The regression theorem is one of the most celebrated contributions of the Austrian School of Economics. This is not surprising given what the theorem achieved in the eyes of many of its proponents:
- The theorem showed for the first time how to use marginal utility analysis to explain the determination of the price of money. This integrated monetary economics with general economic theory, which in turn paved the way for some of the most important future contributions by the Austrian School, particularly in the area of business cycle theory.
- The theorem showed that indirect exchange and money could only have originated out of market exchange and could not have been the creation of the state.
- The theorem is a part of praxeology, which means 1) that it is an priori claim that is deduced from undeniably true axioms, and 2) that it is not possible to imagine, let alone observe, situations or events that contradict the theorem.
In this article I argue, however, that there are two main problems with the regression theorem: It is neither a priori nor true.One of the most remarkable things about the theorem is that these fundamental problems somehow went largely undetected for close to a century. It wasn’t until the arrival of bitcoin, a medium of exchange whose emergence seemed to violate the regression theorem, that many scholars began to examine the theorem more critically. I argue firstly that it is a shame that it took so long as the problems with the theorem should have been clear from the start, long before the apparent counterexample of bitcoin came along, and secondly that the recent re-examinations of the theorem have not gone far enough.
Below I first describe the circularity problem that had stood in the way of previous attempts to use marginal utility analysis to explain the determination of the price of money. Then in the second section I summarize the regression theorem and describe how the theorem is thought to have solved this circularity problem by reasoning back to the first moment that a good was used as a medium of exchange. This transition from barter to indirect exchange (and, in a later stage, money) is the subject of the third section. The fourth section looks more closely at the theorem’s alleged epistemological status. I discuss the concept of a priori knowledge and justification as it pertains to the regression theorem in some detail.
After the first four sections we will know what kind of theory the regression theorem is, what exactly it says, what problem it was intended to solve and what its implications for theories of the origins of indirect exchange and money are supposed to be.
But is the theory really what it is said to be, and does it actually accomplish what it is said to accomplish?
The first doubts emerge when considering bitcoin: As many others have noted, bitcoin seems to represent a challenge to the regression theorem as it has emerged as a medium of exchange seemingly without having satisfied the necessary conditions laid out in the theorem, i.e. without there having been a prior non-exchange demand for bitcoin. In the fifth section I discuss this apparent contradiction between the theorem and the emergence of bitcoin in some detail, and argue that none of the attempts to resolve the contradiction are satisfactory. This raises the question how a theory that supposedly is demonstrably and a priori true can possibly conflict with empirical evidence.
The sixth section answers this question in two parts: I first show that the theorem is in fact not a priori in nature. Instead it is an a posteriori and inductive claim that was not and cannot be derived from from the action axiom. Not only is the regression theorem not a priori in nature, it is also simply false: The propositions of the theorem simply don’t follow from one another and the theorem conflicts not only with empirical observations but also with the results of thought experiments.
The final section briefly discusses where these problems leave the regression theorem and the contributions it was thought to have made to economic theory. I argue that the main value of the theorem lies in its pointing to a way to solve the circularity problem involved in applying marginal utility analysis to monetary economics. But the actual solution presented by the theorem itself is flawed: Where the theorem looks backward (regression) to explain the determination of the price of money, the solution lies in looking forward. This solution, however, requires that instead of trying to explain away the fundamental bubbliness of money, we make peace with it.
Readers who are sufficiently familiar with the regression theorem can safely skip the first three sections.1. What problem was the regression theorem supposed to solve?
Economists use marginal utility analysis to explain the prices of goods and services, but there seems to be a big obstacle to using the same kind of analysis to explain the price of money.
People's valuations of units of non-monetary goods and services are based on the utility that a marginal unit is expected to provide them in satisfying their direct consumption or production needs. These valuations are independent of the prices of these goods and services.
For example, the utility that I expect to get from a specific microwave would be the same if said microwave cost $900 as when it would only cost $200, as long as I know that it really is the same microwave in both cases. The price may affect my decision to buy or not, but not the utility I expect to get from the good.
In contrast, the expected utility that a marginal money unit has for a person, and hence that person's valuation of it, does to a large extent depend on the price of the good, i.e. its purchasing power. After all, people don't value money on the basis of its expected utility in satisfying direct consumption or production needs (unless you’re like Scrooge McDuck and enjoy swimming in money).
Instead, they value it exactly on the basis of its expected utility in helping them buy other goods and services in the future. And this utility depends in large part on its price, i.e. its purchasing power. For example, my decision whether or not to sell my bike for $250 depends on the utility that I think the $250 will have for me, and this utility in turn depends in part on the utility of the goods and services I expect to be able to buy with that $250 in the future.
The problem is that this seems to commit us to a form of circular reasoning: The price of money is in part determined by the demand for money but the demand for money is itself in part determined by the price of money.
2. What does the regression theorem say?
Mises proposed a solution to this problem by distinguishing between the past, present and future price of money: The price of money today is determined by how much people today are willing to give up for a monetary unit, but what people are willing to give up today depends on how much they expect to get back for that unit in the future, and this expectation is based on people’s knowledge of how much that unit was worth in the immediate past.
Put differently, the current price of money is in part determined by the expected future price of money, and the expected future price of money is in part determined by the past price of money.
We are dealing then with three different prices and as a result, the problem of circularity dissolves.
But what then if we ask what it is that explains these past prices? At first, the answer seems obvious based on the analysis above: We explain past prices of money units by referring to the expectations that the people who bought or sold these units had about their future prices, and these expectations about future prices were in turn based on still earlier prices.
To use an idealized, simplistic model: Expectations about tomorrow's price partly determine its current price, and the expectations about tomorrow’s were based on yesterday's price. Yesterday's price was in part determined by the expectations that people yesterday had about today’s price, and these expectations in turn were based on people’s knowledge about what the price was the day before yesterday. And so on.
The regression from present prices to earlier prices to still earlier prices and so on is, however, not infinite. There comes a moment at which a good had its first price as a medium of exchange.
A new problem then emerges: Given our mode of explanation we could only explain that first price by saying that it was based on people’s expectations about future prices, and that the people involved would have based these estimates of future prices on their knowledge of past prices. But in the case of the very first time a medium of exchange received a price, by definition there would be no past price to refer to. Our regression analysis, then, seems to have run into the ground.
Mises proposed a solution to this problem as well: At the moment that a good was used as a medium of exchange for the first time, it did in fact have an earlier price that people could use in order to estimate what its future price would be. It’s just that that earlier price was not based in part on the demand for the good as a medium of exchange, but entirely on the demand for its prior, non-exchange role in the economy.
For example, if grain or gold come to be used as a medium of exchange for the first time, they supposedly already had an earlier price because they were valued and demanded in the barter economy for their use in satisfying direct consumption and production needs.
As noted earlier, this kind of price, i.e. the price of a good demanded entirely for its utility in satisfying direct consumption and production needs, had never presented a problem for marginal utility analysis. The price of non-exchange goods is determined by people’s valuations of marginal units of the good, and these valuations are independent of the price or purchasing power of the good.
The problem for marginal utility analysis instead started at the moment that a good took on an additional role as a medium of exchange. From that point on, the price of a good would be determined by both the exchange demand and the non-exchange demand. And attempts to explain how that part of the price that was the result of the exchange or monetary function of a good is determined had always run into the circularity problem mentioned earlier.
Mises’s regression theorem solved this problem of circularity by making a distinction between between past, present and future prices. And Mises avoided a second kind of circularity problem by demonstrating that the monetary regression is not infinite. Instead, it ends at the exact moment that a good that already had a pre-existing purchasing power as a result of prior non-monetary demand for it comes to be used as a medium of exchange for the first time.
Thanks to Mises, economics could finally use the same method of marginal utility analysis to explain the roles played by both the exchange and non-exchange demand in the determination of prices. Thanks to Mises, monetary economics could finally be integrated with the rest of economic theory.
3. What does the regression theorem tell us about the origins of money?
In his theory of the origins of money Carl Menger described the evolution of a barter economy to an economy of indirect exchange to a full blown monetary economy. In his regression analysis Mises seems to be travelling the same road as Menger did but starting from the other end: The regression theorem’s starts with a full-blown monetary economy (or at least an economy in which a medium of exchange is used) and explains how in such an economy money prices are determined on the basis of earlier money prices, which in turn were determined on the basis of still earlier prices and so on and so forth, all the way back to a barter economy wherein the prices for goods were determined entirely by their original non-exchange function.
Mises’s regression theorem then seems entirely compatible with Menger’s theory of the origins of money. But Mises and other Austrians thought the regression theorem was not merely compatible with the Mengerian story of the origins of money, but actually showed that the Mengerian account was a correct account of the origins of money, and the only correct account: Money could not have emerged in any other way.
[W]henever a good which has not been demanded previously for the employment as a medium of exchange begins to be demanded for this employment, the same effects must appear again; no good can be employed for the function of a medium of exchange which at the very beginning of its use for this purpose did not have exchange value on account of other employments. And all these statements implied in the regression theorem are enounced apodictically as implied in the apriorism of praxeology. It must happen this way. Nobody can ever succeed in construction a hypothetical case in which things were to occur in a different way.
And Rothbard agrees:
Not only does the Mises regression theorem fully explain the current demand for money and integrate the theory of money with the theory of marginal utility, but it also shows that money must have originated in this fashion—on the market—with individuals on the market gradually beginning to use some previously valuable commodity as a medium of exchange. No money could have originated either by a social compact to consider some previously valueless thing as a “money” or by sudden governmental fiat. For in those cases, the money commodity could not have a previous purchasing power, which could be taken into account in the individual’s demands for money. In this way, Mises demonstrated that Carl Menger’s historical insight into the way in which money arose on the market was not simply a historical summary but a theoretical necessity.
A later generation Austrian, Peter Boettke, expresses the same idea:
Not only did Mises' theorem confirm Menger’s theory of the evolution of money, it also refuted alternative theories which argued that the state could consciously create a monetary system through a general agreement independent of commercial activity. In other words, whereas Menger’s theory argued that commercial activity could generate a monetary unit, Mises’ theory argued that the state could not create a monetary unit outside the context of the accepted practice of commercial life. It was epistemologically impossible for the State to create a common medium of exchange outside the context of exchange practice.
The regression theorem laid out the necessary conditions for the emergence of indirect exchange and hence, in a later stage, money: For a good to come to be used as a medium of exchange it had to have had a prior market price on the basis of the non-exchange demand for the good.
4. The a priori nature of the regression theorem
The quotes above also make clear that Mises and Rothbard thought that the regression theorem was a praxeological statement and hence that it its truth is established through a priori deductive reasoning.
In the philosophical literature there are countless articles and books about what exactly it means for a statement to be a priori or a posteriori, and we will not enter into these debates in the space of this article. For now let's just go with the plausible idea that a statement is a priori true if and only if its truth can be established on the basis of nothing more than the meaning of the words in the statement. 'All bachelors are unmarried' is an a priori true statement because 'unmarried' is part of the definition of 'bachelor'. When you need to do more than simply know the meaning of a statement in order to find out if it is true or not, that statement is a posteriori. The truth or falsehood of 'All bachelors are left-handed' on the other hand is established through empirical observation.
This is not to say, however, that in contrast to a posteriori statements a priori statements are unempirical or that a priori reasoning is not grounded in empirics. It is just that the empirical basis for a priori reasoning is not of the inductivist kind typical for positivist science. Instead, the empirical basis and nature of the knowledge lies in our acquiring the language and learning the relevant concepts. We acquire a priori knowledge by acquiring the concepts used in the propositions that express that knowledge. By reflecting on, understanding and combining the basic concepts and axioms we can deduce more complex knowledge that retains the a priori nature of the axioms, i.e. that are true by virtue of the meaning of their constituent concepts.
Praxeology is that body of a priori knowledge comprised of the action axiom and everything that can be deduced from it (in combination with uncontroversial a posteriori knowledge such as the disutility of labor). It is the a priori science of human action, specifically of those aspects of action that can be grasped by reflecting on the meaning and logic of action. Economics starts from the fact of human action, and the concepts and elementary principles implicit in the meaning of action (“opportunity costs”, “means,” “ends,” “reverse valuation of goods exchanged,” “only individuals act” and so on). As Hoppe writes:
Economic propositions flow directly from our reflectively gained knowledge of action; and the status of these propositions as a priori true statements about something real is derived from our understanding of what Mises terms "the axiom of action." […] [The economic] categories —values, ends, means, choice, preference, cost, profit and loss, as well as time and causality—are implied in the axiom of action.
And Rothbard summarizes: “What are these axioms with which the economist can so confidently begin? They are the existence, the nature, and the implications of human action.” Economics then combines these these axioms with some elementary, auxiliary empirical principles such as the disutility of labor, and the fact of differences between human beings and their environments.
The apriorists maintain that economic theory can be deduced from these simple starting points. Examples of elementary principles that they hold can be so deduced are the law of diminishing marginal utility, the law of demand, and the law of diminishing returns.
By subsequently introducing more and more complexity in the environment of actors in the form of other people, and institutions such as money, banking, stockmarkets, regulation, and taxation, more complex theory can be built up by reflecting on what the essence of these phenomena is and applying basic economic reasoning to them.
The regression theorem is a prime example of such praxeological knowledge that can give us true, a priori causal knowledge about aspects of complex economic situations, in particular how the price of money is determined in a monetary economy and what the necessary conditions for the emergence of indirect exchange (and hance, at a later stage, money) from barter are.
This a priori method also means that there is no way for the regression theorem to be falsified through empirical observations. That is, if people observe a situation in which money seems to arise or have arisen in an alternative way, this observation could not mean or establish that the theory is false. If people think they are observing such a phenomenon they are either misperceiving or misunderstanding what they are perceiving. The fault can only lie with them, not with the theorem.
The only way in which the theorem can be shown to be false is if someone were to show that the axioms on which it is based are false or that the steps taken in the supposed derivation of the theorem from these premises are invalid.
And so at most what the observation of a phenomenon that seems to contradict the theorem could do is prompt people to check whether the axioms and deductive steps were in fact correct and valid.
To sum up, in the eyes of Mises and Rothbard the regression theorem is a priori true and shows not just how a certain method, marginal utility analysis, can be applied to a domain to which it had hitherto not been applied, it also postulates a causal empirical claim (that a medium of exchange can only arise out of barter) that is nevertheless a priori true.
Pretty cool if true.
5. Enter bitcoin
As many, many others have noted, the emergence of bitcon as a medium of exchange seems to represent some problems for the regression theorem: While bitcoin is currently clearly used as a medium of exchange, it doesn't seem to have had an earlier non-exchange role, which would seem to directly contradict the regression theorem.
So what's an Austrian to do?
There are a couple of possible responses:
- Conclude that the regression theorem is false.
- Argue that the regression theorem is correct but that bitcoin actually did have a prior non-exchange function.
- Argue that the regression theorem only means that bitcoin can never become money, not that it cannot be used as a medium of exchange.
Bitcoin may be a medium of exchange, but it can never become money.
Money typically is characterized as a widely or universally accepted medium of exchange that also serves as a store of value and a unit of account. Proponents of the regression theorem may argue that while bitcoin is currently used as a medium of exchange, the regression theorem just implies that bitcoin can never become so successful and widely used that it will meet all three of the criteria above.
For example, currently bitcoin is by no means universally accepted as a medium of exchange and it is hard to see how anyone could use bitcoin as a unit of account without piggybacking on the unit of account function of the dollar. With some minor exceptions (bitcoin arguably functions as a unit of account in the market for alt coins), it is only possible to express the prices of goods and services in bitcoin because there already are dollar prices for said goods and services.
There are, however, two problems with this response: Firstly, as far as I can tell nobody has explained what exactly would make it impossible for bitcoin to gradually develop into full-fledged money, serving all three of the functions mentioned above. It may be true that it never will, and it is certainly true that currently it doesn’t, but why would it be impossible in principle?
The regression theorem itself offers no insight here and that brings us to the second problem with this kind of response: The regression theorem is simply irrelevant to the issue of the transition of a good from mere medium of exchange to full-fledged money. The regression theorem only says that in order for a good to come to be used as a medium of exchange in the first place it has to have had a prior price that was the result of the demand for the good in its non-exchange role. For this issue it is simply irrelevant whether or not a good that already has acquired a use as a medium of exchange can become so successful in that role that it becomes widely or even universally accepted, i.e. that it becomes money.
The regression theorem is correct, but prior to its first use as a medium of exchange there in fact was a non-exchange demand for bitcoin that gave it an initial price.
There are a number of problems with this kind of response:
There simply is no obvious or easily identifiable non-exchange role that was played by bitcoin prior to its use as a medium of exchange.
The typical roles that proponents of solution (2) mention are along the lines of people demanding bitcoin as an expression of ideology or idealism, or because they found it just interesting because of its technology. While it is certainly possible that a small number of people valued bitcoin for any of these reasons and were prepared to pay something to obtain bitcoin, thereby providing bitcoin with an initial price, before any of them actually demanded it because of its possible later use as a medium of exchange, this demand would have been tiny, if it existed at all.
Assuming for the sake of the argument that there was in fact such demand, the extremely modest scale of such demand would make bitcoin very unlike the kinds of goods that Menger and Mises had in mind as goods that could take on an exchange function. Menger and Mises are thinking of goods such as grain for which there was a large prior non-exchange demand. A good like grain was widely used in society, and it was exactly this widespread use that made these goods highly saleable, which in turn was the main factor that determines whether or not people will come to use the good as a medium of exchange.
In the Mengerian scenario people would first sell a relatively unsaleable good for a more saleable good such as grain and then sell that more saleable good for the relatively unsaleable good that they ultimately want. Rather than trying to find another person who has the unsaleable good that you want and who is prepared to trade it for the unsaleable good that you want to sell, a more saleable good is used as the medium through which the exchange becomes easier, cheaper and quicker.
But in the case of bitcoin just about any other good out there had a higher degree of saleability than bitcoin, and so it simply would not have made sense for bitcoin to come to be used as a medium of exchange in the same way as goods come to be used as a medium of exchange in the Mengerian scenario.
Moreover, even when it comes to the ideological or idealist or tech interest sources of demand for bitcoin, bitcoin's exchange or monetary role does seem to be part and not independent of them: the reason that people had the kind of ideological or idealist or tech interest in bitcoin that they did likely for a large part had to do with what people thought about bitcoin's possible future monetary role. After all, its promised potential monetary role is what made bitcoin bitcoin in the first place: it is what may have made it interesting for reasons of idealism, ideology or interest in its specific technology.
None of the above, however, means that it is impossible that bitcoin had a prior non-exchange role for which there was a demand such that bitcoin acquired a positive price, only that:
- it is unlikely that it did,
- or that if there was a demand it was so tiny that it would make bitcoin very different from the kinds of goods typically mentioned in the context of goods that come to be used as media of exchange,
- or that the non-exchange role actually was intimately connected with the actual or expected exchange function
So people who want to view bitcoin and the regression theorem as not incompatible with one another could still make this case. The only problem is that it seems to deflate the theorem of meaning and significance as the emergence of bitcoin as a medium of exchange would be very unlike the Mengerian scenario that the Misesian regression theorem is typically interpreted to be about.
It also raises the question what kind of scenario of the emergence of a medium of exchange could not be accommodated, interpreted and hypothesized to be somehow compatible with the regression theorem? What scenarios are actually excluded by the regression theorem?
This brings us to the first kind of response mentioned above.
6. The regression theorem is neither a priori nor true
6. The regression theorem is neither a priori nor true
If the emergence of bitcon does not necessarily contradict the regression theorem, then what could? Recall that its proponents claim that the regression theorem excludes alternative scenarios for the emergence of money. And recall that this supposedly is a statement whose truth can be established a priori.
How could these claims be shown to be false?
Firstly we could simply ask to see the derivation: Show the axioms that the theorem is based on and the steps used to derive the theorem on the basis of these axioms. The remarkable thing is that (to my knowledge) nobody has ever even tried to do this. It is simply assumed that it is possible to do this.
At the same time, the other remarkable thing is that Austrians seem to disagree about the a priori nature of the theorem. Where Mises and Rothbard and many others seem to have no doubt as to the a priori nature of the theorem, others such as Hulsmann don't regard the theorem as a priori in nature.
That's weird. It seems like such a basic question and like such an easy thing to determine who is right about this. And in fact it is.
The regression theorem says that people's expectations about the future purchasing power of money is based in part on its current purchasing power which in turn is in part the result of people's previous expectations. The thing is, this hardly seems like an a priori statement. It is an open and empirical question how people in fact estimate a good's future purchasing power, and whether or not said good needed to have a prior price for them to be able to make this estimate.
The regression theorem then is not actually an a priori claim.
Moreover, it is easy to imagine a scenario in which no such prior price is needed in order to estimate future purchasing power. In fact, bitcoin may very well have been an example of such a scenario.
For example, suppose that in the days after Satoshi launched bitcoin some people thought that this thing might take off as a medium of exchange in the future. They think the probability is very low, maybe .001%, and they know that ultimately about 21 million bitcoins will be created. They also calculate that if bitcoin were to take e.g. 10% market share of gold or of the US dollar, a single bitcoin would be worth millions of dollars. On this basis they think it is rational for them to pay a very small amount to obtain some of these bitcoins, and some other people who had been mining bitcoins are willing to sell them some.
Suddenly bitcoin has a price and can be used (or even is used) as a medium of exchange. Out of nothing. Without any prior non-exchange role.
The price will be volatile as it is based on very limited information (facts, expectations, assessments etc) that can moreover vary wildly between people and change rapidly, and as liquidity is very low. But it's still a price. And the price is purely based on expectations about the future purchasing power of bitcoin, thereby perfectly satisfying that part of the regression theorem while at the same time violating the part of the theorem that says it needed to have a prior price that was based on a prior non-exchange role and the demand for it.
So we can both imagine a hypothetical scenario that would in fact contradict the regression theorem and we have some reason to think that something like this scenario actually took place in the case of bitcoin.
But we can move beyond bitcoin and imagine another possible scenario that would similarly contradict the regression theorem.
Suppose that in a primitive economy without indirect exchange a government or government-like organization decides to issue special kinds of paper notes or shells or other things that are scarce but for which there was no prior demand or that simply did not exist before. The government tells people that they have to pay tribute or taxes using these things and that people can earn these things by working for the government or that they can acquire them by buying them from other people who have earned them by working for the government. Moreover, the government tells people that they will issue one million units of these things, and people have reason to think the government will not in fact issue more of them.
In this scenario there was no prior non-exchange demand for these things and hence no price for them. But by issuing a limited number of them and requiring that people use them to pay taxes suddenly the government has ensured that there now is an exchange demand for these things and hence that prices will emerge. People now know that they can exchange goods they want to sell for these government-issued things and then use these government-issued things to buy the goods they ultimately want, because they have good reason to think that other people will similarly accept these government-issued things as payment as there will always be people who will want them in order to be able to pay their taxes.
Song Dynasty Jiaozi, the world's earliest paper money
In this scenario there had been no other goods that had been used as media of exchange prior to this moment and so there had simply not been any unitary prices in the economy. Some people may have traded one sheep for three basket of apples but there was no one good or a small number of goods in terms of which all the other goods could be priced. This makes the process by which these newly government-issued things take on a role as media of exchange and as a result as a unit of account much more chaotic and volatile than it would have been if there had been prior unitary prices in the economy, but still, prices will emerge with these newly issued things as the unit of account.
What this scenario and the bitcoin scenario I sketched before it show is that prior prices based on prior demand for a non-exchange function of a good are unnecessary for that good to come to be used as a medium of exchange.
The regression theorem then is simply false.
7. Does the regression theorem integrate monetary economics into general economic theory?
7. Does the regression theorem integrate monetary economics into general economic theory?
So far I have argued for the falsehood of two of the three claims about the regression theorem that I mentioned in the introduction: The theorem is not an a priori claim (and hence not actually a theorem), and what it says or implies about the necessary conditions for the emergence of money is simply false.
But what about the other claim? Does the regression theorem show that the method used to explain the determination of prices of non-exchange goods, marginal utility analysis, can also be used to explain the determination of prices of media of exchange?
Well, yes and no. Yes, in the sense that the theorem correctly explains that the determination of the price of money can be explained by referring to people's expectations about the future price of money. But no in the sense that these expectations about the future price of money do not necessarily depend on knowledge about past prices of money.
As we just saw, we can form expectations, no matter how rough or uncertain, about the future purchasing power of goods used in exchange without reference to past prices, although in normal situations these past prices are in fact a useful reference point.
In short then, what we can salvage from the regression theorem as it was formulated by Mises is that the current price of money is determined (in part) by the utility that people expect to get from that money and that this utility is in turn (in part) determined by people's expectations about the future price of money. These expectations in turn may (and typically are) or may not (and need not) be influenced by the price of money in the immediate past.
So we can still say that Mises did manage to (dis)solve the problem of circularity by distinguishing between current and future prices so that the price of money is not determined by reference to that same price of money. Where Mises went wrong, however, was in assuming we need current prices of money for us to be able to form these expectations of future prices.
- Bitcoin, Culture and Value
- The Problem with Austrian Economics (draft; dropbox link)
- Bitcoin, Culture and Value
- The Problem with Austrian Economics (draft; dropbox link)