396 NATURE OF CAPITAL AND INCOME
APPENDIX TO CHAPTER XIV
§1 (ro Cm. XIV, § 3)
When the Interest Rate varies, there are Two Rival Concepts of Standard
Income.
When the rate of interest varies during successive years, the
standard of the comparison of income and capital requires restatement.
We found, when the rate of interest was assumed
constant, that the standard income corresponding to a given
capital was a perpetual and uniform flow, of which flow that
capital was at any time the present value. Tt did not matter
whether standard income Was conceived as income which
was constant and perpetual, or as income which would maintain
its capital-value at a constant level ; for under the condition
of a constant rate of interest, a constant income will
necessarily maintain a constant capital-value. But when we
introduce the possibility of a change in the rate of interest,
these two concepts of standard income are no longer equivalent;
under such conditions only an inconstant income will
maintain a constant capital-value. Thus, if the rate of interest
for the first year is 10%, for the second, 5%, and for the third,
69, etc., the income stream which will maintain the capital
unimpaired will be, in successive years, proportional to the
numbers 10, 5, 6, ete. A person possessed of $100 of capital
can evidently earn with it $10 the first year and still have his
$100 unimpaired, with which, in turn, he can earn $5 the
second year and maintain the principal of $100; and again
$6 in the third year, and so on, receiving each year an income
proportional to the rate of interest. Relatively to this income
stream considered as a standard of reference, the propositions
stated in Chapter XIII will remain true, namely, that if the
real income in any year exceeds the standard for that year, the
capital will be impaired by the excess; and if the income falls
short of the standard in any year, the capital will accumulate
by the amount of the deficiency.
But this concept of standard income is not the only legitimate
one. We may, if we choose, employ the other definition
of standard income, as a perpetual and uniform flow. In this
