APPENDIX

proper bookkeeping, is the discounted value of the future incomeof $100 a year for 10 years, the total amount of which income is$1000. But, according to the abstinence theory, logicallycarried out, the income which the annuitant receives for thewhole period is, as has been shown, not this $1000, but $772,which is just equal to the value of the property. 4 Pursuing themethod of limits, we find that, for the owner of a perpetualannuity, the same proposition would hold good. According tothe true and ordinary method of reckoning, the total incomefrom such an annuity is infinity, although its present capitalvalue is only $2000. But according to the abstinence theoriststhe income itself is not infinite, but only $2000.

Those who are enamored of the alluring simplicity and neat-ness of the formula of the abstinence theorists, by which thecapital value is not greater than past cost of production, butexactly equal to it, can scarcely be attracted by the exaggeratedsimplicity of the inverse theorem which is also involved, namely,that the capital value of any future expected income is not lessthan that income, but exactly equal to it also.

The fallacy of the abstinence theorists lies in the simple factthat waiting has no independent existence as a “cost.” We cannever locate it in time, nor estimate its amount, without firstknowing some other more real and tangible costs. Waitingmeans nothing unless there is something to be waited for, andthe cost of waiting can only be estimated in proportion to themagnitude of that which is so waited for. What is waited foris some payment or other event constituting income or outgo.But waiting for income or outgo is not itself income or outgo.

4 Lest the non-mathematical reader should be puzzled by this result,which seems to contradict the fact already brought out, that, under thepseudo-reckoning of the abstinence theorists, the net income is zero everyyear, it must be remembered that this zero income is repeated an infinitenumber of times, and that when we deal with infinity we can get reliableresults only by the method of limits. The mathematical reader will findno difficulty in showing, by the method of limits, that there is a “remainderterm” which will, in the supposed accounting, make the total income dis-tributed through all eternity simply equal to the capital value, $2000.

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