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. Con- 
trasting 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 in- 
come is double the earned or standard income, being $100 
instead of $50. The excess of $50, however, is compen- 
sated 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 in- 
come 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 in- 
come 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