Geoscience Reference
In-Depth Information
scale of production, C(x). A common assumption is to disaggregate total production
cost into fixed cost (F), and variable cost (V(x)). Fixed cost is the cost of all material
and non-material capital of the production unit and is thus independent of the scale
of operation as soon as the production unit has been established. For simplicity we
assume that the firm is the production unit.
The duration (
˄
) of the production process increases the amount of capital
needed and thus of the fixed cost of production, i.e. F(
˄
˄
>
0. This is
especially pronounced in knowledge intensive production, needing a long period of
research and development before actual production can occur. Typical examples
are firms of the airplane producing industry, the movie industry, and the large
pharmaceutical firms. Such firms regularly invest more than a fifth of the sales value
in creation and innovation of new products and associated production equipment.
The variable cost is normally monotonously increasing with the scale of opera-
tion up to the capacity limit of the capital of the firm. In the sequel we assume that
the optimal scale of operation is smaller than or equal to that upper limit. The
simplest variable cost function is the linear case V(x)
) with F'(
)
¼
vx. The total production
cost function would be P
¼
F + vx; and the average production cost function would
thus be C
duration of the production process.
Transport and transactions or logistics costs depend on the deliveries and other
contacts between firm and customers. With a scattered distribution of customers in
space around the firm, total transport and transaction cost would increase progres-
sively with the increase in the scale of production and sales. Thus average cost of
logistics (L), i.e. transactions and transport, would be increasing with the scale of
operations. Assume L
¼
F(
˄
)/x + v, where
˄ ¼
kx. The term k can be decomposed into cost per unit of
shipments, a, and the frequency of contacts, which is inversely depending on the
durability, T, of the product. The average logistics cost is thus L
¼
¼
(a/T) x. Thus, the
larger the durability, the lower is the average logistics cost.
The total average cost A equals the sum of average production cost C and
average logistics cost L:
A
¼
F
ðÞ=
x
þ
c
þ
a
=
T
ð
Þ
x
;
ð
5
:
9
Þ
Minimization of A implies that the optimal scale of production of the represen-
tative firm is:
r
F
ðÞ
T
a
x op
ðÞ¼
ð
5
:
10
Þ
;
The optimal scale of production of the firm is thus increasing with increasing
duration
of the production process and also with increasing
durability
of the
product.
The optimal number of firms is determined by the total scale of the market. The
maximal total market scale is today the world market, to the extent that it is
integrated by information and transport networks. The existence of an integrated
