their properties explored. Properties of the distance function of a production structure are studied and are related to properties of the correspondence. Homotheticity is generalized to allow discontinuities in returns to scale and to take cognizance of several outputs. The factorization of the distance function into the product of two functions, one depending only on output and the other only on input, is demonstrated. The cost function is then shown to give rise to a production structure. A Shephard-type duality theorem is proven which implies, among other things, that the cost function and the distance function are dually related; that is, given one, a minimization proglem yields the other. The duality theorem is then used to deduce necessary and sufficient conditions, in terms of the cost function, for a production correspondence to be homothetic. A few simple applications of the duality theorem are given which relate properties of the cost function to geometric properties of the correspondence.]

Joe S. Bain, Changes in Concentration in Manufacturing Industries in the United States, 1954-1966: Trends and Relationships to the Levels of 1954 Concentration, The Review of Economics and Statistics, Vol. 52, No. 4 (Nov., 1970), pp. 411-416

Recent literature, as it has been developing in this journal and others, suggests that a significant change has taken place in the field of finance. The “new finance” has broader and deeper analytic and empirical content. Its relevant characteristics are: (1) a weakening of the traditional distinction between security analysis and corporation finance; (2) an increased emphasis upon financial management as an integral part of the overall management function; (3) greater emphasis upon the relevance of economic theory in the analysis of financial relations; and (4) more attention to the measurement and testing of hypotheses.

Probabilistic depreciation is a method of determining the proper depreciation charge in each year of an asset's service life, when the service life is a random variable with known distribution. The paper discusses how the service life distribution is modified as more information is obtained about the actual lifetime of the asset. The problem of determining the proper amount to be charged each year to depreciation while at the same time maintaining the proper balance in the accumulated depreciation account is considered. The analysis is done both for a single asset case and for group depreciation. A final section discusses the use of Bayesian analysis for estimating the particular form of the service life distribution while the assets are in service.