Use the Compounding Process whenever you
want to represent a process that
feeds upon itself. The two inputs to this process are the Stock (or its alternate
measure) and a compounding fraction. The Flow (an inflow to the Stock) is
generated as the product of the two inputs. The compounding fraction can be either
a Stock or a Converter. Its units-of-measure are "units/unit/time," where "units"
is
whatever the Stock is measured in. The compounding fraction tells how many units
are produced per unit of time by each unit of the Stock. Note that "units/unit" cancel.
Thus, the compounding fraction becomes "I/time" or, in words, "fraction per time."
Algebraic Form:
production = Stock * compounding fraction
(urais/dme) = (units) * (units/unit/time)
The behavior pattern generated by the
compounding process, in isolation, is one of
compound growth. Exponential growth is another term for it. Over time, the pattern
looks like Fig 3
.
The exponential pattern occurs because
the base for production (namely, the
Stock) gets larger as the inflow deposits material into it. A larger base for
production means a larger production flow. A larger production flow means a still
larger Stock The cycle continues, with larger production flows yielding ever-larger
stocks, which result in still larger production flows, and so on. Larger values for the
productivity term will accelerate the compounding; smaller values will slow it.
The exponential behavior generated by
the compounding process comes from a
constant (and greater than zero) productivity term. As time passes, the flow adds to
the Stock a constant fraction of what already is in the Stock. This means that the
time it takes for the magnitude of the Stock to double is a constant. For example,
with constant interest rates, it might take 10 years for an investment that grows in a
compounding manner to increase from £1,000 to £2,000 (a £1000 increment). At
the same interest rate, it would take the same amount of time for an investment of
£1 million to grow to £2 million (a £1,000,000 increment)!
The above description and behavior detail
a "pure" compounding process, with a
constant productivity term and a direct linkage between Stock and flow. In reality,
there are few processes that are so pure. As you build your models, you should
watch for relationships which cause the compounding fraction to vary. You also may
want to use Converters to depict indirect linkages between Stock and flow within a
compounding process. As a general rule, however, you should begin with the "pure"
compounding structure whenever you encounter a compounding process. You can
flesh out the details later.
