The marginal productivity theory explains the amount of rental which will be paid for various capital goods. It does not explain the rate of interest, for the rate of interest is not an amount of product per machine but the relation between a certain value of product and the capital value of the machine. In the chapter on rent we saw that the value of land depends upon the rental instead of the rental's depending upon the value of the land. In the case of capital the situation is the same. The capital value of a machine depends upon the rental or the interest which can be obtained for it; the interest does not depend upon the capital value.

Suppose, for example, that the employer in the preceding paragraph should decide to buy a machine from a capitalist. Let us say that the marginal product of the machine was a hundred dollars per year and that it was expected that the machine would continue to render service to the value of one hundred dollars per year for ten years, after which it would be worn out and would have to be discarded as of no value. The employer, therefore, expects to get from the machine, services to the value of one thousand dollars in the ten years to come. But he would not think of paying one thousand dollars for the machine.

We have already learned from our consideration of the discount theory that the hundred dollars in services that the machine renders next year is not worth a hundred dollars today, and that the hundred dollars in services that the machine renders the year after next is not worth as much to-day as the hundred dollars in services which the machine will render next year, and so on for the ten years. The outside amount the employer is willing to pay for the machine to-day will be the discounted value of the future services. If in the market in which he borrows money the rate of interest is five per cent per annum, he will discount the future services of the machine at the rate of five per cent per annum, and the outside price which he will be willing to pay will be approximately seven hundred seventy-two dollars. Similarly, a machine which would be expected to give an income of one hundred dollars a year, not for ten years but forever, would be purchased not for the sum of the value of the services which the machine would render through all of the years to come, which would be an infinite amount, but for the discounted value of those future services, which would be a finite amount. If the rate of discount is five per cent, the present discounted value of this future series of services of a hundred dollars per year forever would amount at the present time to twenty thousand dollars. From the point of view of the purchaser of the machine the value of the machine, therefore, is determined by discounting the future services of the machine; or, in other words, by capitalizing the yearly income from the machine.

Of course, the value of machines is fixed not by buyers alone but by buyers and sellers. At first thought it might seem that while the buyer gauges the value of the machine by the expected income and the rate of discount, the sellers are able to arrive at the value of the machine without any consideration of the rate of discount. One might think that the sellers, if they are producing under competitive conditions, could tell what the capital value of the machine would be from their knowledge of what it had cost to produce it. This, however, is a one-sided and incomplete view of the matter. The cost of producing a machine depends, among other things, on the number of machines produced. As the number of machines produced is increased the marginal product of the machines is lessened, and the machines will continue to be produced to the point where the capitalized value of their marginal product is just equal to the cost of production. Estimated marginal product, therefore, influences sellers' estimates of capital value by regulating the number of machines.