1. The buying of any indirect agent is practically the purchasing of a "rent-charge." To account rationally for the market value of anything, its importance must be traced back to "gratification." We have examined and accepted the proposition that if a good is not affording enjoyment at the present moment it is kept because it will yield a rent until it is used. If it is never to afford direct enjoyment, if it is never to mature physically into the class of enjoyable goods, the explanation for its value must be found in the fact that it is capable of yielding a series of rents of enjoyable goods. In the last analysis the value of anything must be found in its power of affording psychic income, a series of psychic rents./ Now when such a durable income is bought outright, what is the basis on which its value is estimated? What other than the rents it will afford? Exactly as did the purchasers of a medieval rent-charge, the buyer of the durable wealth pays a definite sum in return for the right to enjoy a series of future rents. As was the case with rentcharges, however, the amount paid will be less than the full matured value of the rents. A long series, even a perpetual series, may be exchanged for no more than ten, twenty, or twenty-five annual rents. While therefore the selling value of the good is the sum of the values of the rents, it evidently is that sum discounted. Immediately, when we have reached this point in the reasoning, our proposition must suggest itself as self-evidently true in this form: the value of any good is the sum of the entire series of rents it contains, discounted, at some rate, to their present worth. What determines the rate of discount is a question that will call later for a fuller explanation.

2. There are two modes of approach to the problem of interest: one from the side of income (rents); the other, from the side of the bearer (capital). The rate of interest expresses a relation between two values, the value of the income and the value of the sum loaned, whether it consists of money or of other wealth expressed in terms of money. But which of these values is primary in a study of the causes of value? Which is the base from which the other is derived by multiplying at the rate expressing their ratio? The answer to this question cannot be a matter of indifference to the economic theorist. Universally heretofore the study of interest has been approached from the side of capital. A capital sum was said to be invested and to earn a certain interest, that is, per cent., of that sum. The usage of speaking of the investment of capital as a sum given, and of "interest on capital" predisposes the mind to this view.

Capital value is not primary.

But the approach from the side of income has been shown to be in some important cases the historical origin of the rate of interest, and we need but reconsider reasoning that has gone before to see that this is the logical order in all cases. Rent, or income, is a link in the chain of value, connecting gratification or psychic income, consumption goods, rent or usufruct value, and finally capital value. To one keeping in mind the logical cause of value, it becomes inconceivable that capital value could precede income, a view possible only when a fragment of the problem is seen. This being true, the mere mention of a capital sum implies the interest problem, and assumes the interest rate. The capital is of that amount because the anticipated incomes, discounted at some rate, equal that sum. The capital sum is a certain number of years' purchase of the series of rents which can be secured by the use of wealth in various industries. The owner of a number of dollars (or of an amount of other wealth expressed in dollars) has open to him various investments. The value of any wealth is due to the possibility of deriving incomes from it. If, however, the expected income fails to be realized, the capital loses its value, or it is revalued on the basis of the new rents. The investment is then said to be a losing one. Thus, at each stage in the valuation of capital, before it is invested and at every moment thereafter when the valuation is readjusted to the rents realized or expected, rents are logically primary, the source from which the capital sum is derived.

Expected rents are primary, and capital value is the "years' purchase".

The rate of capitalization of rents is not fixed merely in commerce.

3. The capitalization of comparatively safe permanent incomes from real estate contains within itself all the factors for the independent determination of the interest rate, and is not to be explained merely by reference to "the prevailing rate of interest" in other investments. The value of land usually is explained simply as the capitalizing of its rents at "the prevailing rate of interest/' The rate is assumed to be fixed by conditions in manufacturing and commerce, and if five per cent, can be gotten there the capitalist would never buy land unless investment in it were made equally attractive. The cause of the rate thus is supposed to rest outside the transaction itself, the exchange of land for other capital seeking investment. The economic student is safe in assuming always that explanations of this sort are fallacious. The cause of value in any one exchange or any one industry is not thus to be juggled and shifted into another industry. It is true that the values of goods are so wonderfully interrelated by substitution that as the price of fresh beef will affect that of salt mackerel, so the capitalization rate of machinery affects that of land; but the influence is not from one side only, it is mutual. When anything has value, it must have in itself an independent cause of value.

It can not be otherwise in the particular problem of value called capitalization. The first task of scientific study is to state clearly the nature of the problem. In this case it is seen to be the exchange of a present sum of wealth for a series of future rents. Whenever there are income-bearers and buyers and sellers of them, there are the conditions required for the determination of the market rate at which those future incomes shall be discounted. Manufactures and commerce have no peculiar relation to this process. By a flight of scientific imagination we might assume that the stock of indirect agents in the world consisted only of natural food producers, and that this stock and its yield were absolutely unchangeable by man's will or efforts. Each man in such case would have to stand with hands tied, and take the fruits as they matured. Even in such a case there would be capitalization and a rate of discount on future rents. The fruit-tree (that is, the whole future series of fruits) would bear a certain relation to one year's yield; the field would bear a certain relation to its crop. Wherever there are buyers and sellers of more or less durable agents of it matters not what kind or origin, there are present the elements and causes for the fixing of a rate of time discount.

The exchange of any present and future rents results in a rate of time discount.

4. In practical business may be seen innumerable instances of the capitalization of both permanent and limited series of incomes. The simplest case is the capitalization of an unvarying and supposedly perpetual series of rents. Whatever the rate of time discount prevailing, rents infinitely distant become infinitesimally small when discount is compounded. The present rent is worth most, next year's less, and so on in a decreasing series.

Capitalization of a perpetual uniform series of rents;.

Of a probably increasing series of rents;.

But social changes alter rental values, and so far as these changes are foreseen, these anticipated or expected rents are made the basis for present capitalization. Investors and owners alike may foresee that a piece of land used only for agriculture will, within a few years, be taken up for city lots, or will be needed for a factory or as the site of a railroad station. The capitalized value would not in this case be based upon a series of uniform rents each of the amount yielded annually now, but on the progressive series expected. In some cases the physical output of an agent may decline while the price of the product increases. Modern foresters foresee that the selling price of the timber will be greater twenty-five years from now than it is today, and they therefore estimate the rental value of the forest on the basis of the future price, thus justifying expenditure that would be unwise if present prices were to continue.

And of a declining or fluctuating series of rents.

Again the expected series of incomes may be declining, as the royalties (not typical rents) secured from mines. If the income is expected steadily to fall, and to disappear at the end of the twenty-fifth year, the value of the mine would be the capitalized sum of a limited and degressive series of incomes.

Mode of fixing the rate of time discount in practical business.

Every exchange of a durable agent involves an estimate, rough and imperfect it may be, of that agent's future. The practical men, however, who are thus fixing the "capital value" of goods, are usually only dimly conscious of the logical nature of the process. In fact the process goes on in a way much less analytical and conscious, much more empirical, than this analysis would indicate. Most men simply buy as cheap as they can the agents which at the price they believe will add most to their income. The future changes are only roughly, not accurately estimated. The shrewd bargainer is the one who foresees more clearly than his fellows the complex changes to come. Other men blindly follow. The ability and the inability to foresee such changes make men rich and poor. In all this bidding for capital the logical basis of the value is the series of rents. When the agent is bought outright, the very concluding of the bargain fixes a relation between the expected value of the income and the value of the capital invested. In other words, the exchange of durable agents virtually wraps up in them a net income, which it is expected will unfold year by year when rents mature and are secured. At the moment of the investment, the expected rents are expressed as a percentage of the capital sum.