DISCUSSION OF SECOND APPROXIMATION

This case is illustrated in Chart 21. One option is toconsume the hard-tack at an even rate OA through thetime OB. The total income will then be represented bythe area OACB. Another option is to spread it over OB',double the above-mentioned time, and consume it at therate of OA', half the rate first mentioned, so that thesame total income will be represented by the areaOA'C'B'. The choice of the second use rather than the

a -c

01 - B-- *

CHART 21

Zero Rate of Return, Total Income Fixed, Case 1.

first is at the cost of that part of the earlier income rep-resented by the rectangle AD, and gives a returnexactly equal in amount represented by the rectangleDB'. If the hard-tack is not consumed at a uniform rate,the alternative income streams will not be representedby rectangles, but by the irregular and equal areas OADBand OA'DB', shown in Chart 22. The substitution of thealternative OA'DB' for OADB increases immediate in-come by ADA' and decreases subsequent income by theexactly equal amount BDB'.

The conclusion, that the rate of interest, under such

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