Rising marginal cost and concavity of the production function

Suppose a production function, f, is continuous, quasi-concave and weakly monotone on the non-negative orthant of Euclidean n-space. Let c(·, ·) be the associated cost function. Then it is shown that f is concave if and only if for each w, c(w, ·) is convex.     

THE DETERMINANTS OF THE INTER-INDUSTRY PATTERN OF DIVERSIFICATION BY U.K. MANUFACTURING ENTERPRISES*

Evidence of the diversity of output of larger U.K. manufacturing enterprises’in 1958, 1963 and 1968 is provided in the Reports on the Census of Production. The Censuses show that between 1958 and 1968 diversification was a significant and general trend in manufacturing industries and an important element in the growth of firms during the period. Moreover diversification seems to be part of a longer term trend in U.K. industry and part of the typical development pattern of the large firm. A theory of the firm's diversification decision is proposed and from this theory predictions are made of the structural features both of a firm's primary industry and of outside industries which are likely to encourage diversification from the one industry to the other. The power of the model in explaining the pattern of diversification between SIC manufacturing orders in the period 1963–68 is weak, due in part to the wide variety of factors influencing diversification and to the aggregated form of the data. Nevertheless, the results show the importance of research and development effort in encouraging diversification and the stimulus to diversification given by profitability and risk in firms’primary industries and high rates of output growth in outside industries. While the findings offer no clear conclusions regarding the impact of diversification upon economic performance, the results are consistent with the propositions that (i) diversification encourages technical progress in industry and (ii) diversification increases the efficiency with which resources are allocated between industries.     

Estimation of location of discontinuity in a density

Here we propose a few estimators of θ, in addition to those studied in Goria (1978), the point of discontinuity of the probability density $$f(x,\theta ) = \frac{1}{{2\Gamma (\alpha )}}e^{ - |x - \theta |} |x - \theta |^{\alpha - 1} ,$$ for $$0< \alpha< 1, - \infty< x< \infty , - \infty< \theta< \infty .$$ We establish the consistency and the optimality of the Bayes and the maximum probability estimators. Despite their nice properties, these estimators are not easy to compute in this case and their effective computation depends on the knowledge of the exponent α. Hence, we propose another class of estimators, dependent upon the spacings of the observations, computable without actual knowledge of the value of α as long as it is known that α < α₀ < 1: we show that these estimators converge at the best possible rate. We further demonstrate, using a modified version of the maximum probability estimator's technique, that the tails of the density do not substantially effect their efficiency. Finally a bivariate family of densities, having a ridge dependent on the parameter θ, is considered and it is shown that this family exhibits features similar to the univariate case, and thus, the necessary modifications of the arguments of the univariate case are utilized for the estimation of θ in this bivariate example.     

The maintenance, funding and modification of retiree medical benefits

Retiree medical benefits are an ever-growing concern as costs escalate and the date for implementation of Statement of Financial Accounting Standards No. 106 approaches. These authors summarize case law relevant to employers' right to modify or terminate benefits and discuss methods of funding theses liabilities.     

A comparison of alternative methods of updating input-output coefficients

In recent years there has been a growing number of input-output models of economies ranging in scale from the rural to the national. While offering invaluable insights into the interaction of sectors within an economy, the input-output model suffers from the fact that its coefficient values are altered over time due particularly to technological change. Two of the prominent techniques designed to update these technical coefficients, the RAS and linear programming methods, are compared herein with regard to changes in U.S. national coefficients between 1963 and 1967. Suggestions for improvements to the latter method are outlined.