Implications of Electronic Mail and Message Systems for the U.S. Postal Service Page: 105
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Logistic Substitution Process
The logistic substitution process is one math-
ematical formulation that can be used to describe
the encroachment of one technology on the market
of another. In the field of systems ecology a mul-
titude of models have been used for this purpose.
However, the more complex models require data
that are significantly more detailed than were
available for this analysis, and for all their com-
plexity have no more inherent validity than a sim-
ple model such as logistic substitution. The most
important considerations for any model used for
this kind of analysis are that it be based on sup-
portable data and that it make sense.
The logistic substitution curve (fig. B-1) presents
a reasonable macroscopic model of the encroach-
ment of a new technology into the market of an
established, mature technology. When the new
technology becomes available, it penetrates the
market slowly at first due to relatively high cost
and limited consumer acceptance. As time goes on,
cost declines as volume of use builds, leading to
an accelerating growth. Growth remains gradual,
however, since consumer acceptance can be gained
Figure B-1.- Logistic Substitution Growth Process
Initial exponential - at - t
growth rate = a 1 + e tt
. df = cf when t
only with time. As the available market ap-
proaches saturation, the rate of growth declines.
In mathematical terms, the key variable is the
market share of the new technology, expressed as
a fraction f of the total potential market. Ultimate-
ly, the entire potential market will be penetrated,
and f will equal 1 or the maximum penetration po-
tential P, whichever is less. Initially, the market
share fraction f is very small, but grows with time
at a rate proportional to the market share itself.
Thus, in the early stages of growth, the growth of
f per unit of time is expressed as a X f, where a
is a constant for the particular technology and
market being considered. The factor a will be
referred to as the "growth constant" for the par-
ticular substitution process. It is a measure of how
quickly the technology will penetrate the market.
For example, with a = 0.4 (per year), the market
share will rise from 5 to 75 percent in 10 years,
whereas with a = 0.2 such a change in market
share will require 20 years.
The market share at any time can be computed
from the equation in figure B-1 if the growth con-
stant a and the time of 50-percent market pene-
tration t are specified. Alternatively, some other
point on the curve can be specified along with the
growth constant a. OTA chose to specify a par-
ticular logistic substitution curve by specifying
the growth constant, a , and the time (calendar
year) at which 5-percent penetration of the avail-
able market occurs. This 5-percent penetration
time is designated to. The market share f can then
be expressed in terms of a and to as follows:
f = P
1 + e(2.944 - a (t - to))
1 + 19e - a (t - to)
where 0 5 P 5 1
05f 5 1
0 5a < 1
NOTES P = Maximum penetration potential
f = Market share (fraction of total market) for new technology at
a = Growth constant
to = Time when 5% penetration occurs
t" = Time when 50/0 penetration occurs
SOURCE, Off Ice of Technology Assessment and Fred B, Wood, et al , USPS
and the Communications Revolution Impact, Opt/ens and Issues.
George Washington University, Mar. 5, 1977.
The logistic substitution process has been used
once before to model the penetration of mail by
EMS technology.' However, in that 1977 study
the mainstream was considered a single market and
'Fred B. Wood, et al., USPS and the Communications Revolution:
Impacts, Options and Issues, George Washington University, Mar. 5,
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United States. Congress. Office of Technology Assessment. Implications of Electronic Mail and Message Systems for the U.S. Postal Service, report, August 1982; [Washington D.C.]. (digital.library.unt.edu/ark:/67531/metadc39480/m1/108/: accessed April 26, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.