CHAPTER IV
THE CAPITALIZATION THEORY AND THE VALUE OF MONEY
Money is capital. A dollar is a capital-good. Money is, moreover, a durable form of capital, which gives forth its services bit by bit, and indeed, in a community where the state bears the burden of wear and tear, never ceases to give forth those services. In any case, from the standpoint of a given individual, so long as there is a limit of tolerance prescribed for legal tender, it is a matter of accident if he ever incurs a loss from the wastage of the capital instrument, money, through wear and tear. Moreover, the fact that money is "fungible," and that its use is to be found in a process which commonly returns to the owner, not the same coin, but a different coin, we may, in general, abstract from the wear and tear of the dollar, and look upon the dollar as a capital instrument which promises its owner, if he chooses to use it as capital, a perpetual annuity. The nature of this money service will be more fully described later. For the present it is sufficient to say that exchange is a productive process, that exchange creates values, in as true a sense as manufacturing does, and that money facilitates exchange in as true a sense as coal facilitates manufacturing. There is, at any given time, a demand-curve for this money service, manifesting itself in the money market, a demand for the short time use of money as a tool of exchange, and the "prices" which come out of the interaction of demand and supply in the money market are the short time "money rates" including the "call rates." These are properly to be conceived, not as pure interest on abstract capital, but as rents[58] which are to be attributed to money as a concrete tool.
Now, in general, when such rents appear, they may be capitalized. And the price of the instrument of production that bears these rents, will be the sum of the rents, discounted at the prevailing rate of interest, with considerations of risk, etc., allowed for. The reasoning of the capitalization theory is really quite simple. Take, for example, a piece of urban site land, which is expected to bring a perpetual annuity of one hundred dollars. The whole economic significance of the land is contained in its services, present and prospective. The possession of land under certain circumstances brings other services, as social prestige, than the services which can be alienated to a lessee. But in this case I am abstracting from considerations of that sort, and also from the factor of risk. The whole value of the piece of land under consideration comes from the value of the one hundred dollars a year. But these annual incomes are not all equally valuable, even though all expressed as one hundred dollars. The first one hundred dollars is due one year hence, the tenth ten years hence, the thousandth, a thousand years hence. The principle of perspective comes in—I abstain from any detailed discussion of the theory of interest, simply stating that in a general way I agree with the contention that time constitutes the essence of the phenomenon, or rather, the tendency to discount the future. The capital price of the land is the sum of an infinite convergent series of the "present worths" of the incomes. The formula is as follows: capital price of land = $100/1.05 + $100/(1.05)2 + $100/(1.05)3 ... + $100/(1.05)n when the rate of interest is 5%. The limit of this series, assuming the series to be infinite, is $2000, and a simple formula for calculating it under the assumptions, is to divide $100, the annual income, by .05, the rate of interest. Given the annual income, given the prevailing rate of interest, the capital price is determined. The relation may be illustrated, roughly, by the figure of a candle, a disk, and the shadow of the disk on the wall. The disk represents the annual income, the shadow on the wall the capital value, and the distance between the flame and the disk the rate of interest. Increase the distance between the flame and the disk, the rate of interest, and the shadow becomes smaller; shorten the distance, and the shadow is increased. Similarly, enlarge the disk, and the shadow is enlarged. The capital value varies directly with the annual income, and inversely with the rate of discount. Now my purpose here does not involve a detailed examination of the validity or limitations of the capitalization theory. For the present, the only question is, has this theory any application at all to the problem of the value of money? It offers itself as a general theory of the values of durable bearers of income. Money is a durable bearer of income.
The capitalization theory, however, is of no use for the purpose in hand. Money does not obey the general law in the relation which the magnitude of the income bears to the rate of interest. In general, the income and the rate of discount are independent variables. Their influence, operating in opposite directions, fixes the capital value, increasing income increasing the capital value, increasing discount rate reducing it. In the case of money, however, the two factors are not independent. The short time money rate is not, to be sure, identical with the long time rate of interest, which is the rate of discount for the purpose in hand. But the two tend to vary together in the long run average in fact, and they are related in the expectation of those who are concerned in the capitalization process.
In our chapter on the "Functions of Money," in Part III, it will be shown that normally there tends to be a difference between the money rates and the long time interest rates, the long time rates tending to be higher than the rates on short loans, the rate on very short loans being lower than the rate on somewhat longer short time loans, and the call loan rate being lowest of all. The explanation of this must be deferred till we have analyzed the functions of money. But the important thing, for present purposes, is that the money rates, though lower than the "pure rate" of interest, tend to vary, in long time averages, with that "pure rate,"[59] and that, consequently, the income from renting money, and the discount rate to be applied in capitalizing that income, are not independent magnitudes, but tend to vary together. They thus tend to neutralize one another. If money rates go up, and if they are expected to stay up long enough to justify (on the ordinary capitalization theory) a rise in the capital value of money, we have a counteracting influence in the long time interest rate, which also rises, and tends to pull down the capital value of money. To recur to our illustration of the candle and the disk, as the disk increases in diameter, the distance between the candle and the disk grows greater, and so the shadow tends to remain the same.
There is a further difficulty, to which attention will be called more fully in later chapters, particularly the chapter on "Dodo Bones," and the chapter on the "Functions of Money." In other cases, in general, the capital value is, as the capitalization theory requires it to be, a true shadow, a passive function of the income and the discount, of the disk and the distance between the candle and the disk. In the case of money, however, the income is causally dependent, in part, upon the capital value. Money can function as money only by virtue of having value. The shadow becomes substance in the case of money. It is the value of money which makes possible the money work. The capitalization theory, thus, if applicable at all, must be radically modified before being applied. We shall subsequently, in the chapters above referred to, take account of this fundamental complication. For the present, we can state it merely as a problem: how can we construe the interaction of the income value of money and the capital value of money in such a way as to avoid a circular theory?
But further, the capitalization theory, as heretofore formulated, like the doctrines of supply and demand and cost of production, assumes money, and a fixed absolute value of money. This assumption must be made if we are to be able to predict, on the basis of the capitalization theory, that a given annual income, at a given rate of discount, will give a specified capital value. This may be shown by the following considerations: If men anticipate that the value of the income, which is a fixed sum of dollars, is to grow less in the future, then the present worth of the bearer of that income will shrink to an extent greater than the "pure rate" of interest would call for. The principle of "appreciation and interest" comes in. The nominal interest, in times of falling value of money, tends to exceed the pure rate by an amount which compensates for the loss in value of future income as the dollar falls in value. We have here, however, a principle different from the principle of time discount. It is not the influence of time, which makes a given value appear smaller as it is further removed in time, but it is an anticipated lessening in the value of the income itself, that counts. In terms of our candle and disk illustration, it is a factor affecting the size of the disk, rather than a factor affecting the distance between the disk and the candle. For the purposes of calculation, the two elements in the nominal rate of interest may be lumped together, and the nominal rate, rather than the pure rate, may be taken as the rate of discount for capitalization purposes. But for theoretical purposes, the two must be kept distinct. The capitalization theory rests on the assumption of a fixed value of the money unit.
That the fixed value of the money unit assumed is an absolute value, and not a mere "reciprocal of the price level," may be proved by some further considerations regarding relations among these same factors. Assume a fall in the rate of interest. Then, on the capitalization theory, prices of lands, stocks and bonds, houses, horses, and all items of wealth which give forth their services through an appreciable period of time, will rise, and with them the average of prices, or the general price level, will rise.[60] If one hold the relative conception of value, according to which the value of money necessarily falls when prices rise, because the two are merely obverse phases of the same thing, then this rise in the price level is, ipso facto, a fall in the value of money. But we have seen that a fall in the value of money means, on the "principle of appreciation and interest," a rise in the interest rate! Hence, we would have proved that a fall in the interest rate causes a rise in the interest rate—which is absurd. If, however, we recognize that prices can rise without a fall in the value of money, if, i. e., we use the absolute conception of value, this difficulty disappears. The capitalization theory and the theory of appreciation and interest can be reconciled only on the basis of the absolute conception of value.
The capitalization theory, then, in its present formulation, assumes money, and a fixed absolute value of money. It is, therefore, inapplicable to the problem of the value of money itself.