The Crusoe Economy with Planned, Net Investing.
It is, of course, “income” which people consume or
live on—with occasional, mostly temporary, additions
from “disinvesting” capital previously accumulated.
Theoretical analysis commonly assumes that consump-
tion, at some time, is the sole end of economic activity—
making increased future consumption the end of saving
and investing. (Smith, op. cit., p. 625; but on p. 352
national power is the end of policy, and on p. 397 there
are “two distinct objects,” revenue for the people, and
for support of the public services, in which “defence
is much more important than opulence,” p. 431.) In
social life, consumption is by no means the whole end,
even if we add the security that wealth gives against
events that may disrupt one's income, which might
bulk large with a Crusoe. Social motives such as rivalry
and prestige would be absent, but he would presumably
wish to be purposely active, and would have many
reasons for raising his scale of living—if not explicitly
for the distant future.
Detailed speculation on this point would not be
useful here, and it is simply postulated that he invests
for progress as well as to prevent decline. The usual
assumption makes progress mean an increasing con-
sumable income (also available for further investment).
In a stationary economy, only income is really pro-
duced; reproduction is a part of maintenance. Income
consists of services, rendered by persons or by “prop-
erty” (wealth, capital goods)—only “scarce” things
having economic value. Logically, persons, as yielding
valuable services, are property, but entailed as to own-
ership. (Where there are slaves, they class with work
animals or machines.) In a free society, persons are not
bought and sold, thus are not effectively capitalized
and are reasonably not counted as wealth; but, to
repeat, they are essentially like (other) capital goods
economically. Some personal earnings are in effect
capitalized through contracts for services, and other
obligations; but enforcement of these is limited as a
protection to general freedom.
As just indicated, capital is primarily “capitalized
income,” the present value embodied in a capital-good.
A Crusoe might need the capital concept, if he actively
decided to maintain a constant income, and it is re-
quired for any rational decision on net investment. In
society, there are other facts, especially the production
for sale of income sources, that make it necessary to
know the “present-value” of a future stream or flow
of income. Such production, by net investment, implies
a value result in excess of cost, which must also be
known. As investing requires time, it involves a rate
of growth, which is that of the income to be had by
stopping further investment at any point. This concept
is most familiar as the compound-interest formula and
curve, but applies as well to growth of any population,
and elsewhere. It is pivotal for the understanding of
economic analysis.
Simple compounding by years (or other periods) is
expressed by the formula, A = (1 + r)n, where A is the
amount accumulated by one dollar in n years at the
simple interest rate r, the growth for a year. This r
includes some interest-on-interest as well as on the
principal. To separate the two, compounding should
be continuous, the period being reduced to zero. (The
formula becomes enr, where r and n have the former
meaning, enr replacing (1 + r)n; e is the number
2.7182818..., a mathematical constant, the base of
“natural” logarithms.) A present-value is found by dis-
counting the future income, using the same formula
in reverse (and same rate) to find the investment that
will yield the income stream in question.
Rational investing calls for using that available op-
portunity which affords the highest rate-of-growth. The
discounting is simple where the future income is to
be perpetual (the normal case, as will be shown). Then
the present value is simply ¼ per income unit, the
annual yield divided by the rate as a percentage. (A
dollar per year in perpetuity at 5% annually is worth
$20.) For a time-limited future income, use of the
formula involves some algebra, but that need not be
explained here.
Investment theory is abstract and unrealistic, in that
an investor could never have the knowledge required
for accurate calculation; but (to repeat) that is at least
as true of mechanics, where the procedure is not
questioned. In a social economy, money is used and
is lent at interest, which introduces complications,
calling for further analysis, best taken up under the
next heading. The need to analyze the growth rate of
investment apart from lending and interest is a main
reason for considering the Crusoe economy, where this
is obviously excluded.
