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## Über dieses Buch

In this book Professor Beckmann, with considerable ingenuity, offers a mathematical analysis of productive organizations in the widest sense. Starting with descriptive features he builds up, step by step, production functions, profiting from the rigor of a set of axioms or assumptions and their logical implications. Among the organizations studied hierarchies play a predominant role and are compared with such forms of cooperation as partnerships and "ladders". A number of well-known basic concepts such as span of control, rank, line vs. staff and others serve as starting points. His analysis leads to such refinements as balanced, regular or degenerated organization patterns and interesting comparisons of the efficiency of various structures. Empirical verification of the axioms or assumptions is not the objective chosen by the author--except a few concrete illustra­ tions--but the book constitutes an excellent basis for such research. Several of the results obtained take simpler forms for very large hierarchies. The renewed interest, shown in political discussions, in the bureaucratization of both large enterprises and government machinery makes Dr. Beckmann's work highly topical. Discussions (by Bahro) of the GDR and by many other authors of Japanese management as compared with American or western European are cases in point. Some additional variables may then have to be added, of a psychological nature: for instance satisfaction from work or irritation evoked by excessive supervision.

## Inhaltsverzeichnis

### I. Rank

Abstract
The economics of organization is a subject of some current interest. There are various approaches of which this is only one. The subject has no well-defined boundaries, and this book explores only a small part of it. It is more restricted than my earlier “Rank in Organizations” by excluding the economics of careers in organizations. Its main topics are the internal structure of organizations and such questions as returns to scale, loss of control, and the economic advantage of organizations. The table of contents gives some indication of the various topics pursued. While not exhaustive this is, I believe, a coherent and self-contained treatment of some basic questions that economic theory might ask of organizations.
Martin J. Beckmann

### II. Design

Abstract
Definition. The relationship “supervision” is not one-to-one. By Postulate 2 of Section 2, each organization member, except the president, has one and only one supervisor. Supervision would give rise to unnecessary chains of command, if a supervisor had only one subordinate. The number of immediate subordinates of a full-time supervisor is called his/her span of control s. From now on this span is assumed to be at least 2,
$$s \mathbin{\lower.3ex\hbox{\buildrel>\over {\smash{\scriptstyle=}\vphantom{_x}}}} 2.$$
Martin J. Beckmann

### III. Costs and Scale

Abstract
A balanced organization with constant span of control is called regular.
Martin J. Beckmann

### IV. Organizational Production Functions

Abstract
We are thus led to reconsider the relationship between labor and management inputs and organizational output in terms of the familiar concept of a production function (Beckmann, 1977, 1982, Sato, 1981).
Martin J. Beckmann