THE THEORY OF INTEREST

same present worth as $100 this year. A shift along theOpportunity line, however, does add to a man’s presentworth. Up to the last $100 invested, each $100 yieldsmore than $110 next year and so possesses a greaterpresent worth, reckoned at 10 per cent, than $100.

The sole advantage of any shift along the M line aloneis to gain not more market worth, but to gain in con-venience—to reach a greater total desirability. This istrue in both the first approximation and the second. Everyloan, merely as such, is a shift on the M line alone, andis in itself always a convenience loan. Strictly speaking,no loan, as such, is “productive.”

It is only in so far as the loan makes a difference inthe other shift, that along the O line, that it can claim tobe called a productive loan, and it is quite true, in thecase pictured, that the loan does make such a difference.That is, we call the loan productive because, withoutit, the investment would not be made, or would not beso great—because it would be inconvenient (or even im-possible) to invest so much out of this year’s income.

The essential effect of a so-called productive loan isto enable the individual (under our hypothesis of perfectfluidity and no risk) to disregard entirely what has beencalled the time shape of the income stream P, that is, theproportion of this to next year’s income represented by P.It enables him to push P as far to the left as he wisheswithout threatening him with starvation, or causing himany inconvenience. He need practice no abstinence. Forwhatever P lacks in this year’s income may be made upby loans, that is, by use of the Market line. In fact, P maybe pushed even to the left of the vertical axis, a positionof negative this year’s income, which is physically im-possible except as simultaneously offset by a loan so as

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