SECOND APPROXIMATION

borrowing and lending) it will better serve the purposeof our analysis not to do so.

There are two principal reasons for this. First, borrow-ing and lending, the narrower method of modifying in-come streams, cannot be applied to society as a whole,since there is no one outside to trade with; and yet societydoes have opportunities radically to change the characterof its income stream by changing the employment of itscapital. Secondly, when borrowing and lending, or ordi-nary buying and selling, are employed to modify an in-come stream, the present value of the original incomestream and the present value of the modified incomestream are the same, for each $100 added to this year’sincome has the same present value as the $100 with in-terest, returned out of next year’s income, so that everyloan adds and subtracts equal present values. But whenan income stream is modified by a change in the use ofcapital yielding it, the present value of the alternative, asin the case of the South, may not, and, in general, will not,be the same as the present value of the original. This fact,that the present value is not changed by buying or selling(or, in particular, by borrowing or lending) but is changedby otherwise altering the use of one’s capital, marks animportant distinction between the two methods of alter-ing one’s income stream. The distinction and its impor-tance are most clearly seen by a mathematical analysissuch as that shown in Chapter XI and XIII.

§2. Optional Income Streams

The choice among all available optional income streamswill fall on that one which has the maximum desirabilityor wantability.

We have seen in the preceding chapter that income

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