Chapter 6—Production: The Rate of Interest and Its Determination

 Previous Section * Next Section
 Table of Contents

6

PRODUCTION:
THE RATE OF INTEREST AND ITS DETERMINATION

1. Many Stages: The Pure Rate of Interest[1]

Up to this point we have been treating the structure of production as amalgamated into one stage. One or several firms have all been vertically integrating all the stages of production of a product (with all factors specific), until finally the product is sold to the consumer. This is certainly an unrealistic assumption. We shall now consider the production situation in the real world, where (a) factors are nonspecific as well as specific, and (b) production is divided into numerous stages, as the factors continue to work and advance from the higher to the lower stages of the production process.[2] Instead of assuming that one firm—one set of capitalists—purchases factors and retains ownership of the product up through the sale to consumers, let us suppose that there are different firms and different sets of capitalists at definite intervals, and at each interval the product, in the stage it has reached up to that point, is sold for money to another capitalist or group of capitalists. It is not necessary to make any restrictive assumptions about how many separate stages occur or what the time intervals between individual stages might be. For purposes of convenience, let us return to our example and the diagram in Figure 40. We shall assume that exchanges of product and service take place at each line marked on the diagram. We shall further assume, for convenience only, that each stage takes the same length of time.

     Now, instead of collecting interest income for services in one lump sum at the final stage, the capitalist or capitalists acquire interest income at each stage.[3] If each stage takes one year, then the entire production process for the good takes six years. When the stages are all lumped together, or vertically integrated, then one capitalist (or set of capitalists) advances the owners of original factors their money six years ahead of time and then waits for this period to acquire his revenue. (Strictly, since the work and pay of labor and land would be continual as the product ad­vanced to its final form, the earliest hired labor and land would be paid, say, in year one, and the latest toward the end of year six.) With separate stages, however, each capitalist advances the money for only one year.

     Let us see the picture on a diagram (Figure 41). We must modify the previous diagram somewhat. A lower bar of 100 ounces is added, and the interest income that accrues to the capitalist at this lowest stage is indicated by an arrow going off to the left side. The upward arrow then represents the amount going to owners of original factors, land and labor, at this stage, and the shaded area the amount going to owners of capital-goods factors of a higher rank, i.e., intermediate products. The diagram in Figure 40 did not depict interest income, but simply presented all income as going to the owners of original factors; the time element had not yet been introduced into our discussion.

     The structure of production and payment depicted in this basic diagram is as follows: Consumers spend 100 ounces on the good in question. Of the 100 ounces, five ounces go as interest in­come to the sellers of the consumers’ good, and 95 are paid out to the owners of factors. In our example, 15 ounces go for the use of land and labor (original) factors, and 80 go into the purchase of factor services of capital goods of a higher order. At the second stage, capitalists receive 80 ounces in revenue from the sale of their product.

     Of the 80 ounces, 16 go into the purchase of land and labor factors, and four accrue as interest income to the second-level capi­talists. The remaining 60 are used for the purchase of higher­-order capital goods. The same process is repeated until, on the highest stage, the highest-order capitalists receive 20 ounces of revenue, retain one for themselves, and pay out 19 to land and labor factors. The sum total of income to land and labor factors is 83 ounces; total interest income is 17 ounces.

     In the foregoing section on interest we showed that money is always nonspecific, and the result is that in the ERE the inter­est return on monetary investment (the pure rate of interest) is the same everywhere in the economy, regardless of the type of product or the specific conditions of its production. Here we see an amplification of this principle. Not only must the interest rate be uniform for each good; it must be uniform for every stage of every good. In our diagram, the interest-rate return received by product-owners, i.e., by capitalists, is equal at each stage. At the lowest stage, producers have invested 95 ounces in factors (both capital goods and original factors) and receive 100 ounces from consumers—a net income of five ounces. This represents a return on the investment of ⁵/95, or approximately 5.2 percent. In the ERE, which we are considering, there are no profits or losses due to uncertainty, so that this return represents the rate of pure inter­est.[4] The capitalist at the next higher stage invests 60 plus 16 or 76 ounces in factors and receives a net return of four ounces, again approximately 5.2 percent. And so on for each stage of investment, where, except for the vagaries of the arithmetic in our example, the interest rate is uniform for each stage. At the highest stage, the capitalist has invested 19 ounces in land and labor, and re­ceives a net return of one, again about 5.2 percent.

     The interest rate must be equal for each stage of the produc­tion process. For suppose that the interest rate were higher in the higher stages than in the lower stages. Then capitalists would abandon producing in the lower stage, and shift to the higher stage, where the interest return is greater. What is the effect of such a shift? We can answer by stressing the implications of dif­ferences in the interest rate. A higher interest rate in stage A than in stage B means that the price spread between the sum of fac­tors entering into stage A and the selling price of its product, is greater, in percentage terms, than the price spread in stage B. Thus, if we compare stage four and stage one in the diagram in Figure 41, we find a price spread of 43 to 45 in the former case, and 95 to 100 in the latter, for a net interest return of approximately 5.2 percent in each. Let us suppose, however, that the sum of the factor prices for stage four is 35 instead of 43, while the sum of factor prices in stage one is 98. (The sum of factor prices here excludes interest income, of course.) Capitalists investing in stage four would earn a net return of 8, or 23  percent, while investors in stage one earned about 2 percent. Capitalists would begin to stop investing in stage one and shift to stage four. As a consequence of this shifting, the aggregate demand in stage one for its factors diminishes, and the prices of the factors used in stage one therefore decline. In the meanwhile, greater investment in stage four raises factor prices there, so that the cumulative price rises from 35. Products of stage four increase, and the increased supply lowers the selling price, which falls from 43. These arbitrage actions continue until the percentage spread in each of the two stages is equal.

     It is important to realize that the interest rate is equal to the rate of price spread in the various stages. Too many writers con­sider the rate of interest as only the price of loans on the loan market. In reality, as we shall see further below, the rate of inter­est pervades all time markets, and the productive loan market is a strictly subsidiary time market of only derivative importance.[5]

     Not only will the rate of interest be equal in each stage of any given product, but the same rate of interest will prevail in all stages of all products in the ERE. In the real world of uncertainty, the tendency of entrepreneurial actions is always in the direction of establishing a uniform rate of interest throughout all time markets in the economy. The reason for the uniformity is clear. If stage three of good X earns 8 percent and stage one of good Y earns 2 percent, capitalists will tend to cease investing in the latter and shift to greater investments in the former. The price spreads change ac­cordingly, in response to the changing demands and supplies, and the interest rates become uniform.

     We may now remove our restrictive assumption about the equality of duration of the various stages. Any stage of any prod­uct may be as long or as short as the techniques of production, and the organizational structure of industry require. Thus, a technique of production might require a year’s harvest for any particular stage. On the other hand, a firm might “vertically inte­grate” two stages and advance the money to owners of factors for the period covering both stages before selling the product for money. The net return on the investment in any stage will adjust itself in accordance with the length of the stage. Thus, suppose that the uniform interest rate in the economy is 5 percent. This is 5 percent for a certain unit period of time, say a year. A production process or investment covering a period of two years will, in equilibrium, then earn 10 percent, the equivalent of 5 percent per year. The same will ob­tain for a stage of production of any length of time. Thus, irregu­larity or integration of stages does not hamper the equilibrating process in the slightest.

     It is already clear that the old classical trinity of “land, labor, and capital” earning “wages, rents, and interest” must be dras­tically modified. It is not true that capital is an independent productive factor or that it earns interest for its owner, in the same way that land and labor earn income for their owners. As we have seen above and will discuss further below, capital is not an independently productive factor. Capital goods are vital and of crucial importance in production, but their production is, in the long run, imputable to land, labor, and time factors. Further­more, land and labor are not homogeneous factors within them­selves, but simply categories of types of uniquely varying factors. Each land and each labor factor, then, has its own physical fea­tures, its own power to serve in production; each, therefore, re­ceives its own income from production, as will be detailed below. Capital goods too have infinite variety; but, in the ERE, they earn no incomes. What does earn an income is the conversion of future goods into present goods; because of the universal fact of time preference, future satisfactions are always at a discount compared to present satisfactions. The owning and holding of capital goods from date one, when factor services are purchased, until the prod­uct is sold at date two is what capitalist investors accomplish. This is equivalent to the purchase of future goods (the factor services producing capital goods) with money, followed by the sale at a later date of the present goods for money. The latter occurs when consumers’ goods are being sold, for consumers’ goods are present goods. When intermediate, lower-order capital goods are sold for money, then it is not present goods, but less distantly future goods, that are sold. In other words, capital goods have been advanced from an earlier, more distantly future stage toward the consump­tion stage, to a later or less distantly future stage. The time for this transformation will be covered by a rate of time preference. Thus, if the market time preference rate, i.e., interest rate, is 5 percent per year, then a present good worth 100 ounces on the market will be worth about 95 ounces for a claim on it one year from now. The present value for a claim on 100 ounces one year from now will be 95 ounces. On this basis, the estimated worth of the good could be worked out for various points in time; thus, the claim for one-half year in the future will be worth roughly 97.5 ounces. The result will be a uniformity of rates over a period of time.

     Thus, capitalists advance present goods to owners of factors in return for future goods; then, later, they sell the goods which have matured to become present or less distantly future goods in ex­change for present goods (money). They have advanced present goods to owners of factors and, in return, wait while these factors, which are future goods, are transformed into goods that are more nearly present than before. The capitalists’ function is thus a time function, and their income is precisely an income represent­ing the agio of present as compared to future goods. This interest income, then, is not derived from the concrete, heterogeneous capital goods, but from the generalized investment of time.[6] It comes from a willingness to sacrifice present goods for the pur­chase of future goods (the factor services). As a result of the pur­chases, the owners of factors obtain their money in the present for a product that matures only in the future.

     Thus, capitalists restrict their present consumption and use these savings of money to supply money (present goods) to factor owners who are producing only future goods. This is the service—an advance of time—that the capitalists supply to the owners of factors, and for which the latter voluntarily pay in the form of the interest rate.

2. The Determination of the Pure Rate of Interest: The Time Market[7]

      It is clear that the rate of interest plays a crucial role in the system of production in the complex, monetary economy. How is the rate of interest determined? The pure rate of interest, with which we are now concerned, we have seen will tend to be equal throughout all stages of all production processes in the economy and thus will be uniform in the ERE.

     The level of the pure rate of interest is determined by the mar­ket for the exchange of present goods against future goods, a mar­ket which we shall see permeates many parts of the economic­ system. The establishment of money as a general medium of ex­change has greatly simplified the present-future market as com­pared to the laborious conditions under barter, where there were separate present-future markets for every commodity. In the monetary economy, the present-future market, or what we may call the “time market,” is expressed completely in terms of money. Money is clearly the present good par excellence. For, aside from the consumption value of the monetary metal itself, the money commodity is the one completely marketable good in the entire society. It is the open sesame to exchange for con­sumption goods at any time that its owner desires. It is there­fore a present good. Since consumers’ goods, once sold, do not ordinarily re-enter the exchange nexus, money is the dominant present good in the market. Furthermore, since money is the medium for all exchanges, it is also the medium for exchanges on the time market.

     What are the future goods that exchange for money? Future goods are goods that are now expected to become present goods at some future date. They therefore have a present value. Be­cause of the universal fact of time preference, a particular good is worth more at present than is the present prospect of its be­coming available as a present good at some time in the future. In other words, a good at present is worth more now than its present value as a future good. Because money is the general medium of exchange, for the time market as well as for other markets, money is the present good, and the future goods are present expectations of the future acquisition of money. It follows from the law of time preference that present money is worth more than present expectations of the same amount of future money. In other words, future money (as we may call present expectations of money in the future) will always exchange at a discount compared to pres­ent money.

     This discount on future goods as compared with present goods (or, conversely, the premium commanded by present goods over future goods) is the rate of interest. Thus, if, on the time market, 100 ounces of gold exchange for the prospect of obtaining 105 ounces of gold one year from now, then the rate of interest is approximately 5 percent per annum. This is the time-discount rate of future to present money.

     What do we mean specifically by “prospects for obtaining money in the future”? These prospects must be carefully anal­yzed in order to explain all the causal factors in the determination of the rate of interest. In the first place, in the real world, these prospects, like any prospects over a period of time, are always more or less uncertain. In the real world this ever present uncertainty necessarily causes interest and profit-and-loss elements to be intertwined and creates complexities that will be analyzed further below. In order to separate the time market from the entrepreneurial elements, we must consider the certain world of the evenly rotating economy, where anticipations are all fulfilled and the pure rate of interest is equal throughout the economy. The pure rate of interest will then be the going rate of time dis­count, the ratio of the price of present goods to that of future goods.

     What, then, are the specific types of future goods that enter the time market? There are two such types. One is a written claim to a certain amount of money at a future date. The exchange on the time market in this case is as follows: A gives money to B in exchange for a claim to future money. The term generally used to refer to A, the purchaser of the future money, is “lender,” or “creditor,” while B, the seller of the future money, is termed the “borrower” or “debtor.” The reason is that this credit transac­tion, as contrasted to a cash transaction, remains unfinished in the present. When a man buys a suit for cash, he transfers money in exchange for the suit. The transaction is finished. In a credit transaction he receives simply a written I.O.U., or note, en­titling him to claim a certain amount of money at a future date. The transaction remains to be completed in the future, when B, the borrower, “repays the loan” by transferring the agreed money to the creditor.

     Although the loan market is a very conspicuous type of time transaction, it is by no means the only or even the dominant one. There is a much more subtle, but more important, type of trans­action which permeates the entire production system, but which is not often recognized as a time transaction. This is the pur­chase of producers’ goods and services, which are transformed over a period of time, finally to emerge as consumers’ goods. When capitalists purchase the services of factors of production (or, as we shall later see, the factors themselves), they are pur­chasing a certain amount and value of net produce, discounted to the present value of that produce. For the land, labor, and capital services purchased are future goods, to be transformed into final form as present goods.

     Suppose, for example, that a capitalist-entrepreneur hires labor services, and suppose that it can be determined that this amount of labor service will result in a net revenue of 20 gold ounces to the product-owner. We shall see below that the service will tend to be paid the net value of its product; but it will earn its product discounted by the time interval until sale. For if the labor serv­ice will reap 20 ounces five years from now, it is obvious that the owner of the labor cannot expect to receive from the capitalist the full 20 ounces now, in advance. He will receive his net earn­ings discounted by the going agio, the rate of interest. And the interest income will be earned by the capitalist who has assumed the task of advancing present money. The capitalist then waits for five years until the product matures before recouping his money.

     The pure capitalist, therefore, in performing a capital-advanc­ing function in the productive system, plays a sort of intermediary role. He sells money (a present good) to factor-owners in exchange for the services of their factors (prospective future goods). He holds these goods and continues to hire work on them until they have been transformed into consumers’ goods (present goods), which are then sold to the public for money (a present good). The premium that he earns from the sale of present goods, compared to what he paid for future goods, is the rate of interest earned on the exchange.

     The time market is therefore not restricted to the loan market. It permeates the entire production structure of the complex economy. All productive factors are future goods: they provide for their owner the expectation of being advanced toward the final goal of consumption, a goal which provides the raison d’être for the whole productive enterprise. It is a time market where the future goods sold do not constitute a credit transaction, as in the case of the loan market. The transaction is complete in itself and needs no further payment by either party. In this case, the buyer of the future goods—the capitalist—earns his income through transforming these goods into present goods, rather than through the presentation of an I.O.U. claim on the original seller of a future good.

     The time market, the market where present goods exchange for future goods, is, then, an aggregate with several component parts. In one part of the market, capitalists exchange their money savings (present goods) for the services of numerous factors (future goods). This is one part, and the most important part, of the time market. Another is the consumers’ loan market, where savers lend their money in a credit transaction, in exchange for an I.O.U. of future money. The savers are the suppliers of present money, the borrowers the suppliers of future money, in the form of I.O.U.’s. Here we are dealing only with those who borrow to spend on consumption goods, and not with pro­ducers who borrow savings in order to invest in production. For the borrowers of savings for production loans are not inde­pendent forces on the time market, but rather are completely dependent on the interest agio between present and future goods as determined in the production system, equaling the ratio be­tween the prices of consumers’ and producers’ goods, and be­tween the various stages of producers’ goods. This dependence will be seen below.

3. Time Preference and Individual Value Scales

     Before considering the component parts of the time market further, let us go to the very root of the matter: the value scale of the individual. As we have seen in the problem of pricing and demand, the individual’s value scale provides the key to the determination of all events on the market. This is no less true in regard to the interest rate. Here the key is the schedule of time-preference valuations of the individual.

     Let us consider a hypothetical individual, abstracting from any particular role that he may play in the economic system. This individual has, of necessity, a diminishing marginal utility of money, so that each additional unit of money acquired ranks lower on his value scale. This is necessarily true. Conversely, and this also follows from the diminishing marginal utility of money, each successive unit of money given up will rank higher on his value scale. The same law of utility applies to future money, i.e., to prospects of future money. To both present money and future money there applies the general rule that more of a good will have greater utility than less of it. We may illustrate these general laws by means of the following hypothetical value scale of an individual:

John Smith

        ................................................ (19 oz. future) (10 yrs. from now)
        .......... 4th unit of 10 oz.
        ................................................ (18 oz. future)
        ................................................ (17 oz. future)
        ................................................ (16 oz. future) 
        .......... 3rd unit of 10 oz.
        ................................................ (15 oz. future)
        ................................................ (14 oz. future)
        ................................................ (13 oz. future)
        .......... 2nd unit of 10 oz.
        ................................................ (12 oz. future)
        .......... 1st unit of 10 oz.
        ................................................ (11 oz. future)
        .......... (1st added unit of 10 oz.)
        .......... (2nd added unit of 10 oz.)
        ................................................ (10 oz. future)

We see in this value scale an example of the fact that all possible alternatives for choice are ranged in one scale, and the truths of the law of utility are exemplified. The “1st unit of 10 oz.” refers to the rank accorded to the first unit of 10 ounces (the unit arbitrarily chosen here) to be given up. The “2nd unit of 10 ounces” of money to be given up is accorded higher rank, etc. The “1st added unit of 10 oz.” refers to the rank accorded to the next unit of 10 ounces which the man is considering acquiring, with parentheses to indicate that he does not now have the good in his possession. Above we have a schedule of John Smith’s value scale with respect to time, i.e., his scale of time preferences. Sup­pose that the market rate of interest, then, is 3 percent; i.e., he can ob­tain 13 ounces of future money (considered here as 10 years from now), by selling 10 ounces of present money. To see what he will do, we are privileged to be able to consult his time-preference scale. We find that 13 ounces of future money is preferred to his first unit of 10 ounces and also to the second unit of 10 ounces, but that the third unit of 10 ounces stands higher in his valuation. Therefore, with a market rate of 3 percent per year, the individual will save 20 ounces of gold and sell them for future money on the time market. He is a supplier of present goods on the time market to the extent of 20 ounces.[8]

     If the market rate of interest is 2 percent, so that 12 future ounces would be the price of 10 present ounces, then John Smith would be a supplier of 10 ounces of present money. He is never a sup­plier of future money because, in his particular case, there are no quantities of future money above 10 ounces that are ranked below “1st added unit of 10 oz.”

     Suppose, for example, that James Robinson has the following time-value scale:

James Robinson

       ................................................ (19 oz. future) (10 yrs. from now)
       .......... 2nd unit of 10 oz.
       ................................................ (18 oz. future) 
       ................................................ (17 oz. future)
       .......... 1st unit of 10 oz.
       ................................................ (16 oz. future)
       ................................................ (15 oz. future)
       ................................................ (14 oz. future)
       ............ (1st added unit of 10 oz.)
       ................................................ (13 oz. future)
       ................................................ (12 oz. future)
       ............ (2nd added unit of 10 oz.)
       ................................................ (11 oz. future)
       ............ (3rd added unit of 10 oz.)
       ................................................ (10 oz. future)

If the market rate of interest is 3 percent, then Robinson’s valuations are such that no savings will be supplied to the time market. On the contrary, 13 ounces future is lower than “1st added unit of 10 oz.,” which means that Robinson would be willing to exchange 13 ounces of future money for 10 ounces of present money. Thereby he becomes, in contrast to Smith, a supplier of future money. If the rate of interest were 1 percent, then he would supply 22 ounces of future money in exchange for 20 ounces of present money, thus increasing his demand for present money at the lower price.

     It will be noticed that there is no listing for less than 10 ounces of future goods, to be compared with 10 ounces of present goods. The reason is that every man’s time preference is positive, i.e., one ounce of present money will always be preferred to one ounce or less of future money. Therefore, there will never be any question of a zero or negative pure interest rate. Many economists have made the great mistake of believing that the interest rate deter­mines the time-preference schedule and rate of savings, rather than vice versa. This is completely invalid. The interest rates discussed here are simply hypothetical schedules, and they indi­cate and reveal the time-preference schedules of each individual. In the aggregate, as we shall see presently, the interaction of the time preferences and hence the supply-demand schedules of in­dividuals on the time market determine the pure rate of interest on the market. They do so in the same way that individual valu­ations determine aggregate supply and demand schedules for goods, which in turn determine market prices. And once again, it is utilities and utilities alone, here in the form of time prefer­ences, that determine the market result; the explanation does not lie in some sort of “mutually determining process” of preferences and market consequences.

     Continuing with our analysis, let us tabulate the schedules of John Smith and James Robinson, from their time-value scales above, in relation to their position on the time market. John Smith’s schedule is given in Table 11. James Robinson’s schedule is given in Table 12.

     The Robinson time schedule is of particular interest. Referring to his time-value scale, we find that at an interest rate of 9 percent, 19 ounces of future money is above the second unit of 10 ounces of present money and therefore also above the first unit. At this interest rate, his supply of present money on the time market, i.e., his savings, equals 20 ounces. Because his valuation of the first unit (of 10 ounces—an arbitrary size of unit that we have picked for this discussion) is between 16 and 17 ounces of future money, when the market interest rate is 6 percent, his return of 16 ounces is less valuable to him than his first unit. Therefore, he will not be a saver and supplier of present money at this rate. On the other hand, he will not be a supplier of future goods (i.e., a demander of present goods on the time market) either. In order to be a supplier of future goods, his valuation of the future money that he would have to give up at the ruling rate of interest has to be lower than the present money that he would get. In other words, what he gives up in prospective future money will have to be worth less to him than the utility of the “1st additional unit of 10 oz.” on his scale. While the market rate is in the 4-percent to 6-percent range, this will not be true, for the 14 to 16 ounces of future money that he would have to supply would be worth more to him than the additional 10 ounces of present money that he would gain from the exchange. In Robinson’s case, the critical point takes place when the hypothetical interest rate drops to 3 percent, for 13 future ounces are worth less than an additional 10 ounces of present money, and he will supply the future ounces on the market. If the interest rate were 1 percent, he would supply 20 ounces of future goods.[9]

     It should be evident that an individual, at any one time, will either be a net saver (i.e., a net demander of future goods), a net supplier of future goods, or not be on the time market at all. The three categories are mutually exclusive.

     The diagram in Figure 42 sketches the schedules of Smith and Robinson in graphic form. Interest rate is on the vertical axis, and money on the horizontal. The supplies of present goods are also demands for future goods, and the demand for present goods is also the supply of future goods.

     We cannot compare utilities or values between persons, but we certainly may say that Robinson’s time-preference schedule is higher than Smith’s. In other words, it cannot make sense to com­pare the rankings or utilities that the two men accord to any particular unit of a good, but we can (if we know them) com­pare their schedules based purely on their demonstrated time preferences. Robinson’s time-preference schedule is higher than Smith’s, i.e., at each hypothetical rate of interest Robinson’s val­ues are such that he will part with less of his present goods in exchange for future goods.[10]

     Let us explore the typical individual time-preference schedule, or time-supply-and-demand schedule, more closely. In the first place, there is no necessity for the unit chosen to be 10 ounces. Since money is perhaps the most divisible of goods, it is possible to break down the units into far smaller sizes. Furthermore, be­cause of the arbitrage of the market, the rate of interest return on investments of present in future goods will be equal for all the various sizes of units. We may therefore visualize a compara­tively smooth curve, even for each individual.

     One inevitable characteristic of an individual’s time-preference schedule is that eventually, after a certain amount of present money has been supplied on the market, no conceivable interest rate could persuade him to purchase more future goods. The reason is that as present money dwindles and future money in­creases in a man’s possession, the marginal utility of the former increases on the man’s value scale, and the marginal utility of the latter decreases. In particular, every man must consume in the present, and this drastically limits his savings regardless of the interest rate. As a result, after a certain point, a man’s time preference for the present becomes infinite, and the line repre­senting his supply of present goods becomes vertical upward. At the other end of the scale, the fact of time preference will imply that at some minimum rate of interest the man will not save at all. At what point the supply curve hits the vertical axis depends on the valuations of the individual; but it must do so, as a result of the operation of the law of time preference. A man could not prefer 10 ounces or even less of future money to 10 ounces of present money.[11]

     What happens after the individual supply curve hits the ver­tical axis depends entirely on the time preferences of the indi­vidual. In some cases, as in that of John Smith above, the per­son’s marginal utility of money falls too fast, as compared with that of future money, for him to participate as a net demander of present goods at low rates of interest. In other words, Smith’s time-preference ratio is too low in this area for him to become a demander of present goods and a supplier of future goods. On the other hand, Robinson’s higher schedule of time preferences is such that, at low rates of interest, he becomes a supplier of future goods for present goods. (See Figure 42.)

     We may of course, diagram a typical individual’s supply and demand curve conventionally, as we have done in Figure 42. On the other hand, we may also modify this diagram, so as to make one continuous curve of the individual’s activity on the time mar­ket. We may call this curve the “individual’s time-market curve.” At higher interest rates, down to where it hits the vertical axis, this curve is simply the individual’s supply curve of present goods. But below this, we are reversing his demand curve and continu­ing it on to the left on the horizontal axis. (See Figure 43.)

     Every individual on the market has a similar type of time-­market schedule, reflecting his particular value scale. The schedule of each will be such that at higher rates of interest there will be a greater tendency toward net saving, and at lower rates of interest, less saving, until the individual becomes a net demander. At each hypothetical rate of interest there is a possible net sav­ing, net demanding, or abstaining from the market, for each in­dividual. For some changes in the rate of interest, there will be no change (vertical curve), but there will never be a situation where the supply will be greater, or demand less, with lower rates of interest.

     The time-market schedules of all individuals are aggregated on the market to form market-supply and market-demand schedules for present goods in terms of future goods. The supply schedule will increase with an increase in the rate of interest, and the de­mand schedule will fall with the higher rates of interest.

     A typical aggregate market diagram may be seen in Figure 44. Aggregating the supply and demand schedules on the time mar­ket for all individuals in the market, we obtain curves such as SS and DD. DD is the demand curve for present goods in terms of the supply of future goods; it slopes rightward as the rate of interest falls. SS is the supply curve of present goods in terms of the demand for future goods; it slopes rightward as the rate of interest increases. The intersection of the two curves determines the equilibrium rate of interest—the rate of interest as it would tend to be in the evenly rotating economy. This pure rate of in­terest, then, is determined solely by the time preferences of the individuals in the society, and by no other factor.

     The intersection of the two curves determines an equilibrium rate of interest, BA, and an equilibrium amount saved, 0B. 0B is the total amount of money that will be saved and invested in future money. At a higher interest rate than BA, present goods supplied would exceed future goods supplied in exchange, and the excess savings would compete with one another until the price of present goods in terms of future goods would decline toward equilibrium. If the rate of interest were below BA, the demand for present goods by suppliers of future goods would exceed the supply of savings, and the competition of this demand would push interest rates up toward equilibrium.

     Perhaps more fallacies have been committed in discussions con­cerning the interest rate than in the treatment of any other as­pect of economics. It took a long while for the crucial impor­tance of time preference in the determination of the pure rate of interest to be realized in economics; it took even longer for economists to realize that time preference is the only determin­ing factor. Reluctance to accept a monistic causal interpretation has plagued economics to this day.[12]