6.01. Many Stages: The Pure Rate of Interest

0:00Chapter 6. Production. The Rate of Interest and its Determination. 1. Many Stages. The Pure Rate of Interest. The discussion in this chapter deals with the pure rate of interest, as determined by time preference. On the role of the purchasing power component in the market rate of interest, see Chapter 11 on money. 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.

0:47This is certainly an unrealistic assumption. We shall now consider the production situation in the real world, where A, factors are non-specific 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. Capitalists 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.

1:41It 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, we shall assume that each stage takes the same length of time. Now, instead of collecting interest income for services in one lump sum at the final The Capitalist or Capitalists acquire interest income at each stage. 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.

2:37Strictly, 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. Suppose consumers spend 100 ounces on a particular good. Of the 100 ounces, 5 ounces go as interest income to the sellers of the consumer's good, and 95 are paid out to the owners of factors. 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.

3:29At 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 4 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.

4:16Total interest income is 17 ounces. In the foregoing section on interest, we showed that money is always non-specific. 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. The interest rate return received by product owners, that is, by capitalists, is equal at each stage.

5:06At the lowest stage, producers have invested 95 ounces in factors, both capital goods and and Original Factors, and receive 100 ounces from consumers, a net income of 5 ounces. This represents a return on the investment of approximately 5.2%. 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. In the ERE of our example, the pure rate of interest is THE rate of interest, since, as we shall see, deviations from the pure rate are due solely to uncertainty.

5:52The capitalist at the next higher stage invests 60 plus 16, or 76 ounces in factors, and receives receives a net return of 4 ounces, again, approximately 5.2%, 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 The Interest Rate must be equal for each stage of the production process.

6:37For 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 4 and Stage 1 in our example, 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% in each.

7:38Let us suppose, however, that the sum of the factor prices for Stage 4 is 35 instead of 43, while the sum of factor prices in Stage 1 is 98. The sum of factor prices here excludes interest income, of course. Capitalists investing in Stage 4 would earn a net return of 8, or 23%, while investors in Stage 1 earned about 2%. Capitalists would begin to stop investing in Stage 1 and shift to Stage 4. As a consequence of this shifting, the aggregate demand in Stage 1 for its factors diminishes, and the prices of the factors used in Stage 1 therefore decline.

8:27In the meanwhile, greater investment in Stage 4 raises factor prices there, so that the cumulative price rises from 35. Products of Stage 4 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, the rate of interest pervades all time markets, and the productive loan market is a strictly subsidiary time market of only derivative importance.

9:24In the reams of commentary on J. M. Keynes' general theory, no one has noticed the very revealing passage in which Keynes criticizes Mises' discussion of this point. Mises asserted that Mises' peculiar new theory of interest confused the marginal efficiency of capital, the net rate of return on an investment, with the rate of interest. The point is that the marginal efficiency of capital is indeed the rate of interest. It is a price on the time market. It was precisely this natural rate, rather than the loan rate, that had been a central Capital Problem of Interest Theory for many years. The essentials of this doctrine were set forth by Boehm-Bawerk in Capital and Interest and should therefore not have been surprising to Keynes. It is precisely this preoccupation with the relatively unimportant problems of the loan market that constitutes one of the greatest defects of the Keynesian Theory of Interest.

10:30Not 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 3 of good X earns 8% and stage 1 of good Y earns 2%, 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.

11:26We 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.

12:11Thus, suppose that the uniform interest rate in the economy is 5%. This is 5% 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%, the equivalent of 5% 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.

13:01It 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 labour earn income for their owners. As we have seen and will discuss further, 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, labour 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.

13:52Each therefore receives its own income from production, as will be detailed. 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.

14:48The 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, that is, interest rate, is 5% 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.

15:45The 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. Less 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.

16:31They have advanced present goods to owners of factors, and in return, wait while these These factors, which are future goods, are transformed into goods that are more nearly present than before. The capitalist's 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. As Boehm-Bawerk declared, interest may be obtained from any capital, no matter what be the kind of goods of which the capital consists, from goods that are barren as well as from those that are naturally fruitful, from perishable as well as from durable goods, from goods that can be replaced and from goods that cannot be replaced, from money as well It comes from a willingness to sacrifice present goods for the purchase of future goods, the factor services.

17:45As 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.