398 NATURE OF CAPITAL AND INCOME

that the fall or other change in the rate of interest can never
be foreseen with precision, and thus a perfectly uniform flow of
income secured, whereas it is always possible, in the case of
safe investments, to calculate what is necessary to maintain
the value of the capital at a uniform level.

§ 2 (ro Cm. XIV, §12)
Effect of Foreknown Tax on Increase of Capital

Let us suppose that the three brothers invest in their respective
 annuities without réalizing that a tax is to be imposed.
The first brother has bought with his $10,000 a perpetual annuity
 of $500 a year; the second, a perpetual annuity of $1000
deferred 15 years; and the third, an annuity of $2000 for six
years only. After these investments have been made, let us
suppose that the tax of 109 on income is announced. If “income”
 is interpreted properly, i.e. as simply the annuities,
the value of each of the three properties will immediately
shrink by $1000, so that any of the three brothers could sell
subject to the tax, for $9000. But if the “income
“earnings,” i.e. on income and
ot only

his annuity,
tax” is interpreted as a tax on
increase of capital, the announcement of such a tax will n
reduce the values of the three properties very unequally, as has
been shown, but will have the further effect of altering the very
annual increase in the value of the capital which is subject to
taxation. To show the effect of this « repercussion,” let ¢ represent
 the value of the capital of the second brother (who saves)
at the end of any year during which no (true) income is received.
Thus ¢ is $18,000 at the end of the fifteenth year when the annuity
 of $1000 a year is purchased ; for the capitalization of
the perpetuity of $1000 which begins at that time is $20,000,
from which $2000 is deducted as the capitalized tax. Let ©
represent the rate of interest (as 5%) and t the tax rate (as
10%). We wish first to find «, the capital-value one year
earlier than ¢. It is clear that is the discounted value
of ¢ (ie on ) less the discounted value of the tax, which

he end of the year. The tax
i.e. on

 

we will suppose is due at t
is laid on the increase of capital-value in the year,