IN GEOMETRIC TERMS

cally illiterate that all interest should be zero—should beabolished—so among the economically literate there is aprevalent idea that the rate of interest could under noimaginable conditions ever be zero or below. Let us thensee, under the assumption of the second approximation,what are the conditions, if any, which will permit of azero or negative rate of interest.

A zero rate of interest means, in our chart, that PQhas an inclination of 45°, that is, a slope of 100 per cent.Our question, therefore, is: must PQ necessarily besteeper than 45°. The slope of PQ depends entirely onthe conformation of the 0 curve and the W curves ofeach person in the loan market. The less steep thesecurves are, the less steep will be the Market lines. Wehave seen that toward the southeast parts of the map theW curves are flatter than 45°, that is, a man with a rela-tively large income this year and a relatively small onenext year would be willing, if he had to, to trade morethan $100 today to get only $100 next year. Probably thisis potentially true of everyone. It is also true that sel-dom if ever are actual income situations (Q’s) locatedin this southeast region.

We turn now to the O line. For the average man in aprogressive country and age, like America today, this willbe steeper than in a retrograde country or in a decadentage—a country or an age in which the natural resourcesare becoming exhausted. But if we go sufficiently to thenorthwest, it will always be flatter than 45°, that is, ifany investment opportunity be exploited far enough itwill yield less future return than its immediate cost. Thisis not only true of land cultivation and extractive indus-tries generally but of all industries. Everywhere, in theend, any law of increasing returns will give place to a law

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