 In this talk, we'll cover the topic of subjective value and market prices. In particular, we'll talk about the role of subjective value in human action, covering the complete theory of what Ludwig von Mises calls valuation as a system for decision-making about the use of means to attain ends. And then we'll do the main task, which is to show the relationship between subjective valuations that we all have and act upon and prices in the market. And then the final thing that we'll mention, and this is the topic of a later talk also by Dr. Salerno on economic calculation, we'll mention the role of prices in what Ludwig von Mises calls appraisement, the use of money prices in decision-making about the use of means to attain ends in the social setting. So that's the plan. Now let's begin with, as we always do in the Austrian tradition, we begin with what Murray Rothbard called reflective facts about human action. Facts about human action that we ascertain by reflecting as human beings upon action. We just think about the logic of action. And of course, the first thing we hit upon is just the definition of human action. Human action is purposeful behavior. Human action is motivated behavior on the part of a person to attain an end. It has the goal of the satisfaction of attaining the end. Another thing we recognize right away about human action is that having an end does not constitute action contrary to our lefty friends as Dr. Woods was pointing out last night. We can't just think of having an end and have it accomplish. We can't just stamp our feet and there are no more poor people in the world. This doesn't happen. We have to act with the use of means. We have to perceive the objects in the world and then discover their cause and effect connection in action to the attainment of our ends. Human action is the human mind organizing the elements of the external world systematically in action to attain ends. Once we see the ends means character of action, we see right away the scarcity of means. We understand, again, just by introspection that we're finite beings, we understand through our past actions that when we act, we don't fully attain our ends and we don't attain our ends permanently through a single action, that the means are not capable of creating bliss where no action is ever, then again, necessary. We have unmet ends and to meet these ends or satisfy these ends, we must apply the means as we perceive them to the attainment of these ends. This is where we then get to the central organizing principle of human action in the Austrian view. This is the principle that's called economizing. This is what brings order and a systematic character to human action. All human action is economizing because means are scarce. We have to choose which ends out of the competing ones we'll pursue and because it's possible for any particular end to be attained by different combinations of means, we have to choose which combination of means to apply to any given end that we choose. We do this according to our purposes or as, again, Luriva Mises would say, we do this according to the way that we value the alternatives. So economizing is choosing to attain ends that we value more highly than other ends with given means and attaining each end with a set of means that we value less highly. In other words, we try to achieve the end with the low-cost method of action. And this then is, we're in a position now to talk about the idea of subjectivity in action and choice when we're choosing, making these choices, we're valuing the alternatives. We're just judging in our minds, our own personal assessment in our own minds of what the satisfaction would be of attaining one end versus another or applying one set of means to attain an end as opposed to an alternative set of means. Economizing then is always choosing the more valuable alternative. We always choose the end that we find more valuable, we set aside the end we find less valuable. We have as, again, the term in the literature would have it, we have a preference, we have a value ranking as the basis of our choice. And as Murray Rothbard is, want to emphasize, this preference that we have as human beings in choosing and acting is always logically consistent with our actions. This is what he calls demonstrated preference. So we know another person's preference when they act, they demonstrate their preference because action is always choosing the more valuable alternative and setting aside the alternative that's less valuable. Now since value is a judgment of the human mind, it has no extensive property. And since it lacks an extensive property, we can't define a unit of subjective value. We cannot measure subjective value. It's not a substance to be measured. It's just a judgment of our mind. And since there is no common unit that we could use for assessing the subjective value that I get from doing an action or the subjective value that you get from doing an action, we cannot make interpersonal comparisons of our subjective valuations. We can't say whether one person values one thing more or less than another person values another thing. This just is scientifically not possible because of the nature of the subjectivity of value. Hopefully you can see right away this poses a gigantic problem for organizing social production, right? We want to organize social production and division of labor to get the greater productivity of the division of labor. But we can't really know as producers in the division of labor producing for the consumptive satisfaction of other people what the greatest value of different lines of production that we might engage in would be. We can't just sort of ask people, you know, what do you subjectively value and then produce according to surveys or something of the sort or have votes, you know? We can't democratize this because we're not measuring subjective value, right? We're not getting an indication of the intensity of subjective value through these makeshifts. As we'll see, of course, this is where the whole system of market pricing comes in. Now I want to mention as an aside, there's another element of valuing that needs to be mentioned just for additional study that you would do, more advanced study that you'd done on these questions. And this is the issue of constancy. So we also find, again, just by reflection, just by thinking about our own action, we find that our subjective valuations are not constant with respect to the means that we might apply to the attainment of our ends. They don't stay constant over time. They're not the same from one person to another person. There's no fixed quantitative relationship between means, the use of means in the attainment of the satisfaction of the end. This is in flux as far as we know. This is open to change. The implication of this, of course, is that we can't think of value or utility in a functional way. We can't make a mathematical function out of utility, right? Because we have no constants for the functional expression. All we have are variables and no constants. Now let's go on to the next step. This is the idea of value imputation. Okay, so the Austrians say value is subjective. It's a state of mind. But we also know that, at least in common discourse, we make the claim that objects have value. So I value my iPhone, I value my 2007 Honda Accord, I value my house, and so on. They have value to me. So how does that happen? Where does that value come from? So the Austrian answer to this is in the first row of our slide, which is that value is imputed or given to consumer goods by the person who's acting with the consumer good to attain ends. So the arrow of causality moves from our mind to the consumer good. I value my iPhone subjectively because I get satisfaction from employing it to attain my ends. That's where its value comes from, to me. It's this connection between means and ends, right? This claim of the cause and effect chain here preserves the basic definition of human action. The human action is applying means to attain ends. It's ends that are valuable, and means then have value only as aids to attain the end. Then we can take the other step of the causal chain, the connection between consumer goods and producer goods. So value then would be imputed from the consumer good to the producer goods, by which the consumer good can be constructed. This again preserves the cause and effect nature of human action. It must proceed in this way to preserve the cause and effect structure of things. We can't, alternatively, we can't think of the connection as reversing the cause and effect movement, right? We can't think that producer goods have value in and of themselves, like the labor theory of value, of Karl Marx. And then through production, they transmit this value to the consumer good, and then somehow our mind ascends to, you know, gives a scent to this value of the consumer good. If we are to hold the view that human action is applying means to attain ends, and we understand reflectively what that means, then we have to reject this theory out of hand, right? This cannot be true. The value of producer good can never be separate from its usefulness as a means to attain ends in human action. The same thing would be true of an eclectic theory that claims that the consumer goods price or value is mutually determined by our mind and independently the value of the producer goods. Again, this doesn't work, right? Probably as a theory, it could not be the case. It could possibly be the case that there's some independent value of producer goods independent from human action. The argument is no, no, no, it must be dependent upon the aid that the producer goods gives to the production of the consumer good, and then the satisfaction of the end that's attained by the consumer good. By the way, you may recognize this, some of you studied some economics, may recognize these different patterns, right? The bottom one is the neoclassical theory. It's the Alfred Marshall scissors theory, right? Demand to subjective value, supply is cost of production. But notice it depends upon giving up in order to make this acceptable logically. You have to give up the whole notion that there's a cause and effect structure of action. You have to instead claim that there's something like mutual determination. Everything is synchronously, mutually determined. Now that raises one last point that we'll mention here, and again these are topics that will be covered in more depth later in the week. It may be true, hopefully we all accept this, right? It may be true that there's a logical flow from the mind to producer goods. That's the flow of logic. But the chronological flow does in fact move the other way around, right? In order to consume, I have to have already produced the good. So the chronology is I apply my producer goods to make something and then I use the thing that I make to satisfy my end. So there's logic flows one way, chronology flows the other. How are these reconciled then in the Austrian view? In the neoclassical view, you don't have to reconcile these because you're just assuming mutual determination. So there's no cause and effect, so there's no problem. Well, in the Austrian view, we reconcile this by, again, reflectively understanding the role of entrepreneurial anticipations in human action. So the mind anticipates the satisfaction that will accrue to a person who's about to begin to apply producer goods to make consumer goods to satisfy ends. So it's that that binds the whole structure together, entrepreneurial expectations or anticipations or entrepreneurial foresight, however you want to say this. Okay, so now having covered that basic ground, let's move on to the laws of utility. And here we're going to take an example from every Austrian's friend, Robinson Caruso. Now, it's true that Robinson Caruso is just an imaginary friend, but that's okay. He's very helpful nonetheless, right? You can learn a lot from our imaginary friend, Robinson Caruso. So let me set this up for you. So we have Robinson Caruso and he's on his island stranded all alone. And he finds, you know, using his human skills of perception and intellect and so on. So forth, he discovers consumable things that he can produce. He can gather up coconuts, they're coconut trees and he can gather up the coconuts. And they're berry bushes on the island and he can pick berries. He finds they're edible and he watches to see animals eating them, make sure they're not poisonous or whatever. And so he can produce those and consume them. So we'll limit his consumer goods to these two. And then, of course, he's going to make judgments of value with respect to what he prefers. Does he prefer the coconuts? What uses can he, you know, ends can he attain? What uses can he put them to? How about the berries? You know, what ends can he attain? What would he do with them and so on? And so my example, he would break open coconuts and drink the coconut milk or sometimes maybe he would break open the coconuts and mash the fibers, right? And to, you know, eat the mix. And then with berries, he again could eat the berries. He could just eat them or maybe again for a variety, he would mash them up and drink the berry juice. Maybe he creates a trap for a small game and he uses the berries as bait, you know, to catch whatever rabbits or squirtles or whatever is on the island. Something like this. And then we ask the question logically, are there any laws of utility? Are there any laws of consumption? And we use Robinson Caruso again to simplify the situation so we can expose these laws if there are any. And obviously the answer is yes, there are laws of utility, right? They're laws of consumption. And the first law of consumption says that the larger the stock of a good, the more units of a good a person has, the lower the value of the marginal unit. So if a person has, you know, if I have 10 iPhones, then the value I place on any one of them is lower than if I just have two. So that's the first law of utility, right? The law of diminishing marginal utility. Now again, there's a technical point that needs to be made in order to see the logic of this law that there are no violations of this. It's actually a law of logic and it can't be contradicted or contravened. And this is the notion of the unit. So in my example, the first ranked thing that Caruso wants to do, the preferred thing, most preferred thing that he wants to do, is gather up two coconuts, break them and drink the coconut milk. This is because he is chosen as a human being, the unit of drinking coconut milk, two coconuts. He doesn't want to drink the coconut milk of one coconut. That doesn't satisfy him fully. He wants two, not three, not four. So in every human action, the person acting chooses the unit. The unit is not limited to the technical units that exist in nature or that we manufacture, right? I filled up my car with gasoline this morning. The technical unit is a gallon. So it's, right, it's doled out in gallons and priced in gallons and so on and so forth. I didn't buy a gallon. I bought the amount I wanted, which was what, I don't remember what, how much it was, six gallons or whatever. I wanted to fill my tank, so I bought whatever was, that's my unit. That's my chosen amount that I bought. So in every action, this is the case, right? The unit is chosen. It's a choice variable. And so this is what Caruso does. Now it follows logically that if he fully satisfies his drinking end with two coconuts, if instead he had four coconuts, another unit, he would have to use the second two coconuts for some other end, right? And by choosing drinking, he's demonstrated that that's more valuable to him than his second ranked end. His second ranked end is eating, you know, mashing it up and eating. So the preference rank here illustrates this law of utility. The same for the berries. So the ranking of the berries in the same order of diminishing marginal utility. Now, of course, it could be the case that a person doesn't act in the face of a real, as Barry Rothbard called them, equally serviceable units. It might be that we just act with one unit, right? I only have one house and so on and not thinking of other units. That's why we need economic theory. That's why our imaginary friend is helpful because he allows us to do useful imaginary constructs, thought experiments, right, of what must in fact be the logic of all action. The second law of utility, of course, is that a larger stock of a good is preferred to a smaller stock. So as long as the object is a good, as long as it's a scarce mean, having more of it is preferable to having less. Of course, Carissa could have so many coconuts that it wasn't a good to him anymore, in which case the law of utility doesn't apply because the law applies only to goods, only to scarce means. But given that, yes, it's true that having more of a good is preferable to having less. This is the second law of utility. And then the last thing that's illustrated here by Carissa is the allocation of his consumption. He's got these two different goods that he can use for consumption. The marginal utility, the rank order of each of these units is given on the preference rank. And so Carissa would prioritize his action. The first thing he would do is drink the coconut. When I say first thing, I mean logically, he doesn't have to do that the first thing when he wakes up in the morning, right? The timing of things, the chronology of his action is something, again, we'll talk about later in the week, in the lecture on time preference. We'll talk about the temporal and intertemporal allocation of things. Here we're just speaking logically. This is what he does first. But then once he does that, the marginal utility of the first unit of berries is the second most highest ranked thing, right? He doesn't act with coconuts, again, for quite a while because with six coconuts, he can do quite a few of his, I mean with the two coconuts, he's satisfied his most valued end. And so it becomes clear then that the way in which Carissa or any of us balances our consumption is to continue using each particular good until there are no more value differences at the margin. Between shifting between using berries, the fourth unit of berries, or the second unit of coconuts. We don't see any value in shifting between the two. We don't see a value difference where we could give up one thing of less value and get something else of greater value. Those have been exhausted by our allocation. Okay, now let's do production real quickly with Carissa. And then we have the full picture for valuing. And so these are schedules of the marginal physical product of labor in coconut gathering and berry picking. So MPP, sub-L for marginal physical product of labor. And these schedules exhibit the law of returns. And once again, we think of this in a logical way. We need to stipulate the conditions under which the logic falls out, right? And then see in the real world where these stipulations apply, how we apply them to the real world. So it's the same thing here. We have our imaginary construct. And the idea would be something like this. Carissa has the natural resources of the island. They're coconut trees and they're berry bushes. And so he can apply his labor to a given set of what we'll call complementary factors of production. In this case, just natural resources. He has no capital goods to aid his production. What he'll find, of course, is that the complementary factors of production have diverse production possibilities. This would be the typical case, right? In other words, if he searches around the island for coconuts, what he'll find is the following. There's some usable coconuts on the ground. They've already ripened and fallen out of the tree. There's some usable coconuts up in short coconut trees that he can climb fairly readily and get. Some of the short coconut trees are robust. Lots of coconuts at the top. Some sparse. They're taller coconut trees, harder to get to, right? And so on. So if Carissa's intention is to produce coconuts, if that's the only goal he has in mind, then, of course, economizing means that he's going to pick up coconuts on the ground first. He's going to maximize his marginal physical product. And when he does that, he gets six coconuts. But once he does that, then, that production possibility is exhausted. Now he has to go to something else. It's less physically productive. So this is the typical case. Of course, in the real world, we could have increasing returns and constant returns and diminishing returns to different production processes. We could have a more robust set of possibilities. But the law of return says, eventually, we always get decreasing returns, right? Or strictly speaking, it says, there's an optimal amount of a variable input with given complementary factors of production. Optimal amount means a maximum output per unit of the variable input. That must always be the case. That's a law of production. There can't be any exceptions to this. There can't be any exceptions to this because in our development of the law, we fix the complementary factors of production. They're given. And so since they're finite, material finite things, their productive ability is finite and can be exhausted. If we just add more and more of the variable input, we eventually exhaust it. And so this is the idea. So the same thing would be true of berries, right? He's got more lush berry bushes and spars. He's got berry bushes closer to his shelter and farther away where he has transportation costs to engage in production and so on. So he faces this diminishing marginal physical product. And we would face this, all of us in our social life, in the division of labor, face the same principle of the law of returns. And then the question is, well, given this technical feature of production, how will Caruso value his labor in the different endeavors? And of course he'll value it according to the ends that he can satisfy with the product produced by the labor and the amount of the product produced. This is what we call the marginal value product of his labor. So the marginal value product is just the marginal utility of the output he produces with a unit of his input. So if one unit of his labor produces six coconuts, the marginal value product of that marginal physical product is the subjective value that Caruso places on the ends that he can attain with the six coconuts. And this is how he ranks things. He ranks the first unit of his labor, most valuable in coconuts, but then once he accomplishes that, the marginal value product of the second unit of labor in coconuts would go way down. Six coconuts is enough to satisfy most of his highly valued ends. And when he applies another unit of labor to coconut gathering, he gets fewer than six. So now the second most highly valued use for him is berry picking. Picks berries, gets two quarts of berries, satisfies his eating end for berries. Once that's satisfied though, the second unit of labor applied to berry picking has less value to him. Marginal value product goes down. The marginal utility goes down and the marginal physical product both go down. So this would be the typical case, right, of allocating labor. And once again, Caruso does the same thing that all human beings do. He's got a choice between two alternatives, the best one and the next best. He chooses the best. When he satisfies the best, it drops out. And then he's got the next best. If he's applying labor across different production activities, he's got these different marginal value products, coconuts appear, berries down here. He applies the coconuts first, then to apply more labor to coconuts, the marginal value product goes way down. So now he logically shifts the berries. And so he's gonna do the same thing that he did in consumption. He's going to balance the marginal value product of his labor across all the different production activity that he can engage in. He's going to allocate his labor in such a way that he doesn't see that there's any value difference or gain to be had by shifting his labor away from one thing and towards another. Nothing to be gained, right? And this again is how valuation would lead to economizing in the allocation of both consumer goods and producer goods. Okay, so now the next step is just to see that this process of valuation that Caruso uses to organize all of his production, his whole economy, right? Is organized in his mind, given his perception of the means available to him, applying his intelligence to see what the cause and effect connection is to attain the ends by applying these means and then the way that he values the different ends that could be attained, right? The whole economy structured this way. So now we ask the question, is it possible for the division of labor to be structured this way? And I've already answered this question. No, it's not possible. This is the nub of the great socialist calculation debate. We cannot through central planning have just one person or a small group of people make economizing decisions for everyone in all production processes and consumption throughout the division of labor. That just is not feasible. It's not feasible for many different reasons, but the central point that Ludwig Maumice's stress was this point that we made before, it is not possible to interpersonally compare subjective values. If it's not possible to interpersonally compare subjective values, then we're just at a loss to have a method by which we could sort of directly assess which consumer goods are more valuable to people in society at large when different people in society value different things. So some people want these things, some people want those things with the same means. How do we measure their subjective value to accomplish that? So this can't be done directly. Subjective values cannot be interpersonally compared either by a grand carousel who would rise to the height of the central planning board or whatever, nor can it be done democratically just by all of us get together in a plebiscite and we vote on what things to produce. This will give a result, both of those methods would give a result but they would not be economizing results. The same argument Mises applies to the question of what's the least cost method of production and how do we have a system in society by which we can decide what the least cost means of production are? Because to minimize the cost of production we have to minimize the opportunity cost of the workers and owners of the factors of production throughout the entire division of labor. Again, we only have a couple of logical options. Caruso, we could say let's have socialism. And Caruso and his friends on the planning board own all the factors of production. And so then they're going to allocate them efficiently. Why is this impossible? This is impossible because a division of labor by definition is a system of production where not everyone does every task. That's just what a division of labor is, right? And so Caruso and his planning board members cannot in fact do every task in the division of labor. If they can't do every task in the division of labor then they cannot assess the subjective value to a human person of doing the task. They can't actually exercise ownership in an experiential, you know, by experience of every land site and every factory and every tool and so on and so forth. This take, that's why we call it a division of labor because it's divided among us. So it's not possible to proceed this way. And of course again, we can't do this by vote. Because our opportunity costs that we have in our own minds are not comparable interpersonally. So we can't say who is the low cost coal miner? Who is the low cost mechanical engineer? Who is the low cost, right? None of that works. And so how is this done? So this is a schematic of the way in which this is done, a schematic of how subjective values result in prices in the market. And then we'll go through, we have a little bit of time to go through some of the details of this. But the point is that this is just a transition to what Ludwig von Mises calls appraisement, economic calculation and appraisement. It's once we have this system in place, a market economy where prices are determined by our demonstrated preference of goods, and opportunity costs, of the different factors of production that we own foreign against money, then it's possible to have a method of making economizing decisions. So notice we started at the top with preferences that we said before. Actually of course we have two things going on and I ran out of space to put all this on here. We've got the human mind and we've got the circumstances of acting, right? The external world, the circumstances in which we all find ourselves, the objects or things outside of our mind. We have these two things. We have ends and means, right? We have two elements. And then within that we establish preferences. So whatever our circumstances are in life, we have these external things and then we make a preference with respect to them. So that's where we start logically. And then this gives demand for consumer goods. So we start with, as we said before, the process of imputation is from our mind to consumer goods and then to producer goods. So we have demand for consumer goods. We have then the supply of consumer goods and then Economic Theory explains how prices emerge from this, how prices emerge to clear the market and we'll spend a little bit of time talking about that. Once we get prices of consumer goods, then that generates revenue for the producer. So the entrepreneur who's produced these consumer goods earns revenue. The consumers who have purchased these goods make expenditures. Then the revenue that entrepreneurs incur is a determinant of their demand. So if they're earning a certain revenue stream from production, then they will have a corresponding demand that is a payment that they're willing to make to hire the factors of production that can produce the good to generate that revenue stream. And that demand, along with the supply of the producer goods, which again, is just based upon preferences. Your labor supply into different jobs or if you're a landowner, the supply of your acres of land or whatever it might be. The supply of the producer goods and then the same argument applies, right? What will happen in the market is the price will hit the point that clears the market. And so we'll have prices of producer goods, wages for labor, prices for acres of land, so on and so forth. And these will generate then costs for the entrepreneur. And the entrepreneur can now tell how to arrange the factors of production in the least cost way because there'll be prices for all the factors of production throughout the whole economic structure, just like the entrepreneur can then match revenues and costs, right? Can tell if I produce this product, if I'm a Tim Cook and an Apple Inc. and we produce the iPhone SE and we generate a revenue of $400 per phone and we have a cost of whatever, $320 per phone, then they can decide that whether or not that's a viable line of investment by comparing it to the other lines of investment, we're gonna do a similar monetary calculation. So that's the process of appraisement. And again, you'll hear a lot more about that during the course of the week. Now, with the time we have remaining, let's just run through the first step of that chart. So let's start with preferences and just see the logistics, the technical aspects of how we go from preferences to demand and supply to the market clearing price. And then this would just be, again, repeated for factors of production. So these are the preferences for, this is fiscal year 2017 iPad Pro. Most of you know that the tablet market has been going, right, in the last four or five years there are half as many tablets sold, but there are some, right? And somebody bought these things and fiscal year 2017 includes the quarter of the Christmas selling season of 2016, right? So it's the last quarter of 2016 and the first quarter of, so these are, somebody got these as gifts for Christmas or they bought them back in November or something like this and now they're putting them out on eBay. So that's my scenario here. Let's suppose we have people who acquired these, however they did as a gift or whatever and then now they prefer the money that they can obtain to retaining ownership. Some of them do, but then there's some others who would like to acquire these used iPad Pros. So my example notices for a used good. I do this intentionally just so we can see the kind of step-by-step nature in which the price analysis proceeds. We start with the simplest case, right? Simplest case is we just have two people who have exactly the same interests involved in whether they own the good or don't own the good. They're gonna use it as a consumer and so they get the same kind of interest in having it to do whatever people do with tablet computers and then they have money and they have an interest in money. Having the money or holding it or spending on something else and so on. And so here's my setup. Remember the preferences have to conform to the laws of utility. So let's suppose we have a person who doesn't own an iPad Pro. This is the old model. And the preferences look like this. They wouldn't pay $500 to get the iPad Pro but they would pay $450. So there's a demand, the quantity demand of this person would be one at 450. And if the price was low enough, let's say $300, they'd actually buy two. And they'd give the second one to their oldest son or they'd put one in the office and keep one at home and so on and so on, things like that. And so the quantity demand it could increase if the price is lower. And this would happen only because of the laws of utility, right? Only at lower prices would the less valuable units be voluntarily purchased compared to the price that the buyers willing to pay for the more valuable first unit. And then we can construct the law of supply in exactly the same way, just with the exact same preference rank, just assuming now that this person, instead of not owning an iPad Pro, already has two. Again, how this happened, we don't have to worry about that. Again, it's imaginary construct. So they bought one and then their rich uncle sent them one for Christmas. And then, oh, I got two of these things. And so they're in the market to sell. And now their marginal utility is down here, right? So clearly this person would be willing to sell the second iPad, the least valuable one for $350. But he likes the first one, uses it. And he wants to keep it and wouldn't sell that one unless the price were 500, right? So we see the law of supply only at higher prices would the quantity supply be larger, right? So this is how we go from preferences to the laws of supply and demand. And then we can go to the market clearing price, the last thing we'll do just by introducing a few other buyers and a few other sellers. So again, this is just a reality of our world. We find that when we go into the world that people don't value things the same way we do. And so there would be buyers who are more eager to buy goods and buyers who are less eager. Buyer A would be the most eager, willing to pay the highest price. Buyer B's willing to pay $450, buyer C only $400. So obviously buyer A could out-compete buyers B and C if it got into a bidding war, right? And buyer B could out-compete, out-bid buyer C and so on. And so we set up the same thing for the seller. We've got three sellers. One really eager to get rid of the iPad. One not so much would only accept $400. This one would keep the iPad even if the price were $450. And so we can construct a chart of quantity-demand quantity supply and we see the market clearing price would be at $400 where two iPads, pros are sold and two bought. The reason why the market clearing price would be at $400, the logic of this is that at that price and only that price, all of the preferences of all of the people involved in this activity are satisfied. Everybody who wants to buy at that price buys. Everybody who wants to sell at that price sells. There's one seller who doesn't want to sell at that price and so doesn't. That's seller Z. And there's one buyer that does not want to buy at that price and doesn't. That's buyer C. So everybody's preferences are satisfied. That's why that price emerges and not another. If the price instead, of course, were higher, if the price turned out to be $450, then there would be dissatisfied sellers. There'd only be one buyer, but three consumers who would want to sell and these three consumers who want to sell instead of just saying, oh, what tough luck? What was me? I can't get rid of this dumb iPad. They would just, I mean, if they're entrepreneurial enough, right? They would just lower the price. It's lower the price, right? And clear their stock and then the market clears. And the same thing for demand, right? If the price happened to be below the market clearing price, then the quantity demand would be larger because of the law of demand. The quantity supply would be smaller because of the law of supply. And the buyers who can't find a seller would just up the bid. When they up the bid, the market clears. In fact, we pointed out earlier that it isn't even necessary to assume, and most of the time this doesn't happen, right? That there's a kind of trial and error process and the people grope toward this solution. Actually, this is just an entrepreneurial question as we suggested before. It's just a question of anticipation, right? If people can anticipate where the market clearing point is, well then they can hit it right away. And so we're not making any assumption about the nature of the process by which the market clearing point comes about. We just know that the logic of action dictates that the market clearing price is the best price, right? It's the price they would aim at in the market since all the preferences of the buyers and sellers are satisfied. And let me end on this note. There could, obviously there would be cultural differences as to how the market, how people interact in the market. So in some markets they might interact in a kind of open bidding activity like you see on eBay or in flea markets or things like this, right? And there might be other markets where entrepreneurs take the lead in asking a market clearing price, right? And then we as consumers, you know, express our preferences of that price. And the entrepreneur takes the burden of adjusting the price. And we're okay with that as consumers because maybe we just think entrepreneurs are in the business to do this, right? They're good at this and we're not so good at it than negotiating and, you know, haggling and higgling and trying to find the price. But that again is just a sideshow for economic theory. Again, the point to stress is this point of logic. All right, I've exhausted the time so we'll stop here. Thank you. Thank you.