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## Über dieses Buch

In revising the Tinbergen Lectures I have expanded and restructured the material in an attempt to make the book more readable and more interesting. I have also tried to show more clearly its relevance to managerial and organizational practice. Some mathematical derivations have been moved to appendices. Certain sections that may be skipped in a first reading have been starred. Points that should be of interest to management include • the nature and necessity of rank (4. 1, 4. 2, 4. 4) rank assignment by counting up or down (4. 3) defining an organization's task (6. 2) calculating the required size of an organization (6. 3) • allocating supervisors in the short run (6. 7) when uniform spans of control are desirable (6. 8) • how to estimate an organization's implicit span of control (7) determining the minimal ranks in supervision (8. 3) • the advantage of flexible department lines (8. 4) measuring the leanness of an organization (8. 5) the relationship between average wage and unit labor cost (10. 2) job allocation in the short run (10. 4) • calculating the cost of supervision for particular jobs (10. 5) • recognizing economic choices in substituting managers for operatives or vice versa (11) • determining the optimal size of a research team (12) VI • setting targets (13. 1) • budgeting under full information (13. 2) • budgeting under imperfect information (13. 3) • sources of information loss (14.

## Inhaltsverzeichnis

### 1. Introduction

Abstract
“Observation shows us that all associations are instituted for the purpose of attaining some good” (Aristotle, Politics, Book 1, Chapter 1). For purpose of this monograph organizations are defined as associations of persons
• set up for a well-defined purpose
• requiring more than one person’s effort
• utilizing resources
• not using exchange in markets but other methods of coordination.
Martin J. Beckmann

### 2. Supervision

Abstract
Organizations are charged with tasks that exceed the capacity of a single individual. To handle large tasks, one must divide and further subdivide them in such a way that the final units obtained by this sequence of subdivision can be worked on independently of each other. At each stage the subtasks of the next lower stage must be put together. This could be a physical process of assembly from sub-assemblies. More often it is a decision making process, where each stage works out the details of the next higher stage and delegates further details to the next lower stage. A prerequisite is that such “factoring” of a task into parts is technically feasible repeatedly.
Martin J. Beckmann

### 3. Control

Abstract
Supervision is a relationship between a person and his/her immediate boss or between a supervisor and his/her immediate subordinates. Another relationship is that between a boss and all persons placed under the boss’s authority by means of direct or indirect supervision exercised if need be through intermediate supervisors. This relationship is called control. Its formal definition is as follows.
Martin J. Beckmann

### 4. Rank

Abstract
Some organizations deliberately avoid any ordering of members beyond that necessitated by control. Others go so far as to establish a complete strict ordering by precedence, but in such a way that precedence is consistent with and supplementary to control.
Martin J. Beckmann

### 5. Distance

Abstract
The organization chart serves not only as a description of the supervisory and control relationships but also as that of the official channels of communication. Communication is generally understood to be a two-way process so that there is no single direction attached to it. The organization chart is now to be treated as a graph rather than a digraph. In Chapter 5 the variable of interest is distance in organizations.
Martin J. Beckmann

### 6. Number of Positions

Abstract
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 unnecessarily long 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,
$$s\geqq 2$$
.
Martin J. Beckmann

### 7. Estimation

Abstract
The actual span of control can always be read off an organizational chart. Suppose, however, only the numbers of positions of various ranks nr are given. In this case a lower bound on the average span of control may be inferred. If more information is given, e.g., that the organization is balanced, more precise estimates are available.
Martin J. Beckmann

### 8. Assignment

Abstract
Fractional task sizes may be allocated, starting at the president’s level in order to make full use of presidential capacity. Thus when
$$1<\text{Q}\le \text{s}$$
the president is assigned an amount x of operative work such that
$${\text{s(1 - x) = Q - x}}$$
operatives supervised = operatives hired
$$x=\frac{s-Q}{s-1}$$
Now let
$${{\text{s}}^{\text{R-1}}}\text{Q}\le {{\text{s}}^{\text{R}}}$$
One possible assignment is the following: Assign sR−r persons to rank r, r = 1,..., R. Assign an amount x of operative work to first line supervisors of rank 1. The number of operatives in rank zero is then given by
$${{\text{n}}_{\text{0}}}\text{=Q-x=s(}{{\text{s}}^{\text{R-1}}}\text{-x)}$$
from which
$$\text{x=}\frac{{{\text{s}}^{\text{R}}}\text{-Q}}{\text{s-1}}$$
Generalizing (1). In either case operative work is handled at the lowest possible levels. Now turn to the problem of full-time, i.e., integer assignments.
Martin J. Beckmann

### 9. Regular Organization

Abstract
The condition (7.2.3) developed in Chapter 7.
$${{N}_{r+1}}\geqq \{\frac{{{N}_{r}}-1}{s}\}$$
(1)
states how many higher ranking positions are needed to supervise all positions down to rank r. If the organizational design is efficient, it tells the required positions in ranks above r regardless of what the structure is below rank r.
Martin J. Beckmann

### 10. Costs

Abstract
Small organizations can set salaries on an individual basis. Large organizations require a general schema. The principal variables determining salaries are
rank and
length of service.
Martin J. Beckmann

### 11. Substitution of Management and Operative Inputs: Welfare Agency

Abstract
In this section we consider a simple organization whose output may be measured in terms of “cases handled”. The analysis uses elementary queuing theory. In view of the restrictiveness of this queuing model, the results should be considered as illustrative rather than definitive.
Martin J. Beckmann

### 12. Information Costs: Research Teams

Abstract
In journals like “Physical Review Letters” announcements of research results are published to assure priority. It has been observed that the list of authors occasionally takes up half the space of the entire announcement. In particular in physics, the enormous cost of the capital equipment seems to call for a human effort of comparable magnitude in each project. Technical conditions have generated research teams that may contain several dozen high caliber technicians and scientists.
Martin J. Beckmann

### 13. Loss of Information in Simple Organizations

Abstract
Under perfect management the supervisor knows what to expect from every one of his/her subordinates. Under imperfect information only a probability distribution is known for the achievement potential of a “representative operative” under one’s supervision. This distribution will be less precise, have larger variance, the greater the number of subordinates is under one supervisor, i.e., the greater the span of control x0/x1.
Martin J. Beckmann

### 14. Loss of Information and Control in Multi-Level Organizations

Abstract
One reason frequently mentioned why R affects productivity in a negative way is that communication through many layers of an administrative hierarchy generates information that is filtered, outdated and/or distorted. Therefore, decisions by top management are not as effective as those under shorter lines of communication. This is formalized by the notion of control loss (Section 14.2). We examine first one principal cause for the loss of information.
Martin J. Beckmann

### 15. Uses of Production Functions: Simple Organizations

Abstract
The examples of Chapter 11–14 produced linear homogeneous production functions. We consider first such linear homogeneous production functions and extend the results later to other cases.
Martin J. Beckmann

### 16. Uses of Production Functions: Multi-Level Organizations

Abstract
The considerations of the last chapter will now be extended to an organization with multiple levels of supervision.
Martin J. Beckmann

### 17. Organizations versus Individuals

Abstract
In Section 11 and elsewhere we have considered tasks that can only be performed by organizations. But there are other activities in which organizations compete with individuals. In many areas it appears that organizations are in fact on the advance. Increasingly they are taking over functions previously performed mainly by individuals.
Martin J. Beckmann

### 18. Management Motivation: Principal and Agent

Abstract
From the economic perspective, what drives the advance of organizations are the profits to be made by founding a simple organization to take over functions previously performed by individuals. What if the founder and owner turns over the management to a hired manager? What incentives does such a hired manager have to achieve the organization’s goals? Specifically for profit-making organizations, how should the manager be rewarded to motivate him/her towards the achievement of maximum net profits for the owner?
Martin J. Beckmann

### 19. The Economics of Hierarchy

Abstract
We now turn to the question raised in the beginning of this chapter: If organization is advantageous at the simple level R = 1, what, if any, are the economic advantages of hierarchical organizations with more than one level of supervision, R > 1?
Martin J. Beckmann

### 20. Alternatives to Hierarchy: Partnerships

Abstract
Supervision implies rank and hierarchy. Hierarchy implies special privileges for the top level, including the possibility of appropriating any surplus. But is hierarchy inevitable?
Martin J. Beckmann

### Conclusion

Abstract
No simple conclusion emerges from this analysis. A point repeatedly made is that what appear to be technical constraints in an organizational context turn out to be objects of economic choice, at least in the long run. These include such crucial variables as size of task, span of control, loss of control, and the productivity of operatives.
Martin J. Beckmann

### Backmatter

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