 Well, as the aging knight says in the Indiana Jones movie, The Holy Grail, after Indiana Jones drinks from the true grail, you have chosen wisely. And what we're going to talk about in this time is the very last element of economic theory of the working of the market economy. So we built this up over the last day and a half. We've seen all the essential, at least, features of theorizing about the market economy, understanding it. And we're left just with this final point about the rate of interest. So that's what we want to focus on. And we'll do this in three steps. As we've done previously, we want to talk about fundamentals first, just to see how we build the theory of the interest rate out of these fundamentals. And then we'll talk about the two ways in which people value action with respect to time. And then once we're finished with that, we'll talk about the rate of interest, the theory of the interest rate. So let's begin with the principle that, just like as we talked about on Monday, when we think about human nature and human action, what it means to be a human person engaged in action, we can immediately recognize that we're finite beings. And because we're finite beings, we make this distinction between ends and means. And then from that, we see that we have unmet ends. There must be a scarcity of means. And so we proceed right in that way. We've grounded the principle of the scarcity of things in the nature of the world. And so what we're going to do now is talk about the temporal nature of human existence. We're also time-bound beings. We exist in time, right? So we're neither infinite nor eternal. We're finite and temporal. And because of that, we make two important distinctions. We distinguish between different moments in time, like right at this moment, at lunchtime, Tuesday versus Wednesday, and so on and so forth. We notice the distinction between those things. We recognize that they're different things. And we also then make the distinction between sooner and later. And it's from these two distinctions that the two valuations of action with respect to time stem. So first, let's talk about this principle of the duration of action. And Dr. Rittenauer has talked a little bit about this already. So we've got some background to think about. As Mises puts it in human action, when we think about time from the perspective of our action, we divide it into these three categories. There's the time before action and the time during the action and then the time after the action. Or we could say it this way. For every action, it's a choice variable for us to determine when to start the action and when to stop it. The duration of the action is a choice variable for us. And so we can compress it. We can expand it. We can start it at one moment in time or a different moment in time and so on and so forth. Then the question is, well, how do we make choices with respect to these options available to us? And the answer is the same answer we've always given. We do it according to the valuations we make. We might value different moments in time differently. We might value sooner as opposed to later differently. And therefore, LinkedIn or shorten this duration of action. And then as Mises points out, the other important basic point here is that within the duration of action, within that notion, there are two parts. There's a production part and a consumption part. And the production part, Mises calls the period of production. And so the period of production includes what Mises called the working time or as Dr. Rittenauer explained earlier this morning, the production structure. You have to start by extracting raw materials and produce the intermediate capital goods and then produce the consumer good. And then it may be that once we produce the consumer good, there's maturing time. The flourless chocolate cake has to sit overnight in order to gel into its best form or wine has to sit in a vat and mature before it's consumed, something like that. And then there's the duration of serviceableness of the consumer good that's been produced. So we can produce an automobile and it has a 10-year durability and so we can extend the usefulness of the thing over time by the duration of serviceableness. Dr. Rittenauer mentioned the different spatulas, right? Of course those are producer goods but the idea of durability, that's a choice variable for us, this is the point. So every action looks like this. It's a sequence of steps. Once we start the action, there's a sequence of intermediate action, steps to the action and then it ends at some point. And these choice variables exist for us then with respect to the overall duration, the period of production within that, the duration of serviceableness of the good that we produce. And then I'll just mention, just kind of in passing because we're not gonna make any use of this notion but just for completeness, this last point, Mises also points out that because we're temporal beings and we are foreseeing how action will turn out in the future when we act, we also have this notion of the period of provision. So we're always thinking about with respect to any particular action, we're thinking about the provision in the future, the realization of the ends in the future over some span of time. And this, of course, this period of provision can actually extend beyond our lifetimes. So those of you who already have children, understand this, right? You're doing things now with the anticipation that this will improve their lives once you've gone onto your reward, shall we say. So, right, this is part of human life. We recognize this right away as being a fact of the way that we are as human beings. Okay, so that's the basic point. And now let's turn to this other issue of the valuation that we wanna turn and then examine this question of the two ways in which we value with respect to time. This gets a little bit tricky. This is a kind of, be very careful in the way you think this out because there are pitfalls involved in this just like again with Dr. Rittenauer's discussion of the capital structure as he pointed out. But in any case, we wanna separate out two different aspects of what we just talked about with respect to action. One is just looking internally at the duration of the action. How do we choose internally the period of production, the duration of serviceableness for any action that we take? And then the other is every time we engage in an action, we place that action in the stream of time, so to speak. We choose to start at a particular moment in time and end at another moment in time. So those are two different parameters of choice, right? Two different alternatives of choosing. And this is how Mises puts it. Well, again, we're gonna talk about this in more detail. In our next step, I just wanna introduce these two points. So Mises puts it this way. He says, there's the time, we all recognize there's the time before satisfaction from an action, this is the period of production, right? We're not getting consumptive satisfaction during the period of production. We start the period of production and we have to go through the whole process, right? And finish it, and then we get the satisfaction. And then there's the time during the satisfaction. This is the duration of serviceableness, right? We can produce a good that's perishable. We can produce a good that's somewhat durable, more durable. We can choose an array of different things that we want in terms of perishable and durable. This is what we're doing. And so what Mises points out here is this is where the principle sooner versus later comes in. Once we start a production process, we extract raw materials out of nature and we begin the steps to produce the consumer good. We prefer to get to the satisfaction part of the action sooner, right? This is what Mises calls time preference, right? For a given satisfaction, we prefer that it come to us sooner as opposed to later. This has to be though understood in the context of the duration of the action. This is only within the duration of the action. This isn't talking about when we do the action. It's talking about just whenever we do the action, whenever we choose to start the action, once we start it, then we prefer sooner to later, right? We wanna shrink the period of production, satyrus paribus, if we could get the same satisfaction. Of course, we can't get the same satisfaction with shorter versus longer production processes or periods of production. So we wanna discuss that, but that's the issue, right? And then the second issue, the point about moments in time, about choosing the timing of an action, Mises points out this, and this is another great, when I first read this, it's so pleasing. It's so aesthetically valuable to read human action or great works, right? It has an aesthetic appeal. And sometimes this comes just in the rhetorical flourishes or in the semantic way in which things are put. So Mises says, time is an irreversible flux. Maybe that doesn't strike you, but it just sort of strikes me as a quite satisfying way of putting it. It's an irreversible flux. If you wanna say this in a more explanatory way, as I've got on the slide, each moment actually has a unique place in the sequence of moments of time. That's what he's saying. Moments are not homogeneous and interchangeable. Not every moment in the sequence of moments in time is the same. In fact, they're all different. They're different precisely because they come after one another and things change as time moves on, right, to action. Now because that's the case, it might just be because the moments in time are heterogeneous. They're not homogeneous, right? They're heterogeneous. It might be that certain moments in time, if an action is taken at that moment, it would convey to us greater value than if the action were taken in a different moment. Just because different moments in time will provide different conditions for the subjective value that can be attained from an action. Okay, so again, this is not an explanation, but just I wanted to introduce these notions and then we'll go to the explanation. Okay, so we're gonna do these in reverse order. I'm gonna take the second first because again, this one has nothing to do with interest rates. That's what we wanna show now. That the timing of an action, this question, is not the foundation of interest. Foundation of interest is from the inter-temporal, choosing to start an action, committing resources to that goal, giving them up, in other words, surrendering them to that goal and then only obtaining the satisfaction later. Okay, so we'll call this again, the timing of an action. We choose with respect to the timing of an action and this is the point I just made that the value of a good that we use in action can vary depending on the moment that we use it in action. And so because of that, we will always allocate or we'll always consider, in the allocation of an action, we'll always consider this value difference. It may not be determinative to us because other things could be different too if we take an action at a different moment in time but this is the basic point. And so just one example of this. My wife and I, our wedding anniversary is November 17th. We were married November 17th, 1983. So just like with Dr. Ridenauer, we've gone through several mixers. So and this is a good thing, wonderful thing. So in any case, we'll celebrate our anniversary but I guarantee you that especially for my wife, it has more value if we do it on November 17th than if we do it on November 1st or heaven forbid if I forget then we do it on December 1st. That would really lower the value of the same event. It would change just based upon the moment in time. Okay, so this is what we're speaking about, right? Notice the principle here is we don't have to commit any resources at all now, sooner as opposed to later in that respect. We're just saying we're just gonna commit our resources at the moment that we want to do the action, not now. We're gonna, you know, whatever, you know, decide on a fancy place to go to dinner and I'll get some roses and so on and so forth but I'm not gonna do that now. I'm not committing anything now. I'm just, we're just saying we'll do that in due time. And then once we decide it's gonna be November 17th then we'll have to start the action, right? So I'll have to start the action not to secure the roses and the cake and whatever else we do. That's the duration of the action. That's when the action is, that's when we look at the duration principles of the action. Okay, now let me change my example to go to the market. So here let's just look at this example just because it's a well-worn example. Let's say we look at a commodity price. Let's say the price of oil and we look at the spot price that is the current, you know, purchase trade price and it's $30 a barrel or whatever it is. I don't know what it is but let's just say it's $30 a barrel. Now people who are involved in using oil as a producer good and you know they're buying and selling it and so on they're extracting it and then refining it and they would also be interested not only in that price, the spot price but in what the price will be at some moment in the future. And if they form the, let's say they form expectations financial traders and others involved in this, they form expectations that the fake pandemic is gonna end and we're gonna be locked down, it's gonna end and things are gonna go back to normal and we'll have a pretty normal array of demands for oil-based products and so on. And so in six months the price of oil is going to be $60. At that moment they're saying six months from today it's gonna be $60. So they start to form these expectations, right? Well they can make contracts today called forward transactions, not committing any resources today but just agreeing today to trade at $60 a barrel in six months, they have to obviously they have to have different speculations but if they do you have reverse preferences and they can make trades. So we can get forward prices. Forward prices then give us the market manifestation of the timing of action. They're just nothing more than that, right? There's nothing inter-temporal going on here. People are just assessing what they think the future price of a good will be. They're not committing themselves any resources until that day, just like I was suggesting I would do with respect to my anniversary. Now if it's true that the forward price was $60 and the spot price were 30 then there would be of course a profit opportunity. There's a higher value for oil in the future, higher price for it, right? And you could earn profit by transferring the oil use from the present to six months from today. But again, in order to do the contract for this you don't need to actually own the oil. In fact, it's sort of incidental as to how you come to own the oil in the future to provide the good. Whether you see you're an oil producer and you refine it and you're just holding it in storage or whether you just go into the spot market and buy it, right? That's immaterial. So again, there's no inter-temporal dimension here. And then of course, as the supply of oils being shifted to the future date the spot price and the forward price would come together. Just this is just the same process that we have in any market that we explained again on Monday, right? This is the efficient allocation temporarily of a good from one moment in time to another moment in time to another moment in time. Okay, so having set that aside, let's get to the main point. And by the way, my caveat is there are a lot of nuances and difficult things we have to think out more carefully than I'm suggesting here. I'm just sort of giving you an introductory discussion of these issues and then we'll save the difficult stuff for Q&A. Okay, so let's go to time preference and the inter-temporal dimensions. So this is how time preference is typically defined. Or I think maybe I should say it's best defined. The satisfaction, a given satisfaction is preferred sooner to later. So this is what we had mentioned before from Mises. Now here we wanna stress another point because again, oftentimes people conflate two different notions of preference in general even as well as time preference. What we're using these terms to refer to is something, as we've said, embedded in the nature of the case. It simply can't be otherwise. In other words, you cannot come up with a counter example showing that a person acted contrary to his or her preferences. There is no such thing. This is just what we mean by the word preference that a person's choice and action is always consistent with their preference. That's what we mean by it, right? And so it doesn't do it again to try to come up with counter examples. So we're saying the same thing about time preference. This is also true of time preference if we're right about the logic of this. It's embedded in human nature and therefore there are no counter examples. Every counter example just is misunderstanding what time preference is, or it's confusing timing and time preference. It's confusing these two distinctions we made before, the duration of the action and the moment in time when it's taken or something else like that, right? It's okay, so I won't go into any examples but you've read in the literature some of these examples. Okay, and then I have one quote just again to sort of have this in Mises' words. This quote from Human Action, page 480 in the scholar's edition. So he says, and this is all in these are different paragraphs but it's the same text that's running down to a new paragraph. So there's no separation in the text between these two quotes. Other things being equal, satisfaction in a nearer period in the future is preferred to satisfaction in a more distant period. Disutility is seen in waiting. So that's how he defines time preference, right? Satisfaction in the sooner period is preferred to satisfaction in a later period. And then he adds this aside, disutility, there's disutility seen in waiting. And then he goes on and says, this fact is already implied in the statement stressed in the opening of this chapter that man distinguishes between the time before a satisfaction is attained and the time for the duration of which there is satisfaction. This is the point that I made in the previous slide, right, in every action we always distinguish between the period of production and the duration of serviceableness of the good that we've produced, right? That's just in the nature of the case. And once we distinguish between these two, then we just see right away that we must prefer to shrink the period of production and extend the duration of serviceableness. It's just in the nature of the case, right? It's just what it means to be human to have this preference. Okay, so that's a Mises on these points. And now we wanna talk just about the implication. So time preference is just an implication. It's a logical implication of, excuse me, interest, the pure rate of interest is just a logical implication of time preference. But there's another implication that I want to mention just so you can connect things that have already been discussed. So this is back to Dr. Bittenauer's talk this morning. Time preference determines or maybe we should say the rate of time preference, how intense people's time preferences are, determine the inter-temporal production choices. So this is the basic claim, right? These are, as I put it on the slide, regulated by time preference. So whether we choose to engage in shorter production processes or longer and so on, that is all regulated by our time preferences. And with lower time preferences, we'll engage in longer, more productive production processes. And with shorter time preferences, people would engage in shorter, less productive production processes. So this is the idea. Notice other implications come from this pretty quickly, like this one. At any given moment in time, if you just have kind of a snapshot view of the economy, it must be the case that entrepreneurs have already engaged in the shortest, most productive production processes that they have available that they've created or see as possible. They won't engage in, of course, they won't engage in shorter, less productive production processes because of time preference. And in order to engage in longer production processes, they would have to be more productive than the shorter processes. So you see there's a certain logic of the whole configuration of the capital structure. Dr. Newman will talk about this in the lecture on the business cycle theory. This is kind of a, it's not the most important point, but it's a key element of understanding the cycle where the capital structure gets artificially linked and doubt. Well, why does it have to do that? Well, this is one reason why it has to do that. Okay, so then let's go to the pure rate of interest. And here we've given a definition. So the pure rate of interest, we're isolating just the time preference premium, of present money over future money. So this is not a full analysis of the market rate of interest, which has other sources to it besides the time preference sort. There are other causes of, at least potentially in principle, there are other causes of market rates of interest besides the time preference, besides the pure rates. So in order to have this clear, keep this clear, we'll call this time preference interest rate, we'll call this the pure rate of interest. This is Rothbard's terminology. You'll also notice that this pure rate of interest is always expressed in money, in the exchange of present money for future money. It's never expressed in terms of goods. In other words, nobody engages in inter-temporal trading goods. This, by the way, is a rather important side point to this whole discussion because as we mentioned, I think yesterday, the neoclassical general equilibrium model of the economy doesn't include money. There is no medium of exchange in it. They're just barter goods. And if they're just barter goods, how is the interest rate expressed? And the answer is it's expressed in goods. It has to be because that's all there is in the model. There's no medium of exchange. But if it's expressed in goods, you've got a big problem, which is if you actually had inter-temporal exchange of different goods, the interest rate, the relation between the future price and the present price would be radically different across the different goods. Why is that? Well, that would happen because different goods have different future prices because of the moment in time when they're taken, right? They would have different forward prices. And by the way, those of you who know about finance, you know that these, as I mentioned this point already, I guess, forward prices will come into relationship with spot prices through this arbitrage, but they won't be exactly equal. There'll be a difference. And the difference is the interest rate, well, and other ancillary things like storage costs and so on, right? You see, you can't explain the interest rate that way. The interest rate is what explains the difference between the forward price and the spot price. This is a lot of confusion in this area, a lot of difficulty, right? Then we have to think out carefully. So money is used because money provides us with the unit of economic calculation for all people in all places and in all moments of time. It's a uniform, homogeneous unit of economic calculation, the dollar. This doesn't mean again that the dollar would have the same purchasing power necessarily in the present and the future, but we can account for that, right? What money doesn't have is all the vagaries of shifting consumption demand and demand for producer goods that exist for all the other goods in the economy. Money has demand only as a medium of exchange. And so whatever vagaries it has can be anticipated and adjusted for. And so we get a single uniform, a pure rate of interest when money is used as opposed to exchanging in goods. And this allows us then to have efficient intertemporal allocation of goods. So that's the way the argument runs out. Okay, now let's go through the nuts and bolts. The nuts and bolts again are just going back to the discussion we had on Monday, Monday morning, where, and I've reproduced this right real briefly, the first three steps of price theory that we talked about on Monday are that people have preferences for consumer goods. These preferences are sometimes a reversed. And when they're reversed then trade can take place, mutually advantageous trade can take place. And then the market clearing price is forthcoming to facilitate these trades. And so there's nothing behind the price of consumer goods in this theory except that people's preferences. Now I might add here just a note, just so again we're not thinking wrongly about this claim. It's perhaps better to put the claim this way. Anything that can affect the price of a good only does so by changing people's preferences or influencing their preferences. Then their demands and supplies will change and then the price will change. But if this causal factor that exists outside of a person, situation or other people doing things that they weren't doing before or whatever is to affect the price, it has to change the person's preferences who are in this market demanding and supplying the good. That's the argument, right? It's not that preferences are the end all of everything. It's that we have no scientific theory to explain how these outside factors change preferences. There is no theory like that. And so scientific economics must begin with preferences as a given. We're not saying that that's true in real life, right? We're saying that's our theoretical framework and we can then apply that to real life where all these situations are changing and then people's preferences change and prices change and so on. So we're going to argue then the same thing about time preferences. People have time preferences. We can have some who are more intensely prefer the present satisfaction. Those who less intensely prefer present satisfaction. They can engage in mutually advantageous trade of present money for future money and the pure rate of interest emerges. So let me then run through just a quick numeric example like we did with Caruso's preference ranks before. Let's suppose we have person A with the preference rank as I've depicted. So you'll notice of course that time preference dictates that you'll see on both sets of preference ranks that $1,000 today is ranked above $1,000 a year from today, is it the bottom of each preference rank? That's because of time preference, right? Present satisfaction is preferred to a future satisfaction. We're assuming the purchasing power of these funds are the same, but there might be some amount of future money that would be preferred to this principal amount of present money and for person A it's $100, a $100 premium would be sufficient to get person A to part with $1,000 today in order to get $1,100 in a year. So that's the intensity of person A's time preference. And you can see then that person B has a more intense time preference, a higher rate of time preference. In order to get person B to sacrifice $1,000 today, the premium would have to be $300. So person B's time preference interest rate is 30% and person A's is 10% in my example, right? So obviously they can make a mutually advantageous trade at any interest rate, any pure interest rate between 10% and actually 29%, right? Because person B won't pay $300, but he would pay $290 to get a maximum amount, right? To get $1,000 today. Okay, so that's the idea, they would just get together and I mean they could, conceptually they get together and find out about these preferences they could trade. They could, person A could be the lender of present money and person B could be the borrower of a present money. Then the only other thing we have to do of course is introduce a competitive bidding and offering just like we did again on Monday for goods in general. Of course in a market economy, we'll have more than one potential lender with lower time preference and more than one potential borrower with higher time preference. And the interest rate produces the maximum amount of social cooperation between them. When the market clearing rate is achieved then it's achieved precisely because that will allow all of the lenders to find a borrower and all of the borrowers to find a lender and it creates the maximum amount of social cooperation in the market. And so again there's nothing different here than we argued on Mondays, just a general explanation of preference and demand supply explanation of the rate of interest. Now let's deal with, let me just summarize and then we'll deal with one other issue. So up to this point then we've noted that time preference determines two important, it has two important effects or determines two important things in the economy. It determines first the pure rate of interest and it determines the amount of present money lent and borrowed. And by the way, this is not unusual, it's not something weird to the interest rate, right? This is true for all market prices. So the demand and supply in other words and preferences that stand behind them determine the price of every good and the quantity of the good traded. Simultaneously determines both those things. So it determines as Dr. Rittenauer was pointing out, it determines the extent to which they're saving that can then be invested. And then I wanna just emphasize this point that I made before about money performing the unit of economic calculation function across time. And so I've just reproduced a simple example of compounding and discounting with the present sum. And so what the interest rate is doing is making the alternative to someone who participates in lending and borrowing, making the two alternatives of monetary sums exactly the same. You can either have $1,000 in your hand today or at a 25% interest rate, you can have $1,250 a year from today. Those are exactly, they're made equivalent, right? And then of course, if there's different purchasing power of the money in the future, that can be adjusted for. So this is just another piece of evidence that it's money that's used here always in inter-temporal exchange. So if someone is to acquire through production the sale of a good $1,250 in a year, that entrepreneur will be willing to pay $1,000 today for the factors of production. So those two sums are made equivalent by the interest rate, right? This is how the interest rate is regulating the inter-temporal activity of production. Okay, now let's, this is the last step we'll take really. We'll go in and talk about the different components of the time market, the different options for lending present money and borrowing present money. And this is just straight from Rothbard. So Rothbard very helpfully divides this into credit markets and the capital structure. So credit markets are when people engage in lending and borrowing, supplying present money and demanding present money, where the contract between them is not fulfilled until the future. So you take out a mortgage and then you as the homeowner you get the funds, right? You pay the builder, but that's just the first step of the contract. The agreement, the lending and borrowing agreement isn't finished until you make your last payment. So that's called a credit transaction. Anytime the fulfillment of the contract is only done in the future. And so there are lots of different kinds of credit transactions, right? And then within the credit markets there can be borrowed money that's used by consumer goods. So we say the consumer loan markets. And then we could subdivide those, right? And I mentioned already the mortgage market or the auto loan market or the general merchandise market and so on and so forth. And then there's the producer loan market where entrepreneurs go into credit markets and they borrow contractually, right? And then pay back the money over time. So bond markets and commercial paper markets and so on and so forth, these producer loan markets. And then there's the capital structure. So once again, Dr. Rittenauer was explaining this morning. Here, entrepreneurs borrow from the capitalists or they provide their own capital funding. They save and provide their own capital funding. And then by inputs, that's a cash transaction, right? For them, it's not a credit transaction, they just buy it and get the service. And then they own the command over the services, they produce it good and then they sell it to a different group of people at some future moment in time, right? At the end of the production process. Another cash transaction they sell. I'm not saying they can't sell on credit or anything. I'm saying there's no credit transaction between the lending of the money by the entrepreneur and the receiving back of the money from the consumer. There's no contract there, right? So there's just this production process within the capital structure. As Dr. Rittenauer already explained this morning, the size of the time market, the amount of saving and investing in the economy that goes into the capital structure dwarfs the size of the consumer loans. Hopefully you see already that all the producer loan funding goes into the capital structure. That's the reason the entrepreneur's borrowing the money. He's gonna buy inputs. And so that's really just part of the capital structure in that sense, right? One last point on this. I'll just note that the typical neoclassical treatment of the loanable funds market tends to focus just on producer loans, right? So you'll see this kind of treatment, especially say in Keynesian liquidity preference model of the interest rate. That, again, is not very robust, right? Sure, they're producer loans and we need to analyze that, but we can't really analyze that unless we embed it properly in the broader market in which it's a part of. Otherwise we're just thinking about it wrongly, right? We're thinking about it isolated and we're ignoring these interconnections that exist. So that's the next thing that I wanna mention. And this is just a simple example of this interconnection. Suppose we have consumer loans, suppose the loans demand and supply look like this and we start at point A and we have a very low pure interest rate of R sub zero. But in the capital structure and entrepreneurs are earning an interest rate much higher. They're earning R zero at point A on the right-hand panel. Well, this can't persist, right? Not if these are just pure rates of interest. If there's no difference between these loans that the capitalist might make into consumer or production loans, then this interest rate difference will be arbitraged away. The supply by the capitalist of the loanable funds will be shifted out of consumer loans where the interest rate is low and into loans in the capital structure where the interest rate is higher. But as this happens, the interest rates come together. And so the interest rate in producer loans depends upon the interest rate in consumer loans, depends upon interest rates that permeate the capital structure. They're jointly determined, so to speak, right? They're determined by this uniform process. They can't get very far out of sync with one another before the arbitrage process would earn profit for the entrepreneurs who see this and act upon it. I wanna make one last point on this and then we'll just, I wanna make a summary point because of ignoring these other factors that affect the interest rate. So here I just cited an example and I'm not gonna run through this, you could just read this from the slide about how not only will this pure rate of interest be the same across the credit loans and the capital structure activity, it will be the same in every production process in the capital structure as long as we're just looking at the same time dimension for production. And so the point that, but the point I wanna go on to now is this last point because again, there are a lot of theories about the interest rate that the interest rate depends upon the productivity of capital. But this is again a widespread but fallacious view. It's need, so as I put it here, neither the physical productivity nor the value productivity of assets can affect the pure rate of interest. And Dr. Klein talked about this already yesterday but I'll just, so I just kind of reproduced a simple example of this. Let's suppose that an entrepreneur has a production process with marginal revenue products from the factors. These are capital land and labor in order CN and L in one year and they're 10,000, 5,000, 2,500. So in other words, he's gonna produce a good and sell the good for 17,500. So these would be the marginal revenue products that he's gonna earn from that. We'll assume the ERE, there's no profit here in my example. And then the question is, how much will he pay today right now to get those funds a year from today? And if the interest rate is 25%, the answer is he'll pay $8,000 for the capital that's 10,000 divided by 1.25, right? Discounted by the rate of interest. And so on, 4,000, so you see the prices of the capital goods adjust to the interest rate, not the other way around. It's not that you can suddenly earn a gigantic interest rate because future prices are higher. If future prices are really higher, what's gonna happen is the entrepreneur is gonna bid for the inputs today and drive their prices up. The inputs that can capture those higher prices is just another arbitrage opportunity or a profit opportunity from different price structures, right? And the interest rate, though, is what determines how close together they come. And this is the main point. Okay, so then I'll finish up. That slide, by the way, just reiterates what Dr. Klein talked about. So I'm not gonna go over that. I'll finish with this slide on the sources of market rates of interest. So if we look at any market rate of interest, it could have at least, in principle, four different component part. That is four different causes. One, we've talked about at length, the pure rate of interest. The pure rate of interest then would also generate a yield curve as long as time preferences are more intense for further out into the future satisfactions as long as even later satisfactions are less preferred than even sooner ones, then you would see an upper-soaping yield curve, right? You'd see higher interest rates for longer-term loans and shorter interest rates for shorter-term loans. Then the second source of the market rate of interest is entrepreneurial uncertainty. So every different production process or every grouping of different types of production processes could, in principle, have its own uncertainty associated with it. So in order to give incentive for capitalists to lend into those production processes, it might be that they would command a higher rate of interest to provide compensation to assuming that uncertainty. Then there's the price premium. The price premium comes about in the interest rate because of changes in the money relation. And the changes in particular in the money, well, the last two come about because of changes in the money relation, the particular one that we're talking about here are what are usually called canteon effects, the disparate effects on various prices from an increase in, so let's say, the stock of money. So if the money supply is increased, then some prices will go up sooner and some later. Some prices will go up to a greater extent and some to a lesser extent. So if we have a production process located in the mix of this, where the prices of the output go up sooner and to a greater extent, the net income that accrues to that production process will be greater. And this again would be embedded in a higher rate of return for that production process. Again, this has to be unanticipated. And if everybody anticipates the canteon effects, well, then they bid up the asset prices already and you wouldn't see this. And then there are unanticipated changes in the purchasing power of money. And the same thing, right? It has to be unanticipated. In other words, if most people don't anticipate that the purchasing power of money will be lower in the future, but a couple of people do, then they will only be willing to make lending and borrowing agreements at a higher interest rate that incorporates this declining purchasing power of money in the future. There may be other conditional features that affect interest rates, but these again are considered to be the sort of theoretical ones, right? The theoretical categories. All right, thank you very much for your kind attention.