THE THEORY OF INTEREST

a return of 10 per cent over the cost. A fourth $100 in-vested will cause the annual crop to be increased by $5giving a return of 5 per cent. A fifth $100 will cause thecrop to increase by $3—a return of 3 per cent. Evidentlyit will pay the farmer to invest in draining and improv-ing his swamp up to the fourth $100, but not to the fifth$100. Rather than invest this fifth $100 and receivethereon an annual income of $3 a year, he would preferto invest $100 in the savings bank and receive 5 per centa year.

In other words, the exact degree of intensity with whichhe will improve and cultivate his land is determined bythe current rate of interest. Should the rate of interestin the market fall from the 5 per cent just assumed to2 per cent, it would then pay him to invest the fifth $100.For, evidently, if need be, he could borrow $100 at 2 percent and receive from his land a return of 3 per cent. AsRae has so clearly pointed out, in communities wherethe rate of interest is low, swamps will be more thoroughlyimproved, roads better made, dwellings more durablybuilt, and all instruments developed to a higher degree ofefficiency so as to yield a lower marginal return overcost than in a community where the rate of interest ishigh.

§9. The General Case

In general, the rate of return over cost has to be de-rived by more complicated methods. As already indicated,the rate of return over cost is always that rate which, em-ployed in computing the present worth of all the costs andthe present worth of all the returns, will make these twoequal. Or, as a mathematician would prefer to put it,the rate which, employed in computing the present worth

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