SECOND APPROXIMATION

one may choose an income exclusively on the basis ofmaximum present value. It will then happen that hisincome, as finally transformed, will be larger than itwould have been if he had chosen some other use whichafforded that same time shape.

All this is true under the assumption used throughoutthis chapter, namely, that after the most valuable optionhas been chosen, you can borrow and lend or buy and sellad libitum and without risk. If this assumption is nottrue, if a person were cut off from a free loan market,the choice among optional income streams might or mightnot fall upon that one having the maximum presentvalue, depending on the other circumstances involved,particularly his preferences as regards time shape.

Of course our assumption is a violent one, made in thissecond approximation, as in the first, in order to simplifythe theory of interest. But already it must be evident thatthe principle involved has important practical applica-tions. To a very considerable extent a modern businessman, with access to loan markets, can choose from amongthe various options open to him on the basis of presentvalue, and trust to loans or other financing to rectifyany inconvenience in time shape.

The lines AB and A'B' in Chart 15 picture alternativeincome streams, of which the descending one, AB, has thelarger present value. The choice will fall on AB, and ifthe individual prefers the time shape of A'B', he will thenlend some of the early receipts from the income streamAB and receive back some of the latter, converting hisincome AB of undesirable shape into the income streamA"B" which has the desired shape. This final incomeA"B" combines the virtues of both the original alterna-tive incomes AB and of A'B'; it possesses the superior

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