In the real world entrepreneurs do not buy the services of land as they do the services of workers. They either rent or buy the land as a carrier of services. It is the usefulness of the services which determines the rent as well as the purchase price of land. The rent for a certain period, say one year, is equal to the value of all the services the land renders during the year. The latter, too, are called rent. But what are the principles which determine the price of land to be bought? One would expect the price of land to be equivalent to the sum of the prices of all the services it renders. But the following has to be considered.
In so far as the services of land are perpetual, the price of land would obviously have to be infinitely high, were it not for the fact that the purchase price is paid in money and that money if lent as credit also yields a perpetual service, namely the interest the lender goes on receiving. Thus the price of land must stabilize at the point where the interest on the purchase price is equal to the price of the service the land renders during a certain period. In other words the price of land is, in principle, the price of its service capitalized at the long-term interest rate for credits. If the service is worth $5 a year, and the interest rate is 3 per cent, then the price of the land is $166, for 5/x = 3/100, therefore x=500/3=166.
If the services of the land—of a coal field for instance—are not perpetual but last only, say, 10 years, the calculation is somewhat more complicated. In this case it is not possible to compare the rent with the interest payments because only the latter are perpetual. One has to compare the present utility of the money on the one hand and that of the annual services of the land on the other. The money is, of course, worth its face value. But if a unit of land annually yields $5 for 10 years, it is worth not 5 x 10, or $50, but less. Since present money yields interest as of today, whereas the annuities yield interest only as of their payment, the annuities can only be valued at a so-called discount. At an interest rate of 3 per cent, land yielding $5 during 10 years and nothing thereafter would be worth about $43.
It may be asked: why is the price of land equal to the capitalization of the services it yields, whereas machines sell at production cost? The answer is that machines can never cost more than their production costs, for their number can be increased at will by payment of these costs. Nor can the productivity advantages of a machine ever be greater than the interest on the cost price calculated for the lifetime of the machine. If the advantages were greater than this amount of interest ever new machines would be constructed. Land, on the other hand, is produced by nature once and for all. It is scarce and cannot be increased by work. Its services are fixed and are not influenced either by production costs or rates of interest. But since in the long run money lent as credit and money invested in land must offer the same yield, the price of land must stabilize at a level where the interest on the purchase price equals the price of the services. Changes in the interest rate must, therefore, entail inverse changes in the price of land. A falling interest rate raises land prices and vice versa.