Geoscience Reference
In-Depth Information
5.7
The Importance of Organization of Capital
The theory of the firm as formulated by Oliver Williamson (
1981
) and others, being
based on Ronald Coase's transaction cost assumptions (Coase
1937
), is a useful
starting point for an analysis of the formation of firms. However, it says nothing
about the best spatial and other allocation of material and human capital in the
organization of the firm.
A haphazard arrangement of the carriers of human capital and the machinery and
other material capital will not give the same high level of output as a profit
maximizing organization. However, it could be hard or sometimes impossible to
find such an optimal organization. It can be shown that maximizing the global
profitability between a large number of such discrete interdependent human and
material capital objects can often not be found, even with the aid of powerful
computers.
1
For a firm with only 50 groups of employees with their machinery to be
allocated to 50 different tasks there are in fact more than one trillion possible
patterns of assignment employees to tasks. With quadratically represented inter-
action advantages, there are usually a large number of local profit maxima in this
class of problems and the search for the global maximum is thus very hard.
The quadratic optimal assignment problem of Koopmans and Beckmann can be
approached as in the following integer programming model, proposed by
Andersson and Kallio (
1982
).
Maximize x
0
Sx
þ
Rx
Subject to
X
j
ðÞ
x
ij
1Specialist groups available
ð
5
:
8
Þ
X
i
ðÞ
x
ij
1
Tasks to be fulfilled
;
x
¼
ð
0or1
Þ
S is typically a non-definite matrix giving the positive or negative advantages of
collaborating (possibly at a distance) between each pair of employees and R gives
the revenue effects of each individual if operating a task on her own.
Andersson and Kallio (ibid.) developed a computer algorithm that would effi-
ciently search for a local optimum, when started from randomly selected starting
points. The numerical procedures found a number of local optima, with quite
different organization patterns. For problems with many tasks and groups of
specialists the number of such local optima could be extremely large. In such a
situation there is no guarantee that a global optimum would be found in finite
computer time.
1
If we assume indivisible units of machines and humans and that the productivity of a machine or
a human (x(i)) depends on interaction with (x(j)) and if these interaction net benefits can be
captured by the quadratic form x'Cx, then there is no simple incentive mechanism or computerized
search algorithm that would provide the route to a global maximum for most interaction matrices C
(Koopmans and Beckmann
1959
).
