Mises Wire

Bitcoin and the Theory of Money

[This article is part of the Understanding Money Mechanics series, by Robert P. Murphy. The series will be published as a book in 2021.]

In a modern primer on money mechanics, it is necessary to provide at least an introduction to Bitcoin.1  Consequently, in this final chapter we will first give a basic explanation of what Bitcoin is and how it works. Then we will place Bitcoin in the framework of money that we developed in chapter 2, seeking to answer the fundamental question: Is Bitcoin money? Finally, we will relate Bitcoin to an important component in the Austrian school’s discussion of money, namely Ludwig von Mises’s “regression theorem.”

Explaining Bitcoin with an Analogy1

“Bitcoin” encompasses two related but distinct concepts. First, individual bitcoins (lowercase b) are units of (fiat)3  digital currency. Second, the Bitcoin protocol (uppercase B) governs the decentralized network through which thousands of computers across the globe maintain a “public ledger”—known as the blockchain—that keeps a fully transparent record of every authenticated transfer of bitcoins from the moment the system became operational in early 2009. In short, Bitcoin encompasses both (1) an unbacked digital currency and (2) a decentralized online payment system.


According to its official website: “Bitcoin uses peer-to-peer technology to operate with no central authority; managing transactions and the issuing of bitcoins is carried out collectively by the network.”4  Anyone who wants to participate can download the Bitcoin software to his or her computer and become part of the network, engaging in “mining” operations and helping to verify the history of transactions.

To fully understand how Bitcoin operates, one needs to learn the subtleties of public-key cryptography, which we briefly discuss in a later section. For now, we focus instead on an analogy that captures the economic essence of Bitcoin, while avoiding the need for new terminology.

Imagine a community where the money is based on the integers running from 1, 2, 3, … up through 21,000,000. At any given time, one person “owns” the number 8, while somebody else “owns” the number 349, and so on.

In this setting, suppose Bill wants to buy a car from Sally, and the price sticker on the car reads “Two numbers.” Bill happens to be in possession of the numbers 3 and 12. So Bill gives the two numbers to Sally, and Sally gives Bill the car. The community recognizes two facts: first, the title to the car has been transferred from Sally to Bill, and second, Sally is now the owner of the numbers 3 and 12.

Further suppose that in this fictitious community an industry of thousands of accountants maintains the record of ownership of the 21 million integers. Each accountant keeps an enormous ledger in an Excel file. The columns run across the top, from 1 to 21 million, while the rows record every transfer of a particular number. For example, when Bill bought the car from Sally, the accountants who were within earshot of the deal entered into their respective Excel files “Now in possession of Sally” in the next available row, in the columns for 3 and 12. In these ledgers, if we looked one row above, we would see “Now in the possession of Bill” for these two numbers, because Bill owned these two numbers before he transferred them to Sally.

Bitcoin Car Sale

Besides documenting any transactions that happen to be within earshot, the accountants also periodically check their own ledgers against those of their neighbors. If an accountant ever discovers that his neighbors have recorded transactions for other numbers (i.e., for deals for which the accountant in question was not within earshot), then the accountant fills in those missing row entries in the columns for those numbers. Therefore, at any given time, there are thousands of accountants, each of whom has a virtually complete history of all transactions involving all 21 million numbers.

Explaining the Analogy

We hope our analogy gives a decent first pass in explaining how Bitcoin works. In our hypothetical story, the people in the community kept track of which person “owned” an abstract, intangible number. Of course, you can’t physically hold the number 3, but because the people in the community had adopted a convention where the accountants’ Excel files kept track of which person was “matched” with the number 3, there was a sense in which the person owned it. And then, as our story showed, a person could transfer his claim to a number in order to buy real goods, such as a car.

To keep things simple, in our analogy, we assumed that the community had already reached the end state after all of the bitcoins have been “mined.” In the real world, this will occur at some point after the year 2100, when (virtually) all of the 21 million bitcoins will be in the hands of the public.5  After that time, there will be no more “mining” operations; the total number of bitcoins will be fixed at 21 million, forever.

Just as in our story, when people in the real world want to buy something using Bitcoin, they transfer their ownership of a certain amount of bitcoins (or fractions of a bitcoin, for smaller purchases) to other people in exchange for goods and services. This transfer is effected by the network of computers performing computations, and changing the public key to which the “sold” bitcoins are assigned. (This is analogous to the accountants in our story entering a new person’s name in the column for a given integer.) Rather than physically handing over an object—such as a $20 bill or a gold coin—to the seller, the buyer who uses Bitcoin engages in the necessary electronic operations in order to command the network of computers to edit the blockchain to reflect the transfer of ownership/control of the relevant bitcoins to the seller.

Where Does Cryptography Come In? The Problem of Anonymous Owners

The present book deals with economics, not computer science, and consequently we will only provide a brief sketch of what’s going on during a Bitcoin transaction. (Interested readers can refer to the endnotes for a fuller explanation.6 ) But we can’t really apply economic concepts to something like Bitcoin, if we don’t have a decent understanding of what it is and how it works.

We should first clarify that though you may often hear the term encryption in this context, Bitcoin doesn’t actually use encryption. Indeed, the whole point is to provide a public ledger, recording all of the Bitcoin transactions that have ever occurred. It would defeat the purpose to hide the transaction messages with encryption. Rather, what we want is a way to securely authenticate the transactions involving transfers of bitcoins.7

Let us return to our fictitious world of Bill and Sally, where the money is based on publicly recognized “ownership” of the 21 million integers. Our story above had one glaring problem we need to address: How do the accountants verify the identity of the people who try to buy things with numbers? In our example, Bill wanted to sell his public claim on the numbers 3 and 12 to Sally for her car. Now, in our story, we assumed that Bill really was the owner of the numbers 3 and 12; he can afford Sally’s car, because she’s asking “two numbers” for it. The accountants will verify, if asked, that Bill is the owner of those numbers; under the “3” column and the “12” column in all of their ledgers, it says “Bill” in the last row that has an entry in it.

But here’s the problem: When the nearby accountants see Bill trying to buy the car from Sally, how do they know that that particular human being actually IS the “Bill” listed in their ledgers? There needs to be some way that the real Bill can demonstrate to all of the accountants that he is in fact the same guy referred to in their ledgers. To prevent fraudulent spending of one’s currency by an unauthorized party, this mechanism must be such that only the real Bill will be able to convince the accountants that he’s the guy.

In the real world, solving this problem is where all of the complicated public-/private-key cryptography comes in. To reiterate, in the Bitcoin guide cited in the endnotes, we go over all of this material in a thorough yet intuitive way, but for our purposes here, we want to provide a basic understanding of how the Bitcoin protocol works without wading into technical details.

Unfortunately, at this point our story of Bill and Sally gets a little silly, but it’s the best the present author could come up with. So, without further ado, suppose the following is how the people in our fictitious world deal with the problem of matching the names in the accountants’ Excel ledgers with real-world human beings: each time one of the numbers is transferred in a sale, the new owner has to invent a riddle that only he or she can solve. You see, the people in the community are clever enough to recognize the correct answer to the riddle when they hear it, but they are not nearly creative enough to discover the answer on their own.

For example, when Bill himself received the numbers 3 and 12 from his employer—suppose he gets paid “two numbers” every month in salary—the accountants said to him:

OK, Bill, to protect your ownership of these two numbers, we need you to invent a riddle that we will associate with them. We will embed the riddle inside the same cell in our ledger as the name “Bill,” in the columns under 3 and 12. Then, when you want to spend these two numbers, you tell us the answer to your riddle. We will only release these numbers to a new owner if the person claiming to be “Bill” can answer the riddle. Keep in mind, Bill, that you might be on the other side of town, surrounded by accountants you have never seen before, when you want to spend these numbers. That’s why our seeing you right now isn’t good enough. We need to put down a riddle in our ledgers, which will also be copied thousands of times as the information pertaining to this sale reverberates throughout the community, so that every accountant will eventually have “Bill” and your riddle embedded in the correct cell in his or her ledger.

Bill thinks for a moment and comes up with an ingenious riddle. He tells the accountants, “When is a door not a door?” They dutifully write down the riddle, which then gets propagated throughout the community, along with the fact that “Bill” is the new owner of 3 and 12.

A few days later, some villain tries to impersonate Bill. He wants to buy a necklace that has a price tag of “one number.” So the villain says to the accountants in earshot, “I’m Bill. I am the owner of 12, as everyone can see; these spreadsheets are public information. So I hereby transfer my ownership of 12 to this jeweler, in exchange for the necklace.”

The accountants say, “OK, Bill, just verify your identity. What is the solution to your riddle? Tell us, ‘When is a door not a door?’”

The villain thinks and thinks but can’t come up with anything. He says, “When the door isn’t a door!” The accountants look at each other, scratch their heads, and agree, “No, that’s a dumb answer. That didn’t solve the riddle.” So they deny the sale; the villain is not given the necklace.

False Bitcoin Exchange

Now, a few weeks later, we are up to the point at which our story originally began, at the beginning of this chapter. The real Bill wants to buy Sally’s car for “two numbers.” He announces to the nearby accountants, “I am the owner of 3 and 12. I verify this by solving my riddle: a door is not a door when it’s ajar.” The accountants all beam with delight! Aha! That is a good answer to the riddle. They agree that this must be the real Bill and allow the sale to go through. They write down “Sally” in the next-available rows in columns 3 and 12, and then ask Sally to give them a new riddle, to which only Sally would know the answer.

Thus ends our analogy to explain the basics of what Bitcoin is and how it works. In the real world, of course, rather than generating and solving verbal riddles, there are complex math problems that only the legitimate owners of the bitcoins can quickly solve (using their private keys). But we have hopefully given enough of a sketch of Bitcoin so that we can now analyze it in terms of the economic framework that we developed way back in chapter 2 of the present book.

Is Bitcoin a Type of Money?

Recall our discussion of the theory of money in chapter 2. We first pointed out the limits of direct exchange—remember the farmer who needed his shoes repaired and had eggs to offer, but the cobbler wanted bacon? We saw in that story how indirect exchange could solve the problem. Specifically, when the farmer traded his eggs to the butcher in exchange for bacon, the bacon became a medium of exchange. The farmer accepted the bacon not because he wanted to use it directly, but because he intended to trade it away in the future for something else.

After we explained what a medium of exchange was, we went on to provide this formal definition: money is a medium of exchange that is universally accepted in a given community. This means there are two criteria that must be satisfied for a good to be classified as money: First, the good must be something that people are willing to accept, not because they plan on using it directly, but because they plan on trading it away again in the future. (This makes it a medium of exchange.) Second, (just about) everyone in the community must be willing to do so; if only a fraction of the public accepts a particular good in this way, then it is still a medium of exchange, but it’s not money.

After reviewing this standard terminology, we can apply it to Bitcoin. At this point in its history, Bitcoin is no doubt a medium of exchange; there are thousands of people around the globe, who trade away valuable goods and services in exchange for receiving public acknowledgement—codified in the blockchain—that they control certain (fractions of) bitcoins. The reason these sellers accept bitcoins, of course, isn’t because they intend on eating them or using them to produce mousetraps. Rather, people accept bitcoins in trade because they expect them to have purchasing power in the future; they want the ability to trade the bitcoins away for other goods and services, down the road.

However, even though bitcoins clearly count as media of exchange for some people, we are currently nowhere near the point at which they are universally accepted in any economically relevant community (unless we cheat by defining the relevant community as “those people who are happy to receive bitcoins in trade”). Thus far, then, Bitcoin doesn’t count as money, though in principle Bitcoin—or some other cryptocurrency that surpasses it in popularity—could achieve this status in the future.

Relating Bitcoin to the Work of Mises

In closing, we should address a controversy regarding Bitcoin and the monetary work of the famous Austrian economist Ludwig von Mises. In his masterful 1912 book, translated as The Theory of Money and Credit, Mises took the new theory of subjective value—pioneered in the early 1870s by economists including Carl Menger, founder of the Austrian school—and applied it to the valuation of money itself.8

Previous economists had thought this approach wouldn’t work, because it seemed to involve a circular argument. It made sense to use Menger’s framework for explaining, say, the value of potatoes or wine; people subjectively valued the satisfactions that these goods delivered, and that was the starting point for understanding their exchange value in the marketplace.

But when it came to explaining the market value—or purchasing power—of money itself, Menger’s subjective value theory seemed like a dead end, because the only reason you value money is that it allows you to buy things in the market. Thus it seemed as if the economist had to argue that people value money because people value money. This was a circular argument, and that’s why most economists used Menger’s subjective value theory to explain the market value of all goods and services except money.

Yet in his 1912 work Mises showed the way out of this logjam. The solution was to introduce the time element. Specifically, when people accept money in trade right now, it’s because they expect the money to have purchasing power in the future. And their expectations of this purchasing power are based on their observations of money’s ability to fetch goods and services in the immediate past. To put it succinctly: people value money today because they expect money to have a certain value tomorrow, and this in turn is based on their memory of its value yesterday.

So far, so good: Mises had eluded the apparently circular argument by introducing the time element. But now he faced a different objection: If the economist using subjective value theory ends up explaining the purchasing power of money today based on observations of its purchasing power yesterday, then how do we explain its purchasing power yesterday? Why, we have to go back to the day before yesterday, and so on. The critics then asked, Hasn’t Mises merely replaced a circular argument with an argument suffering from an infinite regress? It still seemed as if applying Menger’s new value theory to money itself wasn’t going to work.

Yet Mises solved this problem too. He pointed out that we don’t need to trace back the purchasing power of money for an infinite distance into the past. Rather, we just have to trace it back to the point at which the monetary good was a regular commodity, before it was valued in its role as a medium of exchange.

For example, in our story involving the farmer, we have no problem using Menger’s subjective value theory to explain why people in the community would value bacon directly, for its ability to satisfy hunger in a tasty way. Then, we could add the complication of how bacon’s market value would be augmented once the farmer accepted it in trade not because he wanted to eat it, but because he wanted to trade it to the cobbler. Notice that there is no infinite regress in this procedure.

This technique is what came to be known as Mises’s regression theorem. By explaining the market value of money with reference to a historical chain going back to the emergence of regular commodities out of a world of direct exchange, Mises was able to solve the problems that had prevented other economists from applying “modern” (i.e., post-1871) subjective value theory to money itself.

Because Mises had to cite the emergence of money from a state of direct exchange in order to satisfactorily explain its current market value, he made some pretty definitive statements about the type of past that money necessarily had to have. Here are two examples from Mises’s classic work, Human Action:

[N]o 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. (Mises 1998, p. 407)


A medium of exchange without a past is unthinkable. Nothing can enter into the function of a medium of exchange which was not already previously an economic good and to which people assigned exchange value already before it was demanded as such a medium. (Mises 1998, p. 423)

In light of Mises’s sweeping claims, we can quickly see why so many fans of the Austrian school have a major problem with Bitcoin: Since Bitcoin was born to be a currency—rather than first serving as a regular commodity—doesn’t that mean it can’t be money? Or, going the other way, if Bitcoin ever did become money, wouldn’t that mean that Mises must have been wrong?

At the risk of being evasive, we are not here going to explore the fascinating question of whether the case of Bitcoin violates the regression theorem, or whether its unorthodox features can be made compatible with Mises’s monetary framework (which he obviously conceived with tangible goods in mind). Other economists familiar with the Austrian school and Bitcoin have weighed in on this intriguing issue.9

Rather, here we are going to make a much more modest claim: whether Bitcoin violates or is compatible with the regression theorem is not an empirical question at this point. As the quotes from Mises above indicate, the regression theorem actually doesn’t refer to a good becoming money, but rather a good becoming a medium of exchange.

And as we’ve already argued, Bitcoin has clearly already become a medium of exchange (though it is not money under any reasonable standard). So it must already be the case one way or the other: either the emergence of Bitcoin as a medium of exchange violated the regression theorem, or it didn’t. (Reasonable cases can be made for both options.) There is no further hurdle that the regression theorem imposes that would hinder Bitcoin’s adoption by the community at large and hence its becoming not just a medium of exchange, but money.

To sum up: whether Bitcoin becomes a bona fide money is still an open empirical question, but at this point—since Bitcoin is already a medium of exchange—Mises’s regression theorem doesn’t have any bearing on the outcome.​

  • 1a1bFor concreteness, in this chapter we will refer specifically to Bitcoin. However, much of what we say will be applicable to other cryptocurrencies.
  • 3Many Bitcoin enthusiasts would vehemently object to classifying it as a fiat currency, because the Bitcoin network is completely voluntary and doesn’t rely on state-enforced legal tender laws or other methods of suppressing competition. However, in monetary economics the term fiat has a very precise meaning, under which (we argue) bitcoins would qualify. (See Ludwig von Mises’s The Theory of Money and Credit for a scholarly treatment.) In particular, it is simply not true that the state can merely declare “through fiat” that something is money. In our judgment, it is more important for the beginner to understand that there is no other commodity or asset “backing up” bitcoins—and this is the sense in which it is a fiat currency—rather than to avoid the possibly negative connotations from our use of a term that is usually reserved for low-quality money issued by modern states.
  • 4See http://bitcoin.org.
  • 5Strictly speaking, the total quantity of mined bitcoins will never quite reach 21 million; the protocol ensures that eventually the reward for mining a new block will be rounded down to literally zero bitcoins (sometime around the year 2140). But it is currently projected that by the year 2108 mining from that point onward will only bring into circulation ever smaller fractions of the 21 millionth bitcoin; see “Controlled Supply,” Bitcoin Wiki, last modified Feb. 11, 2020, https://en.bitcoin.it/wiki/Controlled_supply#Projected_Bitcoins_Long_Term.  Another complication is that some (fractions of) bitcoins will be “lost” over the decades as people die or forget their private keys, and so on. Therefore, even though these (fractions of) bitcoins will have been mined, they will forever be inaccessible in transactions, making them effectively removed from the quantity of bitcoins available to the public. They will be economically equivalent to gold coins that went down with a ship and are sitting at the bottom of the ocean.
  • 6For a thorough explanation of the cryptography behind Bitcoin transactions, see Barta and Murphy, Understanding Bitcoin, in particular pp. 14–35.
  • 7The confusion may come from the fact that both encryption and authentication are topics within the field of cryptography. They are also “dual” to each other in that in public key systems the operation of signing a message is the same as decrypting one, and the operation of verifying a signature is the same as encrypting a message. But to repeat, strictly speaking, Bitcoin doesn’t rely on encryption, even though many people often say that it does.
  • 8For a more detailed treatment of this topic, see Robert P. Murphy, “The Origin of Money and Its Value,” Mises Daily, Sept. 29, 2003, https://mises.org/library/origin-money-and-its-value.
  • 9See, for example. Laura Davidson and Walter Block, “Bitcoin, the Regression Theorem, and the Emergence of a New Medium of Exchange,” Quarterly Journal of Austrian Economics 18, no. 3 (Fall 2015): 311–38, available at https://cdn.mises.org/Bitcoin%20the%20Regression%20Theorem%20and%20the%20Emergence%20of%20a%20New%20Medium%20of%20Exchange.pdf.
Note: The views expressed on Mises.org are not necessarily those of the Mises Institute.
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