Diminishing Returns is a concept deeply rooted in economic thought. After being introduced by Turgot in 1767 it has become accepted as one of the cornerstones of contemporary economic theory. My interest in this area started in the fall semester of 1971 at U.C. Berkeley where I was enrolled in Professor Ronald W. Shephard's class on the theory of production. Shephard introduced me to his work on the Law of Diminishing Returns, and encouraged me to continue that work. This monograph is a result of my inspiring experience with Professor Shephard; and I am sincerely grateful to him for...

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2. APL 3+5 Dyadic functions sucb as +, -, x, +, *, r (max), 8 L (min), and e (log) operate on scalars and 3 4 2+5 1 7 extend to arrays in a systematic manner. Two 8 5 9 array arguments of a function must bave tbe same 3+5 1 7 :shape (ie, vectors must bave tbe same number of 8 4 10 elements, matrices must bave tbe same number of 3r5 1 7 rows and columns). If one argument of a function 5 3 7 is a scalar, it is applied to eacb element of tbe 1 2 3*2 otber argument. 4 1 9 2e1 2 4 8 16 0 2 3 4 1 M 1 2 3 4 5 6 Mx2 2 4 6 8 10 12 M+M 2 4 6 8 10 12 -5 -3 0 2 Monadia funations such as -, I, x -3 5 o 2...

Those familiar with input-output analysis know well that compilation of input-output tables is a difficult statistical work. The very first input-output tables (e.g. such as those for the United States economy in 1919 and 1929 or for the Federal Republic of Germany in the fifties) were the results of applied economic research. But soon after, official statistical bodies, who understood that input-output tables consistent with national accounts can very much improve the quality of economic statistics, started systematic work in this field. It was also obvious that international exchange of...

This proceedings volume contains papers presented at the conference on econometric decision models held at the University of Hagen (= Fern- Universitat), June 19-20, 1981. Included are also two papers by authors from abroad which could not be presented during the conference: one by E.O. Heady et al. from the USA and one by H. and J. Wallenius from Finland. The authors of the 18 papers/extended abstracts included in this volume are econometricians, economists and operations researchers. The papers were contributed by scientists from the following coun- tries: West Germany (10 papers), The...

The Fifth International Conference on Multiple Criteria Decision Making, not suprisingly, had several objectives. First, it aimed at beinq a forum for exchange and intensive discussion of recent ideas on theory and practice of MCDM, following the now well-established tradition of the previous meetings in the series, organized by H. Thiriez and S. Zionts in Jouy-en-Josas (1975), S. Zionts in Buffalo (1977), G. Fandel and T. Gal in Hagen/Konigswinter (1979) and J. Morse in Newark (1980). Second, closer contacts Nere desired between participants in these meetings and other active groups in the...

In this monograph, noncooperative games are studied. Since in a noncooperative game binding agreements are not possible, the solution of such a game has to be self enforcing, i. e. a Nash equilibrium (NASH 1950,1951J). In general, however, a game may possess many equilibria and so the problem arises which one of these should be chosen as the solution. It was first pointed out explicitly in SELTEN 1965J that I not all Nash equilibria of an extensive form game are qualified to be selected as the solution, since an equilibrium may prescribe irrational behavior at unreached parts of the game...

the economics of exhaustible " assets presents a whole forest of intriguing problems." 1 Harald Hotelling ) The two energy price shocks in 1973/74 and 1979/80 have arosed interest in the new area of resource economics. The affluent societies of Europe, North America and Japan were confronted with the new scarcity paradigm of the "space ship earth" with only a limited supply of natural resources aboard whereas population is growing and the environment can not accomodate the increasing volume of pollutants. The problem of natural resource scarcity gives rise to the question how...

The present monograph is a synthesis of what has been contributed during the last decade to the analysis of market demand in large econ omies where consumers may have non-convex preference relations. Al though research in this field has not yet come to an end there exists a variety of interesting results, established in different frameworks by means of different conceptual and formal tools. a It is my aim to give comprehensive treatment of the existing lit erature including my own contributions. In working out differences and interrelations of the various ap proaches I adopted and modified...

Let eRN be the usual vector-space of real N-uples with the usual inner product denoted by (., . ). In this paper P is a nonempty compact polyhedral set of mN, f is a real-valued function defined on (RN continuously differentiable and fP is the line- ly constrained minimization problem stated as: min (f(x) I x P) For computing stationary points of problemtj) we propose a method which attempts to operate within the linear-simplex method structure. This method then appears as a same type of method as the convex-simplex method of Zangwill 6]. It is however, different and has the advantage of...