The Economics of Bitcoin: On Regression

In a storyline sounding all too familiar, libertarian circles have been up in arms with each other over the emergence of Bitcoin, the cryptocurrency and payment system that burst on the scene in 2009. If you do not know much about Bitcoin, I direct you here; and if you do not know much about libertarianism, I direct you here. On that note, if you had to click either of these links, or are not particularly interested in the economics of Bitcoin, I suggest you skip this article, and continue to the article on the “Future”, which will be the next in this two part series on Bitcoin.

Though there have been a multitude of criticisms toward Bitcoin, it must be said that clearly the most important debate is whether or not it “can” be a money; namely, whether or not it violates Mises’ regression theorem. Examples of arguments of this type include those by The Mises Institute’s Frank Shostak and blogger “Smiling Dave” among others. This topic is by far the most significant of the lot, as those libertarians claiming that Bitcoin does violate the regression theorem are directly attacking the character of the formation of money prices put forth by Austrians. But why does it follow that this is important? Well, those libertarians who reject Bitcoin on the grounds of regression are not, and cannot be classified as, Austrian economists in this matter. The de facto Austrian position must be one in which Bitcoin does not violate the regression theorem, for reasons that will be explained later in the article. Thus, those libertarian arguments claiming that Bitcoin violates the regression theorem, and will therein implode in some spectacular crash for this reason, must quickly and emphatically be separated from holding any “Austrian” position. It is not, and cannot be the Austrian position, and to associate such claims with the Austrian school is slanderous to a degree. One may make the argument that Bitcoin will crash due to it being entirely based on the network effect and exchange value, but the classification of this argument must not be Austrian, but one of a speculative nature.

It must also be noted here that there will be a purposeful separation of “libertarian” and “Austrian” in these articles. It seems as though popular media regularly conflates the terms as they are somehow synonymous, when they surely are not. Austrian economics is a positive analysis of human action; libertarianism is an ethical and political philosophy rejecting aggression. Indeed, there is no apparent intersection of the two. Milton Friedman, perhaps the most popular pseudo-libertarian of all time was not an Austrian school economist, and there has, in the past, existed Austrian school economists who were closer to progressive liberalism than anything, von Weiser being a good example.

The Economics of Regression

Before we examine any arguments against Bitcoin’s capability as a money, we must first explain the basics of the regression theorem. The theorem is based on Austrian price formation, applied to a system of indirect exchange.

Under a system of direct exchange, or barter, prices are formed by the dynamics of supply and demand market schedules, which are made up of supply and demand schedules of individuals. These individual schedules consist of the ordinally ranked marginal utilities of the goods: thus, the crux of price formation in a system of barter is the weighing of individual marginal utilities of two goods against each other.

Under a system of indirect exchange, or one using money, the aforementioned price formation cannot occur. The price of x good against money is based on market supply and demand schedules, then individual schedules, and then the rankings of marginal utilities of good x against money. The issue arises when we realize that the marginal utility of money is based on existing prices of the array of all other goods in the economy, bringing us into circularity. In summation, the price of good x is based on the utility of money, which is based on the prices of all other goods, which is based on the utility of money.

Where do we escape this circularity? With the introduction of time. It is clear that the existence of prices for goods today, and thus the utility of money today, are based on the prices of goods yesterday. The prices of goods yesterday, which determine the utility of money yesterday, are based on the prices of goods the day before that. As we see, through the introduction of time, we enter into an infinite regression.

And here, we enter the brilliance of Mises in establishing the regression theorem. As we regress further back in time, Mises claims, we eventually will reach the point at which the utility of money isn’t in determined by its exchange value, but rather its direct use value. The price for a certain money good is thus established through the ordinal rankings of direct use value, which provide the basis for utility of the money good, allowing future prices to be set when the good is eventually used as a medium of exchange.  To put it a different way, a system of indirect exchange will always regress back to a system of barter. This process is perhaps best illustrated with a graphic provided in Rothbard’s “Man, Economy, and State”.

Screen Shot 2014-03-01 at 8.43.13 PM

Here we can see the entire process as described above. Looking at time period 7, the price of gold is shown to be based on the weighing of the utility of all other goods against the utility of gold, which in turn based on the price of gold on day 6, and so on. The key stage for this graphic is time period 3, shown as establishing the price of gold through the rankings of marginal utilities of gold and all other goods in the economy. This is the point at which the price of the money good, in this case gold, regresses back to. At this moment, all utility derived from the good is for direct use, as there is no exchange value for gold established as of yet. So finally, we may conclude that any medium of exchange or money must eventually regress back to a point in which its utility was determined by direct use value, as this direct use value establishes the money prices and exchange value of the money good.

Bitcoin’s Regression

We may now apply our knowledge of the regression theorem to Bitcoin. The foremost issue that must be pointed out is that it is empirically quite apparent that Bitcoin is being used as a medium of exchange. This fact alone defeats any argument claiming that Bitcoin “cannot be money” based on a violation of the regression theorem. There are currently prices for goods in terms of Bitcoins. Using this fact and our knowledge of the regression theorem, we can deduce that because Bitcoin prices for goods exist, Bitcoin must eventually regress back to a point in which its utility was based on direct use value. Those arguing against Bitcoin fail to understand this fundamental point: for Bitcoin prices of other goods to currently exist, as a prerequisite of these prices, there must have been some direct use value for Bitcoin. These prices could not ever have conceivably existed today without Bitcoin regressing to direct use value. Those arguing against Bitcoin from the basis of violating the regression theorem have already lost their argument due to Bitcoin prices for goods existing today. This is a crucial point made by Bob Murphy:

“the certain group of Misesians who keep deriding Bitcoin and saying it will eventually collapse, it’s a passing fad, it will never take off beyond internet geeks, etc. etc., because of Mises’ regression theorem, aren’t making any sense. Mises’ regression theorem wasn’t making an empirical prediction about a medium of exchange never attaining the status of money, unless it started out as a regular commodity. No, Mises is saying we can’t conceive of even a medium of exchange (which is a weaker condition than money) that didn’t start out as a regular commodity. Bitcoin is clearly, unequivocally a medium of exchange right now.”

The regression theorem isn’t a normative claim saying that for money to be “sound” it must have direct use value of some kind. It is an apodictic statement, established through a priori reasoning. In order for people to argue against Bitcoin, they must refute the chain of logic that brought Mises to the conclusion about regression that he came to. Any statement saying “the medium of exchange that is Bitcoin violates the regression theorem” is akin to saying “a circle is square”. The fact that Bitcoin currently is a medium of exchange implies that it doesn’t violate the regression theorem, as defined by the regression theorem. Austrian economists are certainly open to criticisms of the theorem itself; however, self-refuting arguments against Bitcoin such as the example given above need to be dismissed as a misunderstanding of both the basis of the regression theorem, and what Mises was trying to communicate. Until any such criticisms of the a priori logic are brought forth, we can establish that the de facto Austrian position on Bitcoin must be that it doesn’t violate the regression theorem.

With this being said, it seems apparent that the part that gives people trouble understanding this debate is what direct use value a good like Bitcoin could possibly have. As a caveat, it should be known that the character of Bitcoin’s direct use value is irrelevant to any discussion involving the regression theorem, which merely says that Bitcoin must have had direct use value at some point. However, it would not be totally useless to elaborate on this topic if it visualizes what the direct use value may have been, and for this visualization, I once again turn to Bob Murphy’s speculation of what may have happened at its inception:

“when Bitcoin was first introduced and no one had any idea of its purchasing power, the very first people to trade for it did so because it provided them with direct utility because they knew there was at least a chance that it would serve to chafe the governments of the world with their printing presses.”

Bitcoin’s utility, Murphy argues, might have derived from Bitcoin being capable of slaying the current government fiat system, which seems to be a very logical possibility. Utility from seemingly non-material uses like this may be hard for those against Bitcoin to grasp, as it is quite abstract, but this by no means is a negation of this point. It must be stressed once again that, material or non, Bitcoin must have had a direct use value of some kind.

Concerning Fallacious Economic Arguments

At this point, it seems necessary to refute a few of the many fallacious arguments floating around the Austrian community in regards to Bitcoin and the regression theorem. The first is an incorrect interpretation of the theorem in regards to Bitcoin put forth by the blogger “XC”. He/she asserts that the regression theorem is not violated because Bitcoin regresses back to fiat money, then to commodity (gold) money. This proposition entirely misinterprets the theorem, as it fails to ascribe any direct use value to Bitcoin; it doesn’t explain in any way why an actor would exchange his fiat money for an amount of Bitcoins in the first place. To establish a price for a Bitcoin, actors must weigh the utilities of a Bitcoin and a certain amount of fiat money. The regression theorem requires the utility of Bitcoin to regress to direct use value, and XC’s claim that Bitcoin regresses to fiat, then to commodity money fails to ascribe any direct use value to Bitcoin, and therefore misses the point.

The second argument currently being debated in Austrian circles comes from a post by blogger “Michael Suede”. In an slight improvement upon other criticisms of Bitcoin, Suede attempts to refute the regression theorem itself:

“So, once we have a perceived need in a free market for a trade facilitator and a store of wealth, what should we expect the market to do?  We can expect it to try and find a solution to this problem!  Mises attempts to argue that the market solved this problem because people valued gold for its own sake before it became a money, and it was this value they had for gold in ornamental use that allowed it to become a money.

This is patently wrong.  Consider that as soon as the market perceives a need for money, it wouldn’t matter if gold had a pre-existing value in ornamental use or not, because it would suddenly have value as a trade intermediary as soon as the need for a trade intermediary entered the public consciousness.”

Ironically, Suede’s interpretation of what Mises was claiming in the regression theorem is “patently wrong” in itself. Mises’ theorem does not say that the market solved the problem of trade facilitation and wealth storing through introducing money, though Mises would certainly agree that introducing money into an economy will solve these issues. These are but effects of introducing money. It in no way explains the origins of money, which is fundamentally the purpose of the regression theorem. Suede’s statement that “it wouldn’t matter if gold had a pre-existing value in ornamental use or not” is illogical in that if gold had no pre-existing direct use value, prices could not regress to anything. Thus, he offers no explanation for how prices for the medium of exchange could conceivably form without ever having a direct use value in the past, showing an inadequate understanding of what the regression theorem is, making his refutation of it fruitless.

The last important fallacy worth refuting is the notion that because a money or medium of exchange currently has no direct use value, or its direct use value is practically negligible in the face of its exchange value (such as Bitcoin), that it must therefore be a pyramid scheme based economic principle. On the surface, this claim appears to be in accordance with the regression theorem. This, however, isn’t the case, and a quote from Murray Rothbard shows us why:

“it does not follow that if an extant money were to lose its direct uses, it could no longer be used as money. Thus, if gold, after being established as money, were suddenly to lose its value in ornaments or industrial uses, it would not necessarily lose its character as a money. Once a medium of exchange has been established as a money, money prices continue to be set. If on day X gold loses its direct uses, there will still be previously existing money prices that had been established on day X – 1, and these prices form the basis for the marginal utility of gold on day X. Similarly, the money prices thereby determined on day X form the basis for the marginal utility of money on day X + 1. From X on, gold could be de­manded for its exchange value alone, and not at all for its direct use. Therefore, while it is absolutely necessary that a money originate as a commodity with direct uses, it is not absolutely necessary that the direct uses continue after the money has been established.”

Rothbard makes the obvious point that if money prices have already been set by direct use value in the past, there is no requirement that the money good continue to have its direct use value in regards to the regression theorem. Similarly, it does not follow that it is necessarily a “pyramid scheme” because it has no direct use value. A pyramid scheme is defined as “an unsustainable business model that involves promising participants payment or services, primarily for enrolling other people into the scheme, rather than supplying any real investment or sale of products or services”. However, Bitcoin clearly does not fall under this definition, as it is potentially sustainable (as shown by Rothbard), and provides a service in the sense that it holds exchange value. Purveyors of this argument fail to understand that simply because Bitcoin doesn’t hold direct use value, or material uses, it does not imply that there is no “real services” provided. The exchange value it holds is the real service, and with this understanding, it is apparent that the “pyramid scheme” claim collapses under economic analysis.

In summation, with sufficient understanding of the regression theorem, we may conclude that, until Mises’ praxeological chain of logic is articulately challenged, the de facto Austrian position must be one in which Bitcoin does not violate the regression theorem, and thus may function as a medium of exchange or money. People may argue against Bitcoin on the basis of its merits as a money, in that it can’t be the most saleable good, or isn’t a reliable store of value, but these are not praxeological arguments against whether Bitcoin can be a money. They are arguments against whether Bitcoin is efficient as a money. As a community, we must stress the dissociating of Austrians with those libertarians who argue that Bitcoin cannot be a money; most people will associate these claims as being Austrian, whereas it has been made clear beyond reasonable doubt that they cannot possibly be so.

Stay tuned for the next article in this series, which will address the importance of Bitcoin to the libertarian movement, and to non-aggression as a whole!



  1. Smiling Dave has pointed out many times, with quotes from Mises himself in Human Action and other Austrians, as well as explaining from first principles, that bitcoin has never fulfilled a key requirement to be a medium of exchange. It has never been IN WIDE DEMAND. He also showed, from first principles and from quotes from Mises, how wide that demand has to be, and how pathetically short bitcoin falls of meeting that criterion.

    Quench thy thirst for knowledge, oh lover of truth, by moseying on down to these links:

    And let me quote a bit from here:

    We have already quoted Mises as saying that a media of exchange has to be almost as widely demanded as money, which literally everyone wants. And certainly bitcoin has not achieved that. Estimates are that there are 100,000 people who own a bitcoin, and 6 billion people in the world. So the percentage of people who own a bitcoin is 1/60,000 of a percent, a number so low my calculator just gave up and called it zero. The same is true in every country. How many Americans own a bitcoin? Divide that by 350 million. What percent is that? Again, close to zero.
    Not close at all to “almost everyone”.

    About the many flaws in that Bob Murphy article:

    I have dealt with many aspects of the bitcoin topic here:

    1. I actually saw his blog about an hour after I finished my post! But yeah, me and him say the same thing pretty much. He really understands the theorem I think. Him and Peter Surda as well.

  2. I hope to reply to your reply soon, mross12. But can we agree that the statement that:

    …those libertarians who reject Bitcoin on the grounds of regression are not, and cannot be classified as, Austrian economists in this matter. The de facto Austrian position must be one in which Bitcoin does not violate the regression theorem, for reasons that will be explained later in the article…

    has been shown to be a bit exaggerated? It comes down to the q whether a medium of exchange has to be in wide demand to qualify as a contender for money. There are theoretical [=praxeological] as well as textual arguments that this is so. Hopefully, I will elaborate, since it seems not everyone gets this. In any case, I don’t think it anti-Austrian to have that position.

    1. Perhaps a bit of hyperbole, yes. But until I see someone refute Mises’ chain of logic, or in your case, definitively show that he required a medium of exchange to be “wide spread”, I will stand by it. There is rarely a grey area in praxeology, being a priori, so like I said, until this position is disproved, I would believe the Austrian position would have to be that Bitcoin doesn’t violate the theorem. That being said, of course I will hear any arguments to the contrary, yours included! I’m open to learn and be humbled if I am wrong.

  3. 1. I think I found a flaw in this article. Your position about use value, as I understand it, is that once there is exchange value, the use value can wither away, as Rothbard wrote [and so did Mises], just like with fiat money.

    You linked to this reasoning in your next article, citing it as a refutation of my claim that bitcoin has no use value. I guess you mean that it doesn’t need a use value, once it has an exchange value.

    So what’s the flaw? Simple. The essential stages to becoming money are these. First stage, it has only use value. Then it has use and exchange value. Then, according to Rothbard, there is an optional stage, that the use value can wither away.

    You see the problem. Bitcoin never went through the first stage. If you carefully reread my article,, especially point 2, you will why Stage One is essential.

    Put another way, your argument here is valid to refute those who say bitcoin still needs use value once it becomes money. I agree that Rothbard is saying that. But it does not refute the point that bitcoin has to have started with a use value before it was ever used for exchange, which it never did. Thus whatever is happening now is not bitcoin being used as money, for that would violate the reg. thm. It’s something else, as i explained in my articles.

    2. I may as well reply here to the point you raised in your next article about the big prison and the small prison. The way it works is this. Mr A will only accept a cigarette as payment if he knows it will make his life easier [with respect to trading for things] than having to wait around for a double coincidence of wants. In a prison, where the inmates are closed off from the outside world, but have most of their dealing with the prison population [whatever its size], and where cash is scarce, accepting cigarettes makes life easier. So it becomes a medium of exchange, because almost everyone they are willing and able to trade with accepts them. But if most of the people a person deals with [=buys from and sells to] are unwilling to accept cigarettes as payment, for whatever reason, then he won’t either, even if three people are.

    What about the prison guard? He has access to both the prison and the outside world. If the prison economy has a lot to offer him, and he knows that the prisoners prefer cigarettes to cash, then he will accept cigarettes as payment occasionally. But should the warden tell him he will have to get his salary in cigarettes, he will surely refuse, because he needs cash , and a lot of it, for the outside world.

    The point is, most people in the world now either have never heard of bitcoin, or refuse to accept payment in it, or instantly convert it to cash, or are willing to take in a small amount of bitcoins as payment because they want to speculate in bitcoin. But nobody, including the most loyal bitcoin fans, are willing to have their salary tied to the bitcoin, and be paid only in bitcoins. Ever so much more so [and I mention this as a thought experiment] if all the places that offer goods and service for bitcoins continue to do so, but the exchanges will no longer trade it for dollars.

    Nobody accepts a bitcoin because he thinks, “This is so much more convenient than being paid in dollars. I will so be able to get anything i want with these bitcoins, unlike those clumsy dollars. With bitcoins, I can pay my rent, buy gas, pay the electric bills, shop at the mall in all the stores, something I could never do with those dollars nobody wants.” Meaning he is not accepting bitcoin because he regards it as money.

    Mises sums up the whole idea of money like this: A man who finds it hard to obtain in direct barter what he wants to acquire, renders better his chances of acquiring it in later acts of exchange by the procurement of a more marketable good. What I’m saying in the previous paragraph is that bitcoin does not fit this description of money.

    Mross12, I apologize that I can’t continue this fascinating discussion. My humble blog has over a dozen articles on bitcoin, and I’ve moved on to other interests for now. And I see that careful reading of what I already have published would have answered your q’s, as in the instance above about use value.

    All the best.

  4. I’m sorry, one last point. When Mises and Rothbard wrote that a money that loses its use value does not violate the reg, thm. they were not saying that it would continue to be used as money. It would stop being used if there was any alternative whatsoever. I wrote about this in my article The Kickstart Fallacy.

    1. I think you misinterpret Mises in the “Kickstart Fallacy” as well, as when he is talking about value, he is talking about both exchange and direct use value, not just direct use value as you presume. If the value of both of these things falls, then yes, the demand for the money would fall. But in something like Bitcoin, which has virtually almost always held only exchange value after the first bartered transaction setting the price, the exchange value isn’t decreasing. If anything it is increasing as more people begin to accept it as legitimate.

      As for criticisms (1.), my refutation is that because prices even exist at all today, it HAD to have had a direct use value. That is a requirement of the regression theorem. Like I said, saying that “a medium of exchange that has currently existing prices violates the regression theorem” is like saying “a circle has four sides”. It has no logical sense. Unless you criticize the theorem itself, you have no argument here.

      As for criticism (2.), you err here: “if most of the people a person deals with [=buys from and sells to] are unwilling to accept cigarettes as payment, for whatever reason, then he won’t either, even if three people are.” You do not know that he will not accept them, you are making an invalid assumption here. He may still use the cigarettes as a medium of exchange with the other two inmates, as if he does not, he cannot trade with those people. There is nothing to say he will not use the cigarettes as a medium of exchange still. Apply this to Bitcoin, and you see that if certain people want to trade with those who ONLY accept bitcoins, which is a possibility, they will have to use Bitcoin as a medium of exchange or money, and thus may potentially accept some bitcoin.

      You also err here: “The point is, most people in the world now either have never heard of bitcoin, or refuse to accept payment in it, or instantly convert it to cash, or are willing to take in a small amount of bitcoins as payment because they want to speculate in bitcoin. But nobody, including the most loyal bitcoin fans, are willing to have their salary tied to the bitcoin, and be paid only in bitcoins.” First of all here’s this, and second of all you are not arguing whether Bitcoin IS or ISN’T a medium of exchange, but whether it will operate efficiently or not as a money. I made this point in my first article. Most criticizers of Bitcoin on the basis of the regression theorem are actually arguing whether or not Bitcoin is efficient as a medium of exchange/money, whereas the regression theorem is a positive analysis of what IS or IS NOT money, what CAN and CAN’T be a medium of exchange.

      Anyways Dave fair enough. I enjoyed debating you. All the best to you as well!

      1. Just a short note about one point in your reply:

        If that police chief wanted to be paid in tomatoes, would that make tomatoes money?

        First of all, one person does not a money make. Second, he is not being paid, say, .5 bitcoin a month. His contract is in dollars, and every payday he gets more or less bitcoins depending on the going rate. [Otherwise, how could they deduct taxes in advance, which are not payable in bitcoin?] For these two reasons, that police chief story, though interesting, is not relevant.

        By the way, I wonder how feels having his pay lose 50% of it’s value since January.

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