 So, yesterday we talked about pricing and now we want to make another distinction and continue on to a second topic in pricing. So yesterday we talked only about what we might call cash prices or what in finance would we call spot prices. We were just talking about the immediate actual trade price of goods and factors of production and of course you did this for money as well in the market. You know, what's the actual exchange value of the things that we're buying on the spot in the market. So you go to a restaurant and you pay for lunch and that's the spot price or the cash price. The transaction is completed right there. There's no temporal dimension to it, right? There's no time dimension. You're just taking the money and paying and you're getting the service or the good. So those are the prices that we've talked about so far and the same is true of money. If we want to talk about money's price it too has a spot price so to speak. It has exchange value right now for buying things but then there are prices that have a time dimension to them and that's what we want to talk about now. What about prices that where there isn't a synchronous element to the trade of money and goods? What if one part of the trade is done earlier as opposed to another part of the trade or what if people are agreeing to make trades today at some future date at a price they agree upon today, forward prices, right? What about those? So that's what we want to delve into in this session. And we'll proceed in three steps very similar to what we did on Monday. We'll talk first about some fundamental things. With respect to human action, what do we know just by reflecting on who we are as human beings about the time element in action? We'll start there. And then we'll talk about the two valuations that are made by people with respect to time concerning their actions. And then we'll get to forward prices and then the rate of interest. We won't spend much time with forward prices, but we want to make distinctions, right? We want to see the principles and then make the proper distinctions. And then the third thing we'll do, of course, is give an explication of the theory of interest. We'll lay out the explanation for interest rates. And we'll try to deal with some of the nuances that are involved in this at the end. So we're proceeding from the basic to the more complex elements of this. OK, so the basic principle with respect to the time element in human action is that the different moments in time that we experience as human beings are not homogeneous with respect to our actions. The different moments in time have different conditions for action, at least potentially, different conditions for action that are more or less conducive to the success of our actions. So when we're thinking about the time element in action, we have to take into account the fact that today the conditions for the success of a particular action may be different from the conditions for the success of that action next week. Or right now the conditions for the success of an action might be different from an hour from now, and so on. So even though we have a kind of technical notion of time where the clock is just ticking away, with respect to action, we actually have a different experience of time as human beings. So that's one element of it. The other feature of action with respect to time that we take account of in our actions is just the distinction between sooner and later. As soon as I say that, hopefully it clicks in your mind that, yeah, there's a difference between getting a satisfaction sooner and getting the satisfaction later, regardless of the time element, right? Regardless of the clicking clock time. If we just think about this in the abstract, there's a difference between sooner and later for our actions. And so these are the two basic elements. Now, let me provide one further thing that we know sort of fundamentally about time in action. And then we'll proceed to the particular things that we need in order to build our analysis. And this is that we all realize that action involves a sequence through time of particular steps that we take. And this is what Dr. Rittenauer discussed yesterday in talking about the capital structure. He'll talk more about that today, but about the division of labor, right, in the capital structure. And think about any particular action, like a Monday we talked about having a smartphone. But in order to produce a smartphone, we had to first extract certain raw materials out of nature. And then work on them to produce components of the phone. And then take the components and assemble the phone. And then ship it to the consumer who can use it as a consumer good. So all of the goods that we use in action follow the same kind of process, right? We take labor, we extract a raw material out of nature. We use it to produce some capital good. And then in combination with other capital goods that we produce in a similar way, we eventually reach the attainment of the end, which is to have the consumer good to act and satisfy our preferences. So this time element that exists in action is always present. The start of the action is always sooner than the satisfaction of the end that we attain through that action, right? Okay, now we want to deal in particular, though, with this particular element, which Ludwig von Mises calls the duration of action. This is the key to understanding the two principles of valuation that I mentioned already. And the duration of action can be defined in the following way. Every action has a duration, it has a start. And therefore, there's a time before the action occurs. And then we choose the start of the action. And then the action has this duration, this period of time over which the action is processed in motion by the actor. And then the action has an end point. So there's a time before the action, there's a duration of the action, and then there's a time after the action. And the basic point that I mentioned already is that when we start an action and when we end an action is a choice variable for us. How do we decide when to start an action and when to stop it? And the answer is we decide according to our preferences. This is a decision that we make with respect to how we value the attainment of the end in the action. So this is the first step. And then the second thing to point out about the duration of an action is that the duration of action, because it involves production and consumption, we can subdivide the duration of the action into those two component parts, two time elements. There's a period of production. Again, let's say we want to produce an automobile. Then we start the action by mining iron out of the ground and extracting rubber out of rubber trees and so on and so forth. And then we produce the body steel and then the body fenders for the car. And we take the raw rubber out of the trees and we'd make tires for the car and so on and so forth. Then we would assemble the car. And so there's this period of production. And the period of production, of course, could vary. We could have different technologies which would allow variation of the period of production. It's a choice variable to decide. Do we want a period of production this long? Or do we want a shorter period of production? Or what would happen to the output if we shortened the period of production or lengthened it out? There are automobile companies, for example, still today, that hand make the assembly process. And this undoubtedly takes longer than doing it on the assembly line. So why do they do this? Well, they think it's more valuable. They think they have customers who would like the greater quality or whatever difference in the output exists from engaging in this longer production process. It's a choice variable for us. And you can see that there could be even subcomponents within the period of production. The working time that I've just mentioned is the stages of production. Mining iron, producing steel, making fenders for a car, producing the car. That's the stages of production. But there also might be instances of maturing time. For example, the car, the body panels of the car have to be painted. And in modern factories, auto factories, they have the equipment, automatic computer equipment that sprays the paint or however it's done onto the body panels. But the paint has to cure. You have to wait for a period of time. It's doing nothing. You're just sitting there waiting to take the next step for the paint to cure. So sometimes there's maturing time when the process that we've undertaken has to come to fruition. This may not always be the case, but there are certainly examples of such instances. So that has to be taken into account. Can we adjust that? Do we have different technologies which allow us to have longer, shorter maturing times? And does the maturing time make a difference to the value that we place upon the end product? And then the consumption part of the duration of action is what Mises calls the duration of serviceableness of the good. So once we produce the good, we can use it over and over again, at least in principle. Some goods, of course, are perishable, like food. But there are other goods that are durable. And even sometimes food can be somewhat durable. You can buy a large pizza and eat half of it and refrigerate the other half and so on. It's a choice variable. This is the point. We choose, according to how we value, the different options available to us. And so there's a duration of serviceableness. You could build a car that has a lifespan of 20 years. You could build a car that has a lifespan of five years. You choose between these options according to the way that you value. If you build a cheaply constructed car, then maybe you could get a lower price. And if you build a more durable car, you'd pay a higher price and extend the life. And then you can extend the life of the car, right? Do maintenance and so on, right? This is how we think about, or conceptually, this is a good framework for how we think about our action. There's a duration of serviceableness of the good. OK, so now with this background, we can address these two ways that I mentioned already of valuing our actions with respect to time. And the first to have a name for this, Joe Salerno has suggested, and this is, I think, a very apt name. He's called this the time schedule. This is referring to the timing of action. When do we start the action? When do we stop it? Will the action have more value to us if we do it today, or tomorrow, or next week, or two years from now, or so on and so forth? So this is the idea. We have a timeline from the left to the right. Time is just passing on, right? This is maybe 8 o'clock in the morning today at the left side and 6 o'clock in the evening today at the right side. Or this is 2022 on the left side and 2025 on the right-hand side, right? It depends on our action, how we're thinking about the time frame of it. And we're choosing where to place our action in this stream of time. That we can do, right? And as Mises likes to put it, he has these felicitous phrases in human action where he says, time is an irreversible flux. That is to say, each moment is different with respect to the application of action, the success of the action that we would take in different moments of time. Moments of time are not interchangeable. They pass by in a certain order. And this order has to do with their ability, the circumstances in that moment, the ability of those circumstances to be conducive to the success of our action. And so this is the time schedule then. We're going to choose when to schedule an action with respect to its suitability or achievement of the action within the frame of time when it's appropriate, when we deem it appropriate to engage in the action. So this is the idea. We could put this then in terms that we used on Monday. We could talk about economizing our action with respect to time. And here we see the principle is, since time is just passing by, it's this irreversible flux that just moves, right? We can't do anything about that. That's what it means to be a temporal being. We're in the stream of time. And it's simply moving forward. And therefore, we can't allocate time in the way that we allocate our labor or we allocate our money to different ends. We simply can't do it. We can't accumulate time and then apply it to a particular end, right? We don't accumulate a day and then apply it to an end like we accumulate money and then use it to buy a good. But we can't economize our action with respect to time. We can choose when to take an action with respect to what we think the value of the action will be if we take it at that moment in time as opposed to another. Just to give you a mundane example of this. Well, it's not mundane to me, but it's a kind of a mundane example. My wife's birthday is August 18. And so if we're, let's say I take her to a nice dinner at a nice restaurant in Pittsburgh, Pennsylvania, well, it would have more value to us if I do it on her birthday. If I did it on September 1, that would not have the same value to us as if I do it on her birthday. That's what we're talking about. There's a timing, right? We can economize that action by taking it on the day that we think it would be the most valuable to us. And then that's a general principle that is at least possible for us to do with any action. Again, maybe sometimes we're engaged in an action where it's incidental as to when we take it and we don't pay much attention to this. But in principle, this is always in play, right? That's the point. Now, if it's true, so far as we've said, if this is true, then it would also be the case that goods would have different value. The same good would have a different value at different moments in time. At least potentially. Because the good is just getting its value imputed to it from the value of the consumptive end that it's satisfying. So here, let me switch examples just again to use a kind of mundane example for this. People are often doing things like, especially nowadays, doing things like trying to be more self-sufficient in their food production. So we have friends from church who live on a farm. And they're like 90% self-sufficient. They grow 90% of their own food. And one of the things they do, of course, in order to accomplish this, since the seasons, the production seasons don't correspond to the consumption patterns, is they find ways of storing what they produced. So they'll produce something and then can it or preserve it, somehow freeze it, or they'll butcher a cow and then freeze the meat. And then they'll eat the meat over the winter. They'll thaw it out and eat the meat. And OK, so the point of that example is that if they butcher a cow and they've got whatever, 100 pounds of meat, the marginal utility of a pound of hamburger at that point to them is very low. Because their stock of meat is very large. But the marginal utility that they would anticipate for that pound of hamburger in the cold winter days of February is very high. And so what they want to do is transfer the consumption of the, they want to store the meat in a way that they can transfer the consumption of the good to where the value of the good is greater. And so that's what they're doing, right? And again, this, in principle, could be done in actions, more broadly speaking. So the good itself, then, can be allocated, not just the action, right, but the good itself could be allocated with respect to the differing value at different moments in time that are anticipated by people. And this is where we get, then, to forward prices. So let me switch my example again to a market case, because pricing is a phenomenon of the market. And we've just been talking about the personal economy in my examples. Let's say we look at oil markets. So there's spot prices for oil. And there are forward prices for oil. And forward prices come into existence, as it says on the slide, when people today who are buying and selling oil, right there, it's an oil producer and a refinery company, entrepreneur. So the producing company's selling and the refining company's buying the oil, and then using it as an input to produce gasoline and other consumable products. So the refining company and the oil producing company could agree on spot transactions, cash transactions today, but they could also agree on a trade in the future at some date in the future. And that would be a, or at least one instance of this would be a forward transaction, where the two parties simply make an agreement. They don't trade anything today. They just make an agreement to trade the good at a price they stipulate today at some date in the future. So they say, six months from now, the oil producing company will sell 10,000 barrels of oil to the oil refining company at a price of $90 a barrel. They make that agreement today. That price is called a forward price. And forward prices are the source of all derivative contracts, which we won't talk about some more advanced topic. The point is, suppose then that people are making forward contracts, these oil traders are making forward contracts. And the price, the forward contract price is $200 a barrel, six months from today. And the spot price today is $100 a barrel. Well, then, this provides economic calculation possibilities, profit possibilities, for arbitraging that is transferring the oil from the present moment into the future. So if I'm an oil producing company, I've got a big storage facility, and I can sell the barrel of oil for $100 right now, or six months from now, I can get somebody to agree to pay $200 a barrel. I'm going to do that. I'm going to sell forward, right? So as the supply of forward traded oil increases, the forward price would fall. And as the supply is restricted from being sold in the spot market, the spot price would rise until those two prices came roughly together. This is how the market works, right? This improves the allocation of the good, because the good is anticipated to be more valuable in the future. We need to conserve it now and transfer its use to the future. This is what markets are doing, forward markets are doing, right? OK, well, having gone through that, we'll leave that issue behind. So again, our main task is to talk not about forward transactions and forward prices, but about the interest rate. And so part of my reason for going over forward prices is to clearly show you that interest rates are different. They're based upon an entirely different element of time in action, the second element of time that we mentioned, about sooner and later. They have nothing per se to do with forward prices. That is with the timing schedule of things. They have to do only with sooner and later. And we'll see why as we go through this discussion. OK, so this is the next step, right? We want to move now to the second way in which we value action with respect to time. And here, we're concerned with this duration. We're concerned with the sooner and later aspects of the duration of a particular action. So now what we're saying is, suppose that we have action already set in the proper time schedule. So this action that I'm displaying on the slide is already being taken or placed in the time frame that the actor thinks is most economizing. So we've taken that problem off the table. We're not talking about that anymore. We're saying suppose the action is already placed in the proper time to get the most value. Then what about the duration of the action? What about the start and the finish of the action, right? And the answer to this question is that people will always prefer to start the duration of serviceableness that is the satisfaction that they get from the action sooner. That principle is called time preference. So there's a time schedule in action. How do I time my action? When do I decide to take an action? There's time preference. For any action that I've decided to take at the best time, there's a period of production, and there's a duration of serviceableness. And people always prefer to shrink the period of production. In the abstract, you always prefer to have a shorter period of production. You always prefer, in other words, to start the consumption, the satisfaction of the action, closer to the start of the action. Notice it might be that a person has economized this action by saying, I want the duration of serviceableness to start here. I want to have the consumer good on Friday. They say that. Why Friday? Well, because that's what they think is the most valuable point at which to have the duration of serviceableness of the good in their hands, right, using it for consumption, as opposed to next Monday, or a month from now, or whatever. Then time preference would say a person would always prefer to have the start of the action move to the right. They prefer to shrink the period of production, right? If it costs them, in the production process, if it costs $1,000 to produce the good, and the production starts a week ago, and then you produce the good and deliver it to the consumer on Friday of this week, it would be way preferable for the producer not to expend the $1,000 two weeks prior, but only one week prior. It would be even better if you could expend the $1,000 just a minute before delivering the good. That would be even better. That's what time preference says. That's the principle of time preference. Mises, again, has a very felicitous phrase that he uses for this. He says, time preference means that there is disutility in waiting. There's a disutility in starting the production and having to wait until the good is produced so that you can get the satisfaction of the consumer good, that people don't want this. They want to shrink this. This is a aspect of action that they want to minimize. Now, whether or not a person can minimize the period of production, we've already pointed out, it depends upon the technological possibilities, it depends upon the conditions of their environment, right? Whether there are alternatives which would allow them to shrink the period of production. This is an open question. What time preference is saying is that people would always prefer the shortest, most productive production process possible. That's what it's saying, right? They prefer to shrink the period of production. Okay, so that's the basic idea. Now, sometimes you'll see the definition this way and so once again, there's a lot of terminological, I'll say ambiguity, a lot of terminological nuance and difficulty in all of the language that's used in this field, but sometimes you'll see the definition written this way that a satisfaction is preferred sooner as opposed to later. A given satisfaction is always preferred sooner. Now, that's not quite as crystal clear as Mises' notion of the disutility of waiting. But it's a shorthand, right? A given satisfaction is always preferred sooner from the start of the action, it's always preferred sooner as opposed to later. The other thing to emphasize here, by the way, you would also see another phrase which I'm not gonna talk about anymore. I don't even have it on the slide. I just wanna mention it in passing. Sometimes you'll see the phrase, present goods are preferred to future goods of the same goods, right? Present goods are preferred to those goods in the future and that's the worst way to say this. That's the most ambiguous way to give a definition of time preference. But you can see why that would be so. You'd see the sense of that, right? But in any case, I'm setting that aside, maybe we can have a discussion later if you're interested in all of that. The thing I wanna emphasize here is that time preference is a logical necessity of human action because we're temporal beings. When we talk about the existence of time preference, we're not talking about psychology. We're not talking about physiological needs or things like this. Physiological conditions of the human body or psychological conditions of the human mind could alter a person's rate of time preference. It could make them more desirous of having present gratification or less desirous. But it doesn't create, it's not the origin of time preference. Time preference originates because we're temporal beings. Just like scarcity originates because we're finite beings. It's not that this is a psychological condition that we could overcome if we just put our minds to it or something. Okay, so this is the definition. Now there are few implications that we wanna highlight and then we can get to the last topic which is the explanation of the rate of interest. First, as we've alluded to this already, time preferences that people have will determine the economizing inter-temporal allocation of their production and consumption. So here's the terminology. If people have low time preference, this means that their intensity of desire for sooner satisfaction is less. And if people have high time preference, we're referring to people whose intensity for sooner satisfaction is more intense, greater. So you can see that with this terminology, you can see that if people have lower time preferences then they're going to be more willing to commit to longer production processes because they're less urgently desiring the beginning of the duration of servicefulness. They're more willing to save and invest and to extend production processes out in time, inter-temporally. How far they extend production processes depends upon their rate of time preference. How high and low person's time preferences happen to be. And remember, what economic analysis is showing us is that each of us as individuals will have our own personal time preference. And then when we integrate our personal economies in the market, the market will collaborate all of our, we'll be able to integrate all of our personal economies and we'll get market prices as a result. So we get a kind of social result from the integration of our personal economies in prices of consumer goods, prices of the factors of production and the interest rate. And the interest rate then will provide the necessary feature for economic calculation for entrepreneurs to be able to say, oh, interest rates have gone down from lowering time preferences and now we can invest in this project. It's financially feasible now to invest in this project. Whereas before with the higher interest rate, we couldn't justify this on the basis of the profitability of the investment or the equity conditions of the asset that we're buying. So this is the principle. And then what we wanna show, the main thing we wanna show of course is that time preferences determine what we'll call the pure rate of interest. I mentioned already there's some nuances involved in all of this that we'll hopefully get to at the end. But we're just talking about the rate of interest that would emerge on a market if the only factor that influenced interest rates was time preference. This is what Rothbard calls the pure rate of interest. So we'll deal with that first and then again if we get to the material at the end, we'll add the nuances on. There are other causal factors that would enter into any particular market rate of interest. But the pure rate of interest is always expressed as a trade of present money for future money. It's the premium that we place on present money over future money. When we're engaged in an exchange, this inter-temporal exchange, right? We have someone who lends present money. We have a borrower who obtains the present money, he's demanding the present money. And the borrower will pay a premium to the lender. The interest rate will be positive. The pure rate of interest will be positive. And the reason the pure rate of interest rate is positive is because of time preference. The reason that this trade is done in money and not in goods, and we'll elaborate a little bit more on this upcoming, is because that allows it to be integrated into economic calculation. All other prices are in money too, right? And not in goods. And so to have the interest rate expressed in money allows for inter-temporal, more accurate inter-temporal appraisement that entrepreneurs can do. And again, we'll elaborate on that particular point in a minute. So this is the way where the theory, our explanation runs out for the theory of interest. So the top row of this slide, I've just reproduced what we talked about on Monday for consumer goods, right? If we have consumer goods, we just have people's preferences. We have some reverse preferences between the buyer and the seller, right? The buyer prefers the good relative to the money price offer. The seller prefers receive the money and give up the good. And then we have a market with lots of people and the price emerges in this market where the market clears so that everyone who wants to buy can find a seller and everyone who wants to sell can find a buyer. And so we get the maximum degree of economizing movement of goods and satisfaction among people in the market. We get the prices of consumer goods. So the interest rate, the pure rate of interest emerges in the same way. We have people with different preferences, time preferences. We have some people with lower time preference, some people with higher time preference. They can meet and find this out and then they can negotiate a mutually advantageous exchange for lending and borrowing and that rate of interest would emerge. Again, we're just dealing with this pure rate of interest that rate of interest would emerge through their negotiation about what they would find acceptable. And I'll give an example here in a minute. And so it's the exact same logic, right? There isn't any difference here. We don't need a separate way of thinking about the interest rate in order to explain it. Now let's get to this question that I mentioned about the money being used in the trade. So if people tried to make loans in goods, let's say they made loans in men's dress shoes or bags of apples or something of the sort and not money, then the result of the market value in the future of the goods would have two components to it, right? It would have this rate of interest that people are trying to obtain and it would have this timing element, right? It would have this difference, let's say in a bag of apples if suddenly people come to believe that all the apples are tainted and the demand six months from now falls to zero. But money doesn't face the different conditions of consumption and production, right? Money is just the medium of exchange. And as long as money continues to perform as the medium of exchange, well then it can't suffer from the vagaries of different demands for consumer goods or producer goods which makes it more suitable for lending and borrowing. It isolates the lenders and the borrowers from the vagaries of the different demands for goods that are occurring over time. Or to put it as I did before, and again we wanna show this more strictly. Money performs the function of economic calculation for all different dimensions in which economic calculation is relevant. Money provides economic calculation across persons regardless of their preferences for things, across geographic locations, across space and across all goods, right? And also across time. So it's an integrated system of economic calculation. That's why money is used in lending and borrowing. Now let's go to some of the details of this. So here's just a simple case just like we did on Monday of a simple case of the trade of consumer good where we can have a mutually advantageous trade between two persons who have different preferences for different time preferences, preferences inter-temporary for money. So the person on the left, person A, has lower time preference than person B. Person A's premium or time preference interest rate would be a minimum of 10%, right? Person A is willing to give up $1,000 today to get $1,100 in one year. So the premium that they placed upon $1,000 today is $100. That's the minimum that they're willing to give up in order to trade away the thousand in the present to get $1,100 in a year. But person B has higher time preference. Person B's premium is $300. Person B would only lend $1,000 today if someone were to offer $300 as a premium. And therefore person B could make an offer to borrow from person A at any interest rate of 29% or below. So $1,290 would be the maximum buying price for obtaining present money from person B and $1,100 is the minimum selling price for person A to lend. So they could find a mutually advantageous pure interest rate somewhere between 10% and 29%. It's just a matter of them negotiating an interest rate, right? So that's where the pure rate of interest comes from. It comes from the dis-consideration. Then we have a market. So again, this is no different than our discussion of consumer goods prices on Monday. And what we're depicting on the market, remember, is point A, we're just looking at the empirical evidence. We're just looking out into a market and we're seeing the rate of interest on some instrument, financial instrument. And the amount traded, we're just looking at that and we're saying, why is it that the interest rate on that financial instrument on this day, under these conditions, happens to be 2%? Why isn't it 5% or why isn't it 1%? And the answer is, if it were 5% under the conditions under which it occurs, if it were 5%, there would be excess supply of loan of a credit, right, or present money lent. There would be more people coming into the market to lend, but there would be fewer people who would want to borrow at that higher rate of interest. And so that interest rate never occurs, right? The demand and supply curves, remember, are just conceptual tools of analysis. The real data is just a single intersection point. And in like manner, the interest rate can't be below that because there'd be excess demand. There'd be borrowers at that low interest rate who couldn't find lenders. And therefore, they would just bid up the interest rate to be able to, the ones that are more eager would bid up the interest rate in order to borrow, right? And this is how the market is always adapting to the preferences of people to make sure, or at least to bring about as close as possible, the full mutual advantage of trade. So this is extending the analysis to the market. So we see that time preferences then determine the pure rate of interest, and then the amount of present money lent and borrowed. And then just like with consumer goods, the process of the market trade will allocate the present money to the borrowers that value it the most, right? The borrowers that have the highest time preference, the most urgent use for present money will obtain the loans, and those with less urgent uses will not. And in similar fashion, those people with lowest time preference who are more eager to make the loans will be able to make the loans, and those with higher time preference will be unable to make the, they'll be cut out of the market by the lower time preference suppliers. Now, let me give you this further point about why it is that economic calculation integrates the trade of present money for future money, whereas it does, it would not integrate the trade of present goods for future goods, but only money for, present money for future money. And this is just a simple fact that comes from the lending and borrowing process. So I've just reproduced a simple example where the amount of future money that a person could acquire by lending $1,000 on interest at 10% for one period is $1,100. This is called compounding, right? And you do the compounding by taking the $1,000, the future value, right? You take the $1,000 and you multiply it by the term one plus the rate of interest. That gives you the principal back of $1,000 and the interest payment of $100. Then, if we can just reverse the calculation, right? What if somebody then had an agreement to be paid $1,100 in a year? What would be the present value? What would be the equivalent amount of present money that would accumulate into $1,100 in one year? Well, it's $1,000, right? The present value is just found by reversing the calculation, taking the future sum and dividing, that is discounting or dividing by this interest rate term, one plus the rate of interest. So, notice what the time market, as we call it, does, is equate present money with future money. There's simply alternatives that the lenders and the borrowers can have. You can have either $1,000 in your hand or you can have $1,100 in a year. They're equivalent, right? And therefore, the economic calculation is accurate if people are basing it upon the 10% rate of interest because that's the inter-temporal valuation that people have made in the market. So, this is the idea. Now, the other thing we wanna do is quickly subdivide the time market just to see, again, the full extent of the argument that we're making here. So, the time market for economic analysis purposes can be broken into these two sub-components. All the exchange of present money for future money then would either be in the credit markets. This is what we mentioned before, where the transaction that people make is not fulfilled until the future. So, one party fulfills their part of the transaction sooner and another party later. So, people are just making loans, right? Contract loans. So, this is called the credit market. And then in the credit market, they're consumer loans and producer loans. The entrepreneurs can borrow in the credit markets, too. And then use the money to buy producer goods and consumers can borrow in the credit markets and use the money to buy consumer goods. But this will be integrated with the capital structure because in the capital structure, even though it's not part of the credit markets, the entrepreneurs are fronting money to the owners of the factors of production. They're paying money sooner to get the factors of production services. Then they're producing a good and they're selling the good and getting their payoff later, right? So, there's a inter-temporal dimension to this. And they'll judge the, you know, the entrepreneurs investing in these input purchases will judge the suitability of the purchase not based just upon factor prices, but based upon the rate of interest. And so, this is the key, right? Just as a side point, neoclassical economists tend to not include the capital structure as part of their interest rate analysis, right? They have a loanable funds market where the interest rate is determined. But this is inadequate. This is not the full story. The two will be in fact integrated. That is to say, if we're still thinking about the pure rate of interest, there'll be a uniform pure rate of interest across the whole time market, regardless of what type of loan is being engaged in. There will be differences based on non-time preference causal factors between different loan interest rates. But there's a fundamental pure rate of interest for a given time structure, let's say one year or five years, that will be uniform. Because if not, you would have something like this. Suppose a pure rate of interest were low in the consumer loan market and high in the capital structure, point A in the two diagrams. Well, then the lenders would simply arbitrage the funds. They would simply withdraw the funds from the consumer loans or when they're paid off, they wouldn't renew them. And they'd make loans into the capital structure. And then the interest rates would come together. So this process is continuously going on in the market. The pure rate of interest is continually reasserting itself as uniform across all these different loanable activities. And I'll end with this other element of how the interest rate, the pure rate of interest is. What impact it has on market activity. And this is to look at not the big subdivisions of the time market, but to look at just different production processes. So suppose that we had this case where we had a huge difference in the rate of return, the interest rate of return in two different investable projects. Smartphones could earn 7.5% interest and tablet investment would only earn 2.5% interest. Well, that could also could not persist, right? The capitalist entrepreneurs would then sell assets out of the tablet investments, the specific assets and tablet investments, right? They'd sell out of these, lowering their prices and thus increasing the interest return on those investments. And they would buy into smartphone assets and that would push those asset prices down and lower the rate of return on smartphone investment. And this would continue until those investment returns came roughly together, right? The pure rate of interest, again, and there may be other differences that cause rates of return to be different, right? But we're not gonna get to those particular points. So the bottom line on this then is that neither physical productivity nor value productivity of assets affects the pure rate of interest. The pure rate of interest is independent from those things. The pure rate of interest is simply the discount that people place upon whatever they, entrepreneurs, whatever they anticipate the physical and value productivity of the asset to be. So if a new technology comes into existence and is very productive of value, it will have a very high price, but its discounted value will still be the same as the discounted value of any other asset, right? It's the price of the asset that embodies its physical and value productivity, not the rate of interest. Okay, thank you for your kind attention.