Production: The Rate of Interest and Its Determination

0:00In this chapter, we see illustrated again Rothbard's approach, which is to systematically proceed on these questions, only reaching the final culmination of the question at hand, the termination of the rate of interest, when the entire apparatus of theory has been built. And so, one of you posed a question about this. He said, well, here we have a chapter on the interest rate determination. What about the Fisher's equation? What about all the components of the rate of interest? And Rothbard, again, puts off that question, right? In order to answer that question, you first have to deal with the question of the determination of the purchasing power of money.

0:49And so the answer to the final determination of the rate of interest is actually in Chapter 11, where Rothbard fully deals with this question of Fisher's equation and the relationship between money and the purchasing power of money and the rate of interest. In this chapter, he's dealing only with the pure rate of interest, only the originary rate of interest or the time preference rate of interest. Now, to distinguish this view, Rothbard points out that the standard neoclassical argument would be based on loanable funds. They would treat, in other words, the question of the rate of interest as they would any price. There was demand for it that is based upon some particular objective features of the world, in this case rates of return on investment.

1:36And then there's the subjective factor, in this case the time preferences of savers. And these two factors combine to give us the loan rate of interest. So, here the rate of interest is perceived just like another price. Look at the price of apples, the price of shoes. Oh yeah, the rate of interest is just one in the many set of prices. So, the first thing that's striking about Rothbard's presentation, of course following in this tradition from Mises, is that Rothbard and Mises conceive of the rate of interest as all-pervasive. So the rate of interest permeates all time relevant human action.

2:23So the time market where the rate of interest is determined is actually like the whole of economic action, it's a whole economy. So you can't even conceive of the rate of interest as a price in the standard sense. As Rothbard points out, it's actually, so to speak, a ratio of prices. It's the inter-temporal rate of exchange between present goods and future goods, wherever present goods and future goods exchange. And so it's the ratio of the prices of these monetary sums, the future sum of money to buy the goods in the future, and the present sum of money to buy the goods in the present. And of course, Rothbard's explanation of how this ratio of prices is determined and is based upon time preference.

3:17So he gets to the topic of the chapter title, the topic that's embedded in that chapter title, right up front. So he gets right away to this question of how is production related to the rate of interest in his determination. So he gives us this diagram of the structure of production and embedded in this diagram One of them then is the assumptions that Professor Salerno mentioned about the production in the ERE. Some of these relax so that we have nonspecific as well as specific factors. We have independent entrepreneurs buying the inputs and selling outputs at each stage of production. We have the higher stages, in this case the highest stage is six, the production process of the first capital good, and then sequential capital goods as we proceed down to the production and sale of the consumer good at the lower stage.

4:18And so what happens in terms of the rate of interest, and remember since we're in the ERE, we don't have profit embedded in these prices that are being paid between the stages of production. What happens is the emergence of simply the rate of interest. of Interest, these prices will differ only by the rate of interest, right, because what's being undertaken in the stages of production is the entrepreneur, let's say, in the sixth stage is advancing to the factor owners of labor and land 19 ounces of gold, he's paying that then today, and then he's producing a good that he will sell to the fifth stage capitalist who's going to pay 20 ounces of gold for this good in one period. So he's paying present money, he's advancing the present money of 19 ounces, he's receiving then the future money of 20 ounces when he sells the output that he's produced.

5:12And this would command then the time preference rate of interest, which in this case is roughly five and a quarter percent. So the entrepreneur in the sixth stage pays out the 19 ounces, at the end of the period when he produces he sells this good for a premium right of 20 ounces he earns the one ounce interest and that on 19 ounces is a roughly five and a quarter percent then the fifth stage capitalists buys the capital good produced by the six stage capitalists for 20 he purchases labor and land factors of 8 so he pays at the time that his production begins 28, then at the end of his production process he produces a good that he sells for 30. Again, why is he selling this good? You know, why can this good command a price of 30? It's again because of time preference. Because the fourth stage capitalist, if he didn't have access to buy the fifth stage capitalist a good, he would then have to start at the earlier

6:16to produce this capital good himself and then proceed to have it and use it in his production process. So as Rothbard points out, the value, this premium value that is accruing to the capital goods as we proceed down the stages is for advancing the capitalist in any particular stage toward his end, which is receiving the revenue from selling the good that he's producing. So as he points out, in this process, it's time preference that would rule this difference between buying prices of inputs and selling prices of outputs. It's not the productivity of capital, it's not the marginal revenue product of capital, but the spread between the prices is determined only by time preference.

7:09So, in each instance for the factors of production, they, of course, will be paid corresponding to their marginal revenue product. But the interest rate that's commanded on the market will be the difference between the input prices and the output prices. He further points out, of course, that this will all be, by arbitrage, this will all be made uniform. The interest rate would be, the pure rate of interest would be uniform across all the stages, Because if there were a higher interest rate to be earned in any one of these production processes, entrepreneurs then would shift production into those processes. They would bid up the input prices. The output prices would moderate because of increased supplies. And this would continue until the interest rate conformed in that stage to the interest rate in all other stages.

7:59Now as he points out then, the interest rate that exists throughout the stages of production is simply conforming to any exchange of present money for future money. So here we just have one part of the time market where capitalists are saving and then advancing present money and then receiving and exchange future money. But in fact, this would be going on in other parts of the time market as well. This would in fact be going on in the loanable funds market or in the credit markets. So, the interest rate is, again, simply the spread of prices between present money as it exchanges for future money. Okay, now he gets to the next section is the determination of this, the determination of the rate of interest itself.

8:50And here he systematizes or categorizes the parts of the time market, saying, We can divide the time market then into first the credit markets. In the credit market we have a credit transaction. This means the transaction is not consummated until the future. So one party fulfills his obligation under contract in the present, but the other party won't fulfill his contractual obligation until the future. And this and the credit markets then would be either for consumer loans or producer loans. And you can see already then that Rothbard's conception of the time market includes the standard neoclassical analysis of the producer loan market as a subcomponent, right?

9:38In other words, the producer loan market is just a part of the overall time market. And so the interest rate that's being determined in the economy as a whole will be reflected on the producer loan market, not determined by it, right? is just determined by the overall time market. Okay, and then the second part of the time market we've seen already is the structure of production itself. Okay, now, in terms of the process of determination of the rate of interest, Rothbard gives us this analysis based upon time preference. Alright, so he says this, just like any result in the market, any exchange ratio in the market, the interest rate is resolvable back into its cause, which is the time preferences, subjective values of people, in this case, people's preferences for present versus future money.

10:41and if we look just at, let's say, James Robinson, preference rank here, this is the one where we get the full possibilities that it would exist for someone with respect to time preferences or again in the standard way that Rothbard presents this, things in parenthesis are not possessed by the person, things without parenthesis he does possess, so this person possesses 20 ounces of present money and Because of the law of diminishing marginal utility, he would be willing to lend this first unit of 10 ounces if the interest rate on the loan were 7% or more. Only at higher interest rates than that would he be willing to lend his full 20 ounces, only at 9% rate of interest.

11:32He could, at lower rates of interest, then become a demander of present money. First added unit of 10 ounces he would be willing to accept at 3% interest and then again the law of diminishing marginal utility would imply that only at lower rates of interest would he in fact increase his demand. So again he's just applying the same framework of determination of exchange rates that we had before. So here we get then to the schedule. This is James Robinson's schedule of supply and demand for present money in exchange for future money. So these high interest rates, he's a supplier at the low interest rates, demandor. At an intermediate interest rate, notice he sits out.

12:19Neither supplies nor demands. So these would be the three possibilities depending upon a person's time preference and the going rate of interest. where the person could supply present money, demand present money or not participate in the market, right? This would be the third possibility. So then we just, as before, we just add up all of these demands and supplies. Analytically, this is how we approach the market clearing. We see that the market would clear at some particular rate of interest and not at any other. You know, at higher rates, it would be excess supply and at lower rates, excess demand. and so the market would adjust to clear and that the interest rate then would emerge. And that this interest rate then would be uniform throughout all elements of the time market.

13:07Remember, we're just speaking about the pure rate of interest, that pure rate of interest would be uniform across all parts of the time market. Okay, then the next part of this analysis that Rothbard gives us is to go back to this question of the production structure. And he gives us this summation chart on page 395 of this structural production diagram that we looked at before. So he's just culling out the summary figures from that previous diagram.

13:57And here what he wants to do of course is to analyze the production structure in terms of its time market element. He wants to add up all the suppliers of present goods, wants to add up the total supply of present goods and the total demand for present goods from that previous example. And so he builds this again from each stage of production. The capitalist one, remember, is the capitalist that sells the consumer good for a hundred, who pays 95 for the factors that he buys, 15 ounces for land and labor, 80 ounces for the capital good that he buys from the second stage capitalists, so that he gets this, as we said before, the five, he would get the five ounces of interest.

14:49Capitalist II, right, his figures are the 76, this is the amount that he advances, 16 ounces plus the 60 that he's buying the capital good from the third stage capitalists and so on. So he's just again calling out these numbers for what the time market would look like from the structure production. And then we get this as the result.

15:28So this is the summary result, right? The net income that accrues to the producers in this example is 83 ounces to labor and land. The 17 ounces of net income, this is the interest income to the capitalists for 100. And also we know that the consumer good in this example has a value of 100 ounces. So it must be in this case that there's no net saving in this particular example. Income, all the income is spent on consumption. Rothbard does this intentionally to bring out a few particular features of looking at the analysis in the way that he does versus the standard approach.

16:14Then from this last chart that we had, when we add up a gross saving, even though there's no net saving, there's a huge amount of gross saving and investing, right? The gross saving and investing being done by the capitalists at each stage. So the sixth stage capitalist, remember, is taking 19 ounces of money that he's saved from the past, advancing it to the owners of labor and land. That then is part of gross saving, right? The 19 ounces. And the fifth stage capitalist has 28 ounces that he's saved from the past or he's borrowed from other savers, whatever, but he's advancing it from savers or the capitalists. So we're adding the 19 plus the 28 and so on and so forth. We get the gross saving of 3.18. And so as Rothbard calculated, it's the total expenditures on production then would be consumption plus gross investment.

17:01So it's the 100 to buy the consumer good plus the 3.18 to buy all the intermediate capital goods So that gross expenditures are $4.18 and the total gross income then is the $100 earned by the consumer goods producing capitalists plus the $83 that goes to labor and land plus the $2.35 that's earned as gross income by all the intermediate producers of capital goods. So this also then adds to $4.18. Now, what Rothbard makes of all this, of course, is that production, contrary to the standard view in macroeconomics, that the macroeconomy is dominated by consumption, and in this sort of Keynesian net sense, the actual economy is dominated by gross saving and gross investment, that all the production, if we take it in the gross sense, as the entire set of production processes is actually dominated by saving, not by consumption, by saving and investing.

18:09As he points out, if in any of the intermediate stages, one of the capitalists who's advancing saving from the past to proceed on that productive step, would instead just, you know, as time preference would rise dramatically, he would go to the Bahamas and take a vacation, Then the whole production process at that point would break down. That good would never be produced, there would be nothing for, no input for the next stage. So that the whole production process, the whole structure of production actually depends upon the advancement of saving and investing by the capitalists at each stage. It isn't dependent upon consumption per se, right? It's aiming at a consumptive end, but the actual processes of production require saving and investing at each step.

18:58Okay, so what does he make of this point? He says, first of all, that the standard view that this kind of Keynesian view or this net view, the standard view that this tends to lead to the implication or tends to justify the implication that, in fact, this idea of saving, that saving and investing isn't even necessary for the maintenance of the capital structure. I think we can have something, remember in Rothbard's example, we don't have any net saving, and yet it appears that production would continue on in the evenly rotating economy, right? This particular pattern of production would just continue on, right?

19:45So, it makes it appear that there isn't any saving that's necessary for continuous production with a given capital structure. And Rothbard points out, no, this is completely wrong. It's just an artifact of the implication from this particular view, this wrong-headed view, of looking only at the net results. If we look at the gross income and gross investment, we can see that this is certainly not true, right? It does require a huge amount of saving and investing to keep any particular production system going. Then the second implication he draws from this is that contrary to the standard view in macro, consumption doesn't dominate business prosperity.

20:31It isn't necessary, in other words, to have a huge amount of consumption in order for businesses Businesses to have sufficient net income to be able to continue operation. Actually, as he points out, the different, well, the prosperity of the businessman depends only upon the spread of prices between his input, what he pays for his inputs and what he receives for his outputs, and that even that spread is variable, right? In other words, the businessman doesn't need a particular spread, he doesn't need to get 10% or whatever to justify his investment. He only needs to get the going rate of interest. And so if time preferences go down, let's say the general time preferences go down on the part of people, then the rate of interest would fall.

21:18This doesn't affect adversely business prosperity. It simply opens up other lines of investment for lengthening out the structure of production that then would command, let's say, a 3% interest return, right? So the economy, in other words, what's happening with the structure of production is that entrepreneurs are allocating the factors of production into viable business activities according to time preferences and that they'll adjust the pattern of production based upon what these time preferences happen to be, whether they're high or they're low. So business prosperity, again, is completely malleable to what the pattern of preferences by the way, this is just a generalizable point, right, that we saw before that the pattern of production of consumer goods would also be malleable.

22:13Consumer preferences might change. This doesn't adversely affect the business profitability. This just means that there would be a reallocation of resources. There'd be a transition period and then a reallocation. and reallocation, but the end result would be there would be no permanent disability on the part of entrepreneurs to earn profit. So Rothbard is just extending this argument to the capital structure. Okay, then the next point, he gets to another point that we might cover here just because it seems puzzling, or at least Rothbard considers it a puzzling feature of his analysis. He says, what would we say about someone sort of, we've sort of pictured this so far, he's pictured it so far in the sense of, you know, a person has a time preference and then enters into the time market based upon his time preferences, is either a saver, a lender, or he just sits it out, or as a demander, a borrower, but Rothbard points out that this, this is true, that analysis is true, but there's a complication that makes it seem paradoxical, which is wouldn't it be possible for someone to be both a demander and a supplier on the time market

23:46regardless of what the rate of interest might be. And he says, sure, that can happen. In fact, this is embedded in the analysis that he's developed, so he wants to bring this out. But it could only happen at different points in time, right? So at a given interest rate, it might be that a person would demand, you know, at one point in time and supply at another point in time based upon his stock of present assets or his stock of present money. So he gives us this analysis, where we have some particular person, right, who before he earns income, this is a worker, a laborer in the structural production, before he earns his income from the payment from the capitalist, he's a debander.

24:34So this is the top diagram. Here, because his present income is very low, his time preference schedule, his time market schedule has shifted, so that he is a demander at this point. But then after he gets paid his income, he could wind up being a supplier, right? So this is his post-income position, right? So a person could, over the sequential events of the market, of earning income and then this disbursement of his income, He could be at one point a supplier and another point a demander. But as Rothbard points out, when we add up, when we analytically address this difference and we add up the supplies and demands, there is a distinction between these two positions of being a demander in pre-income and a supplier in post-income.

25:30And as he points out, the distinction is that the pre-income demand is always is on the basis of production. The worker, in other words, is saying, I'll advance my labor services, I'll sell the capitalist my labor services, but I would prefer to be paid a discounted value of my marginal revenue product today as opposed to waiting until the good is sold and receive my full marginal revenue product. So he's a demander then of present money. So this is a producer demand, right? and the producer is demanding the present money. Whereas the post-income demand would be a consumer demand, since at this point the individual is not selling, right? At this point in time, he's not selling his labor services.

26:19He is not being paid for the sale of his labor services. He's earned his income and now he's dispersing it. So at that point, whatever demand he might have, Rothbard pictures in his supplying, but he could demand here too, right? Whatever demand you might have at that point would be consumption demand, or consumer demand, you'd be in the consumer loan market. And so the final analytical point that Rothbard makes with this diagram, where this diagram he's summarizing then his analysis. He's saying, okay, here we have the time market, we have gold ounces that are being exchanged, present money, being exchanged at the rate of interest.

27:05We have the supply of all the savers. We have the consumer demands for present money. And then the difference between B and E, or the difference between CC and DD, is the producer demand. And so, what he's saying, the point he wants to make here is that And time preference not only dictates then the level of the rate of interest and the total amount, this is the AE, the total amount of present money that's lent and borrowed, it also determines the split of that amount into the various sub-components of the time market, right? The amount that goes into consumer loans and the amount that goes into producer loans.

27:51And the reason why this is relevant for the economy is because the greater the amount The larger the amount of A.E. that goes into consumer loans, the larger A.B. is relative to A.E. The less saving and investing there is for capital accumulation, so the higher consumer time preferences are in society, the less saving, or the less present money that's being lent, is available for actual buildup of the capital structure. also, this analysis also then determines the extent to which the capital structure would be built up over time. Okay, then the very last thing that we want to mention here is his criticism, his full criticism then of the producer loan market.

28:39So before we just said, well, the defect in Rothbard's view of this analysis of the mainstream that the interest is determined in the producer loan market, the Loanable Funds Market, is that this is just a subcomponent of the time market. And so it's really embedded in a larger economic phenomena, and it's more or less reflecting this larger economic phenomena as opposed to being the determining factor, the sole determining factor. But Rothbard makes a few other interesting criticisms of this view, and one of them is is that, of course, this view entirely overlooks his analysis of gross saving and investing. It's only in its narrow sense looking at the sums of money that are being lent and borrowed in the producer loan market.

29:32And so it completely misses the overall extent to which there's saving. When the saving curve, in other words, is drawn on here, it's not gross saving. But it's gross saving that is the factor in determining the rate of interest. And then he also points out that the other curve, the marginal efficiency of capital, let me put this back up, is also in fact not correct because it isn't true that separate from the rate of interest you can determine the rate of return on investment. The rate of return on investment, of course, is just the price spread between buying prices of inputs and selling prices of output.

30:18It is just the interest rate, in other words. And so to think that you have this schedule of rates of return where you have higher rates, you know, you can calculate somehow independently a rate of return for any given investment where one would be 10%, one eight, one six, and so on and so forth, is mistaken. And in the ERE, all those, in fact, all those rates of return would be exactly the same. They would be the going rate of interest. There is no other manner in which there could be a price spread between input prices and output prices. Oh, and then the very last point that he makes, just again to emphasize this idea that the The producer loan market, this loanable funds market, is subsidiary.

31:07He points out that in the ERE where there isn't any uncertainty and therefore no profit could be earned for capitalist investment, the equities markets and the producer loan markets, the bond markets, are exactly the same. They're analytically exactly the same. There's no distinction between them. So if anyone actually wants to earn the rate of interest, of Interest, they could directly invest in capitalist enterprises. They don't even need a producer loan market, right, a bond market to lend to the entrepreneur. They could just buy equities. And in buying the equities, they would in fact receive the rate of return, the interest return, in exactly the same way as they would by buying a bond. And so again, he's just saying, look, we don't even need the producer loan market.

31:55It might not even exist in the ERE. It of course will in the real world because it includes the capturing of profit as well as interest but in the ERE they're equivalent alternatives.