IN GEOMETRIC TERMS

not be pictured as traveling along the Opportunity lineat all, even on a non-stop flight to Q x . He may, more prop-erly, be pictured as making a more direct jump, acrosslots, directly from 0/ his income position on the Oppor-tunity line to Qi.

The reader may, starting at 0/, trace the individual bysmall steps of combined $100 investments and loans.Thus the first $100 step would carry him from 0/to B. Successive investments and borrowings of equalamounts would increase the individual’s next year’s in-come while leaving his present year’s income the sameas before. On the chart his income position would movefirst from 0/ to B and then step by step in a verticalline above B. But he will not necessarily confine his bor-rowings to the amount of his investments. The chartrepresents a man whose impatience leads him to borrowfor this year’s consumption the amount represented byCF. His borrowings represented by the horizontal dif-ference between 0/ and P x (that is the distance CE)is what is often called a productive loan, while the hori-zontal difference between 0/ and (that is the distanceCF) is what is called a consumption or convenience orpersonal loan. 4

Properly speaking, however, no part of the loan isitself productive. It is the investment which is properlyto be called productive. To shift along the M line addsnothing to the total present worth of the individual, forit merely substitutes $110 next year for $100 this year,or a series of such sums, and each $110 next year has the

4 With another individual, on the other hand, the most desirable pointmight be very different. He might borrow only part of what he invests,or even not borrow at all but lend as well as invest. All depends on theparticular shape and position of his 0 and W lines.

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