Sec. 5] EARNINGS AND INCOME 237
compare other incomes with it. Consider, for instance, the
possessor of a property yielding $100 a year for 14 years.
He will, if he discounts this income at 5 per cent, value that
property at $1000. He thinks of himself as possessing
$1000 “invested in” that property. From it he gets the
income of $100 a year for 14 years. But he knows that he
might sell this property for $1000 and reinvest in another
property yielding the standard $50 a year forever. Contrasting
with the standard income of $50 a year forever
which he might receive, the income of $100 a year for 14
years which he does receive, we observe that at first his income
is double the earned or standard income, being $100
instead of $50. The excess of $50, however, is compensated
for by a reduction of $50 in the capital-value of his
property, for at the end of the first year the value of his
property will be the discounted value of $100 a year for
thirteen (instead of fourteen) ‘years, which, if interest is
still reckoned at 5 per cent, is $950. And so it is in general
that the owner of $1000 invested at 5 per cent can obtain a
higher income than the standard $50 only at the cost of
trenching on capital to the extent of the excess.
Suppose, on the contrary, that the $1000 is invested at
5 per cent, but in such a form as to yield at first less than
$50, e.g. in a form which yields the above-mentioned income
of $25 a year for 10 years, followed by $167.50 a year
for 10 years. In that case, during the first year the owner
receives only $25 instead of $50, which is the earned or
“standard” income. But the deficiency of $25 in his income
is made up by an augmentation of his capital by that
amount.
The principle is perfectly
familiar to require a rigorous
is no difficulty in framing one.
(1) When a property yields a
and is valued by discounting
specified rate of interest, if the income r
general, and perhaps too
lemonstration, though there
We may therefore state : —
specified foreknown income,
that income according to a
ealized is equal to
