What’s a Bitcoin Worth? (Wonkish)

This might be one of those questions I’ll eventually be embarrassed for asking, but…..

Imagine a future in which Bitcoins (or some other non-governmental currency) are widely accepted and easily substitutable for dollars, at an exchange rate of (say) $X per Bitcoin.

Then if there are M dollars and B bitcoins in circulation, the money supply (measured in dollars) is effectively M + X B .

Money demand is presumably P D, where P is the general price level and D depends on things like the volume of transactions and the payment habits of the community. (If it helps, we can write D = T/V where T is the volume of transactions and V is the velocity of money.)

Equilibrium in the money market requires that supply equals demand, so

M + X B = P D

Now M is determined by the monetary authorities; B is determined by the Bitcoin algorithm, and D, as noted above, is determined outside the money market.

That leaves me with two variables (X and P) but only one equation. What pins down the values of these variables?

Note: Of course, one feature of Bitcoins is that they’re an international currency, not a national one, so that a full-fledged model would accout not just for interchangeability with dollars, but also with pounds, rupees and yen. But if I can understand how things would work in a single country, I don’t think I’ll have much trouble extrapolating to the world. So let’s start with this simple case.

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71 Responses to “What’s a Bitcoin Worth? (Wonkish)”


  1. 1 1 David Pinto

    X = (PD – M)/B

    I take it this means the monetary authorities can destroy the value of the bitcoin by printing lots of money.

  2. 2 2 Robert

    Isn’t X just a function of M and B? Seems like X is simply M/B since it is dollars per Bitcoin. If they are 100% substitutable, then X is just a ratio of outstanding monies. Whenever Bitcoin (Central Bank) prints more B (M), that reduces (increases) the exchange rate. The equation is still essentially the quantity theory of money and you can think of the money supply either in terms of M or B. And if you can think of money supply as either M or B, then one can conceivably think of price level in terms of M or B.

    From a Econ 101 perspective of saying that increases in the Money Supply will cause Inflation, it seems to be the case here as well except there is an inflation rate for M and B. Bitcoin cannot influence the inflation rate for M because if Bitcoin prints more B, that only reduces the exchange rate and keeps the total available M the same. But in that scenario, Bitcoin would put upward pressure on the price level of B.

  3. 3 3 Steve Landsburg

    David Pinto:

    I take it this means the monetary authorities can destroy the value of the bitcoin by printing lots of money.

    No, this doesn’t follow at all, because we don’t know how P adjusts.

  4. 4 4 Matt

    To a first approximation, M + XB = M, which means M = PD.

    So X = (PD – M)/B = zero.

    ;)

  5. 5 5 Steve Landsburg

    Robert:

    Seems like X is simply M/B since it is dollars per Bitcoin

    I don’t know where you’re getting this, and I doubt very much that there’s any reason to expect it.

  6. 6 6 AMTbuff

    Steve, it would help to highlight the differences between Bitcoins and other assets like Pokemon cards or artwork prints whose prices are at least temporarily far above cost of production.

    It seems that two factors are at work: subjective desirability and limited supply. In most cases the producer cannot resist the incentive to increase supply. This is why the work of a dead artist is more desirable than the work of that artist while he or she was living. (Artists need to give artwork to their heirs BEFORE they die to minimize taxes!)

  7. 7 7 Jonathan Campbell

    It seems to me it will be a function of the fact that the distribution of bitcoins per person is not the same as distribution of $ per person (where distributions are normalized). So for example, given we are at the equilibrium for X and P, we cannot simply increase both X and P, because that would harm people who do not own bitcoins. That harm would manifest itself as a lower demand to buy things (by them), which prevents P from increasing.

  8. 8 8 Nick

    This makes me wonder then why this isn’t a problem between dollars printed at different points in time. There is a different quantity of dollars printed in 1974 than in 2004, yet this doesn’t seem to stop us from having an exchange rate of one between them and then pinning down a price level. Why does the exchange rate of 1 hold? Is it because the printer of the currency tells us it must? Is it the label of dollar on both? hmm…

  9. 9 9 Steve Landsburg

    Nick: The reason for the exchange rate of 1 between 1974 and 2004 dollars is that you can pay a dollar’s worth of taxes with either. The govt’s willingness to accept both in payment of taxes nails down the exchange rate. But unless the govt starts accepting Bitcoins for tax payments, there’s no analogous phenomenon between bitcoins and dollars.

  10. 10 10 Will A

    (not wonkish)

    How do you see this being different from an once of Gold?

    Gold in a non-governmental, can be converted between different currencies.

    The bitcoin algorithm calls for more bitcoins to be added every year, every year more gold is found.

    There will eventually be a capped number of bit coins, until they come up with a Midas machine, the amount of gold on earth is finite.

    I would think if you could come up with a way to pin down X and P for a non-governmental currency, then you could make a gazillion buying and shorting gold futures.

  11. 11 11 Steve Landsburg

    Will A: Gold is not terribly convenient for everyday transactions (you can’t order a pizza and pay in gold), so the demands for gold and money are separate. This gives us two separate “supply=demand” equations. But I am envisioning a future in which bitcoins and dollars serve all the same functions, so that there’s just one demand function for bitcoins/gold, hence one equation in two unknowns.

  12. 12 12 Will A

    Prof. Landsburg:

    I’m asking these questions more for learning than a challenge.

    The last question I have (if you or anyone chooses to answer) is:

    How is this different than when Egyptians and Israelis decide to trade using U.S. dollars?

    From the Egyptians and Israelis point of view how is using U.S. dollars to conduct business different than using a bitcoin?

  13. 13 13 Steve Landsburg

    Will A: The difference is one of degree, not kind. Egyptian and Israeli currencies are not interchangeable with US currency, especially within the US. The problem arises when/if two currencies are perfectly interchangeable.

  14. 14 14 Jonathan Campbell

    Run a simulation. Tom owns a bitcoin, Tim owns a dollar, and Tad owns a can of tuna. Tom and Tad have already eaten dinner. Tim is willing to pay up to 1 dollar for the tuna, Tad is willing to sell for something greater than 0, and Tom has no interest. Thus a bitcoin will have very little value relative to a dollar, and a can of tuna will be worth $0 and $1.

  15. 15 15 Eric Johnson

    If the Monetary authority’s strategy is level targeting, then instead of simply manipulating M, they would have to take in account the effect changes in M would have on X.

    At first glance, I’d think M creation would cause X to fall, partially mitigating the effect the central bank would be hoping for.

  16. 16 16 Jonathan Campbell

    Scratch that last post, it is totally wrong. Seems like, assuming you can pay taxes only in dollars, there is no reason bitcoins can’t be worthless (they have no fundamental property that distinguishes them from monopoly money). And yet we know bitcoins are not worthless. Thus the problem must indeed be underdetermined in some sense.

    To the extent that there is a missing constraint not mentioned in the post it is this: the probability that the U.S. govt goes bankrupt, and the dollar becomes a broken currency. The higher that probability, the more valuable the bitcoin with respect to the dollar. So we can think of the value of a bitcoin as a reflection of the probability that the U.S. govt (and Federal Reserve) go defunct.

  17. 17 17 Steve Landsburg

    Jonathan Campbell:

    Seems like, assuming you can pay taxes only in dollars, there is no reason bitcoins can’t be worthless (they have no fundamental property that distinguishes them from monopoly money). And yet we know bitcoins are not worthless. Thus the problem must indeed be underdetermined in some sense.

    Well, bitcoins *do* have important properties that distinguish them from monopoly money (they are more secure in many ways), but your fundamental point seems right to me — despite all those differences, there’s still no clear reason that bitcoins couldn’t be worthless; they nevertheless have value; therefore the system is undetermined. The question I’m raising in the post is: Is this all there is to say, or is there something more that I (and presumably you) are missing?

  18. 18 18 Mike H

    There already exist (rare) example where there are two currencies in circulation simultaneously. How are exchange rates determined there?

    How is the exchange rate between $1 bills and $100 bills determined? Is it 1:1000 always?

    I suspect that X would be free to move, hence would be determined by expectation of future exchange rates, leading with probability 1 to an eventual permanent crash in the value of the bitcoin.

  19. 19 19 Steve Landsburg

    Mike H: The exchange rate between $1 bills and $100 bills is largely nailed down by the fact that 100 $1 bills and one $100 bill are perfect substitutes when it comes to meeting one’s tax obligations.

  20. 20 20 Neil

    I’d prefer to write the equation as (M+XB)V=PQ where Q is rate of transactions in goods and V is velocity. P is the price of goods in dollars or $/Q. What seems to be missing here is the price of goods in bitcoin units–lets call it P’. If the velocity of money is the same for dollars and bitcoins, then shuldn’t purchasing power parity fix X at P/P’? In other words, there are three prices out there–$ per unit of good, bitcoins per unit of good, and dollars per bitcoin. If I can buy goods using one form of money cheaper than another the arbitrage would be possible, and the exchange rate between dollars and bitcoins (X) must adjust until the purchasing power parity of both currencies are the same.

    I think. I’m not a monetary economist.

  21. 21 21 Neil

    Sorry, scrap that comment. After checking there do not appear to be prices for goods quoted in bitcoin, so PPP can’t nail it down. Looks indeterminate to me. Perhaps bitcoin is an asset whose value is simply determined by whether people think it can be sold to a greater fool. The wide fluctuations in its value supports that view.

  22. 22 22 Mike H

    Steve #19 Mike H: The exchange rate between $1 bills and $100 bills is largely nailed down by the fact that 100 $1 bills and one $100 bill are perfect substitutes when it comes to meeting one’s tax obligations.

    So in your hypothetical world, wouldn’t this principle tend to push X towards 0?

  23. 23 23 dave

    http://www.npr.org/blogs/money/2013/04/18/177742944/adam-davidson-explains-bitcoin-to-stephen-colbert

    i think the point is that non-governmental currencies like gold and bitcoins and disney bucks are valueless compared to governement backed currencies.

  24. 24 24 PG

    I think fundamentally this goes back to Scott Sumner’s debate with other Market Monetarists as to whether the key function of money is unit of account or medium of exchange. This example to me seems to prove Scott was right – if you’re still measuring everything in dollars, then the left side of the equation should only have dollar money supply and the price of bitcoins is still just one of the prices in the set of relative prices, just like the price of any other scrip that isn’t the medium of account.

  25. 25 25 Nick J

    If they’re perfect substitutes then the price is their willingness to trade one for the other.

    That seems wrong because the price of bitcoins is nominal so how can people have hard preferences over it? But I think when you say they’re perfect substitutes you’re implicitly assuming some marginal rate of substitution.

    If the question is what determines those preferences then it seems right to me that they’re determined by some complicated behavioral stuff based on people’s perceptions of what the bitcoin makers and the government are going to do or are doing.

  26. 26 26 Harold

    perhaps a way to approach this is to ask what would cause a change in X rather than P?. I will write it down so I can understand it. Please correct me if I am wrong.

    If we had only dollars, and we issue more dollars, then prices rise.

    Lets say we had a bitcoin equal to $1 to start with and we issued more bitcoin. The equation can be satisfied either by prices rising and exchange rate staying the same, or prices staying the same and exchange rate falling (or some combination). What determines which occurs? I think that is a re-phrasing of the problem.

  27. 27 27 Mike

    If Bitcoins and dollars are easily exchangeable, why does the ability to pay taxes in one matter? I can’t pay my taxes easily in quarters either, but that doesn’t make 4000 of them less valuable than a check for $1000. I still don’t understand why the situation would be different if you just replaced the word “bitcoin” with “euro”…

  28. 28 28 Bob Murphy

    Yay! I was wondering when you were going to start writing about Bitcoin, Steve. You’ve got to be one of the few economists on the planet who could absorb the protocol (public/private key signatures etc.) quickly and then speak knowledgeably on the topic.

  29. 29 29 Harold

    Mike: #26. I think the difference with euro’s is they are not widely accepted in USA.

    I suspect if you wanted to pay someone $1000, or $10,000 for something in quarters they might want to charge a bit extra.

  30. 30 30 Neil

    I retract my retraction. Prices of goods are quoted in BTC. PPP can determine X (in theory). However, the fact that X wildly fluctuates suggests PPP isn’t enough, just as it is not enough to determine currency exchange rates. This is probably because there is an asset demand as well as a transaction demand for bitcoin.

  31. 31 31 Jonathan Campbell

    Mike (26): a key difference is that European countries accept tax payments in euros.

  32. 32 32 Dan

    I think the problem is artificially created. Why are we assuming that D is independent? Why there is one D for both bitcoins and dollars? Why is M and B not dependent on D (if there is a large increase in demand for money they may change the bitcoin algorithm and increase the money supply)? Why is X endogenous?, etc

    The point is that when you think of an equilibrium in a market you have to be consistent with the assumptions.

    I think Neil had it right before the two retractions :)

    With Steve’s assumptions, if you introduce an exchange market to determine X, the problem disappears (you’ll have your 2 eqns and 2 unknowns). We’d still need to assume that D is the same for bitcoins and dollars. So if there is a goods market where bitcoins/dollars are traded for goods and an exchange market where bitcoins are traded for dollars, then X will be determined by the relative supplies M & B. If it did not, then there would be arbitrage. You’d exchange bitcoins for dollars (or vice versa) and buy the same good at a lower cost. Everybody does this until X clears the market.

    If you ask what if there is no exchange market? Then you’ll have different D’s for bitcoins and dollars complicating the original equation. If you ask, what if we assume that the D is the same, then you are essentially assuming that people are irrational or indifferent between paying different prices for the same good, in which case X and P are perfectly interchangeable.

  33. 33 33 Steve Landsburg

    Harold:

    Lets say we had a bitcoin equal to $1 to start with and we issued more bitcoin. The equation can be satisfied either by prices rising and exchange rate staying the same, or prices staying the same and exchange rate falling (or some combination). What determines which occurs? I think that is a re-phrasing of the problem.

    Yes, this is an excellent rephrasing of the problem.

  34. 34 34 Al V.

    I agree with Dan that Neil had it right (the 1st and 3rd times). However, given (M+XB)V=PQ and that X had been swinging around wildly, isn’t the implication that B has also been expanding and contracting? Just as the supply of dollars can be measured via M0, M1, and M2; so we have B1 and B2, where B1 includes only transactional bitcoin, while B2 includes both transactional and asset B2. B2 is the supply of all bitcoin, while B1 is the supply that is available for exchange for dollars. (M1+XB1)V=PQ.

  35. 35 35 iceman

    Perhaps it would help if we call dollars cats and bitcoins dogs

    Sorry just enjoying the comments and hoping to learn something

  36. 36 36 Neil

    A transactions theory of the bitcoin exchange rate. M*V=P*Q is the usual quantity equation for dollars. B*V’=P’*Q’ is the corresponding quantity equation for bitcoin where V’ is the velocity of bitcoin, P’ is the price of goods in bitcoin, and Q’ is the volume of transactions in bitcoin. Goods arbitrage requires P’=X*P. We can now solve for X=(B/M)*(V’/V)*(Q/Q’). The exchange rate for bitcoin is higher 1) the higher the stock of B relative to M, 2) the greater the velocity of bitcoin relative to dollars, and 3) the lower the flow of bitcoin transactions relative to dollar transactions.

  37. 37 37 Neil

    Sorry, here X is the price of dollars in bitcoin. Just invert everything to get the exchange rate as the price of bitcoin in dollars.

  38. 38 38 iceman

    Quick take on #26:

    If we increased B to offset a decrease in M or an increase in D we would expect X to change and P to remain the same

    If we increased B to match (proportionately) an increase in M (with no increase in D), we would expect P to change & X to remain the same

    If we increased B with no change in M or D, I’d like to say we’d expect both X and P should change: P to reflect the increase in M+B, and X to reflect the change in B/M. Is the puzzle that this could be double-counting?

  39. 39 39 Al V.

    Neil (#36), I like what you’ve done. There is the additional complication that the arbitrage between bitcoin and dollars is imperfect, in that there is a transaction cost to converting dollars to bitcoin. If, over time, that transaction cost goes to zero, your model becomes true. Until then, the cost of bitcoin will be surpressed (X is higher).

  40. 40 40 Neil

    Al V.

    Yes, that would determine an exchange rate band, which might be quite wide allowing substantial fluctuations not explained here.

    Worse, the explanation ignores substitutibility between bitcoin transactions and dollar transactions as if they take place in separate worlds. I don’t know if that is important nor how to deal with it.

  41. 41 41 jgreene39

    Prof. Landsburg,

    Is there any substantive theoretical or empirical research in bitcoins? Seems like a pretty interesting topic ripe for analysis.

  42. 42 42 Daniel

    Until we can pay taxes in bitcoins, how can we ever be indifferent between dollars and bitcoins? If there’s any kind of exchange cost than why would I ever prefer to receive payment in bitcoins, unless my intention is not to pay my taxes in which case isn’t the value of bitcoins based on it’s ability to be taken seriously as an alternative black-market currency, and why would the US government allow bitcoins to exist as a viable and substitutable currency given it’s current monopoly on legal violence and the printing press? The exchange rate from dollars to currency in this scenario to me would be determined by the preference of consumers to participate in this black-market.

    Assuming that bitcoins are excepted by the government as taxes, wouldn’t its exchange rate be determined by the amount the government taxes as a percentage of each bitcoins earned relative to the percentage the government taxes on each dollar earned? That’s I think way to simple an answer and I must be missing something egregiously.

  43. 43 43 djp

    I think you may have dismissed the gold analogy too quickly.

    I’ve wondered many times about what money is, and the role it plays in the world. There is something interesting about the MMT view on fiat currency — the dollar has value because the IRS can ruin your life, and you need to pay them off in dollars.

    But I don’t think that’s the whole story either. We want to save, and saving is really, really hard. I can never find a way to make those health packs or charge-ups you find in the cozy world of games. Saving is really difficult for a society. People, in total, have a net desire to save. They have some desire to save in dollars (see above) and some to save in other assets. Bitcoin is possibly just another of those assets.

    They also have a desire to save in gold, and when that desire goes up, the price of gold will rise (because production is relatively small). Likewise with bitcoin.

    As far as convenience goes, I have a really hard time paying my bills or paying for pizza with my 3 month Bills, but they sure do issue a lot of them, and they are readily exchanged for dollars. Likewise gold (especially once GLD came along) is easily exchanged into dollars. Why do we have so many bills, notes and bonds? Maybe it’s because the public demanded and increase in net dollar assets as their desire for savings in dollars increased.

  44. 44 44 ep285

    Interesting. I just happened to be reading up on Kiyotaki-Wright money models.

    Their paper “A Search Theoretic Approach to Monetary Economics” seems particularly relevant; section VI deals with “dual currency regimes” (the conditions required for their existence).

  45. 45 45 Robert

    If X is $X per B, then is not money supply measured in dollars M + B/X?

  46. 46 46 Robert

    Ah, no. I see. Sorry.

  47. 47 47 iceman

    Daniel #42 — “given it’s [sic] current monopoly on legal violence and the printing press”

    I like this…from an unexpected source(?)

  48. 48 48 Dmitry

    Somebody was writing about the necessity of considering the prices in bitcoins, and I agree. Please, consider my modest proposal.

    Bitcoins are valuable because they give us an opportunity to buy goods and services. This is the reason why people want to give dollars in exchange of this Internet currency. Of course, in the equilibrium the prices of goods must relate exactly according to the exchange rate, i.e. if a banana costs $2X then it must cost 2 bitcoins. However, the bitcoin prices must also satisfy the same money demand – money supply equation. Here is what we get. Let’s denote the dollar money velocity as V1 and the bitcoin money velocity as V2. Then

    M + XB = YP/V1
    (1/X)M + B = YP’/V2
    P’=XP

    Substituting P’ to the second equation I get a system

    M + XB = YP/V1
    M + XB = YXP/V2

    From which it follows that X = V2/V1, which makes sense, as we prefer the currency which allows us to pay quicker. Then we get

    P = (M*V1 + B*V2)/Y

    What do you think?

  49. 49 49 Will A

    Daniel #42:

    To your point on why would the US government allow bitcoins to exist as a viable and substitutable currency:

    http://www.washingtonpost.com/blogs/wonkblog/wp/2013/05/15/the-coming-political-battle-over-bitcoin/

  50. 50 50 Daniel

    @iceman

    Who would deny that the government has a monopoly on violence and the printing press. They wouldn’t be government if they didn’t have a monopoly on violence.

  51. 51 51 Daniel

    @Will A,

    I take this to mean that the government won’t allow the currency to continue, meaning Landsburg’s assumption of a perfect substitution for the dollar would be impossible and this is probably irrelevant. If it ever could, I think the value of the currency would be what I said in #42 in this case.

    And then there’s this little non-sense.

    “In his view, the federal government would have as much difficulty shutting down the Bitcoin network as major content companies have had shutting down peer-to-peer file sharing. ”

    A currency is not exactly the same as an exchange of information. Currency needs to be readily available and easy to use for it to be relevant. If I have to find a new website every time the government shuts down an exchange, how much confidence am I going to have in this market? How is it ever going to become any more than what I think it’s proper equivalent is, using expensive stolen paintings as an exchange for illegal activities.

  52. 52 52 Daniel

    @iceman,

    BTW, if you like that phrase than you should read more Max Weber, because that’s where it comes from.

  53. 53 53 Daniel

    I take the part about it being equivalent to using stolen painting as an exchange, the only part that’s equivalent is that it’s only value to the user is in it’s ability to make illicit transactions.

  54. 54 54 iceman

    #51 – some think that phrase provides a healthy perspective for fiscal policy issues

  55. 55 55 Alan Wexelblat

    Looked at from the point of view of an FX trader, which is as close as I can come to having any knowledge of this, it’s an unanswerable question. Fiat currencies like bitcoins aren’t really measurable in value because they don’t circulate freely nor participate in exchanges.

    You would get a similar puzzlement if you asked the same questions as you’ve asked but instead of Bitcoins you talked about Disney Dollars or casino chips or whatever it is that Club Med calls its beads. These are, at some level, money substitutes, but they’re sufficiently closed and constrained that one can’t say much about them in the way that one can speak about dollars, yen, or euros.

    FX trades claim to represent “true values” of money because they are the measures of direct unit-to-unit valuation. Measuring in terms of buying power introduces seriously distorting effects. If I can buy a pizza for example at a price of $10 and a similar pizza elsewhere for 10 dinglebucks that doesn’t mean that a dinglebuck is worth $1 because it contains the hidden assumption that pizzas everywhere cost $10 which we know not to be true, even for essentially identical pizzas.

  56. 56 56 Skyler

    Easily substitutable implies that the exchange rate must be stable. Thus, the must be an institution with the ability to insure stability: credibly maintain willingness and ability to exchange bitcoins and dollars at a fixed exchange rate. This institution fixes X.

  57. 57 57 Robert

    Dmitry sounds right. It all depends on velocity. With two currencies, one becomes the medium of exchange (high velocity); the other, a store of value (low velocity.)

  58. 58 58 Daniel

    @iceman 51,

    How does that result follow from what I said?

  59. 59 59 Dmitry

    I made a silly mistake in my calculations, but the new answer is very similar.

    M + XB = PY/V1
    M + XB = (X^2)*PY/V2

    X = Sqrt(V2/V1) and P = (M*V1 + B*Sqrt[V1*V2])/Y

  60. 60 60 Harold

    Dimitry: perhaps you could elaborate what your equations mean? Since we have introduced two more variables, v1 and v2, are we any closer to answering the problem? For example, if we supply more bitcoin, what effect does that have on v1 and v2? Can we say how this will affect the exchange rate and prices?

    off-topic: I am legally allowed to use violence in self defence. I am not the Government. Therefore Govt does not have a monopoly on legal violence.

  61. 61 61 Harold

    Dmitry – sorry- I have mis-spelled your name again.

  62. 62 62 Dmitry

    Harold: I would say that, if my equations are true, issuing money or bitcoins wouldn’t influence the relative price (exchange rate) of two currencies. I look at it in the following way: if the government issues one additional $20 bill it doesn’t make $20 bills less attractive in comparison with, say, $10 bills. However, if the government announces that now you should sing a song each time when you pay with a $20 bill, the price of a $20 bill will be affected: you would demand more than 2 $10 bills in exchange for it. That is why velocity matters.

    So, from the equations it follows that if you increase the supply of bitcoins, the prices will go up (other things equal) — the same happens when the government print dollars.

    But it is crucial to remember that professor Landsburg discusses a world where bitcoins are ‘widely accepted and easily substituted for dollars’, and so do I. I don’t know, whether the same kind of analysis is applicable to the current state of affairs in the bitcoin world.

  63. 63 63 Harold

    “But it is crucial to remember that professor Landsburg discusses a world where bitcoins are ‘widely accepted and easily substituted for dollars’” I too interpreted it in this way, but to some extent this is just to make the effects noticeble and important. SL has used examples of burning $1 bill and bidding prices down by $1. This emerges from the equations. The Govt issuing 1 x $20 and 2 x $10 has exactly the same effect. So issuing 1 bitcoin (assume X=1) should have the same effect if it is accepted. However, common-sense suggests that if you flooded the economy with billions of bitcoins, they would drop in value relative to the dollar. This means that each bitcoin has less than $1 effect on prices.

    So to get at your equation, is it that the velocity has less direct link with supply, but not totally unconnected? Can we quantify effect of B on V2?

    To look at another analogy, a perfect forgery has an exchange rate of 1. Issuing a forged $1 must push up prices, because it cannot adjust its value. Issuing bitcoin may not push up prices (as much) because it can adjust.

  64. 64 64 Daniel

    @Harold,

    “I am legally allowed to use violence in self defence. I am not the Government. Therefore Govt does not have a monopoly on legal violence.”

    Who defines the laws of how to define self defense? And I wouldn’t exactly define self defense as violence.

    From Wiki’s definition of violence:
    “This definition associates intentionality with the committing of the act itself, irrespective of the outcome it produces.”

    I’m not exactly intentionally committing self defense, it’s in reaction to someone else’s illegitimate use of violence.

  65. 65 65 Dmitry

    Harold “However, common-sense suggests that if you flooded the economy with billions of bitcoins, they would drop in value relative to the dollar”

    I think, this is not right. Money looses its value because you can buy less goods with them, If you flood the economy with bitcoins, they will drop in value, but so will the dollars do, because now, given new high prices, $1 and one bitcoin are can bring you less goods. Their relative price will remain the same. Again, if the government issues a lot of $20 bills, all the bills loose their value, but a $20 bill still costs two $10 bills.

  66. 66 66 Harold

    Dmitry – it would not be the first time common-sense was wrong, I just don’t see how we can know it for sure. Is it just a best guess, or is there a theoretical basis? If the velocity equation is correct, then changes in velocity would alter the exchange rate. Can we be sure this would not happen?

  67. 67 67 Al V.

    Re. djp’s comment #43, on what money “is”, it has always seemed to me that money largely represents one thing: a unit of labor. Different people’s labor is exchanged for money at different rates, but at the most fundamental, money is labor.

    I just bought a cup of coffee for $1. Some of that paid for the labor of the person who poured it for me, some for the rent for the building, some for the paper cup, and some for the coffee itself. But the $0.25 for the coffee is really for the labor of the grower, the harvester, and the shipper. The $0.05 for the cup is for the labor of the people who made the cup, and the distributor. And so on. In the end, everything we pay for is labor.

    Except… If I buy a bond, what am I buying? I’m not buying labor, I’m just buying a promise to pay. If I buy a stock, I’m also buying a promise to pay – I’m buying a discounted stream of future dividends.

    This is why I have never understood the mania for gold. It’s price is far higher than what one would pay for its usefulness, but it has no inherent value as an asset. The value is only what somebody else is willing to pay me, which is the definition of a bubble.

    Anyway, so what is money? It seems to represent the rate of exchange between a unit of labor and the return on an asset. If I have a dollar, I can do one of two things with it: (A) I can buy someone’s labor (or a product representing an aggregation of labor), or (B) I can buy a promise.

    I think’s that’s a bit of the problem with bitcoin. I can only use it for (A), and given the transaction costs inherent in bitcoin currently, I only want to use if when either a product is discounted in bitcoin as compared to the price in dollars, or if I want to somehow hide my participation in the transaction. To become a real currency, I need to be able to store wealth in it, by using it to buy assets, and there must be minimal arbitrage between bitcoin and dollars.

  68. 68 68 djp

    Re: Al V #67
    Thanks for the response Al.

    Thinking of dollars in terms of a unit of labor is very natural. Walter Williams has often referred to dollars as Certificates of Performance. You performed a service for someone and earned so many Certificates of Performance, and now you are giving some to me for my performance (labor).

    I think we all strongly desire a way to store labor (or more generally to save). But there is no natural way to do this effectively. And why should the piece of paper we call a dollar be that way? Well, one reason is because the gov uses its monopoly of the right to initiate violence to guarantee that people will need dollars to pay taxes. That is certainly a good Schelling point distinction of the dollar from some other “promisory note” (yes Steve, I have long loved Friedmann’s Schelling point discussions) or fiat currency.

    But society as a whole seems to have naturally gravitated towards gold as a reasonable means of storing wealth (labor) too. It’s really, really, really hard to think that somehow it’s stupid to use gold as a store of value when it has acted as such for longer than any other store of value. Indeed, simply the fact that it has been a good store of value (vehicle for saving) for so long actually means that it IS a good store of value (from the point of view of it being a Schelling point itself).

    The argument you give for gold being strange (that it has too high a value because it’s higher than your perceived value as a commodity — though people DO still buy it to use as a commodity, so …) could just as easily be used to claim that dollars are overvalued. A thousand years from now, which is more likely to buy an hour of a man’s labor: (i) a pound of gold or (ii) $25,000 ?

    I think trying to get to the bottom of what money is, is a very interesting topic. And I think it can be rather profitable too — those MMT guys that put their money where their mouths were in 2009 did very, very well.

  69. 69 69 Al V

    djp, I agree that gold is useful as a means of storing wealth, or in other words a means of storing labor. But what is the advantage of gold over Monopoly money? Three things: it is shiny (easily identifiable and hard to fake), it has been used for a long time by many societies, and most importantly, there is a constrained supply.

    Really, anything can be used as a means of exchange, so long as it meets some basic criteria: constrained supply (but enough to go around – Picassos wouldn’t work), hard to counterfeit, and easily recognizable.

    Actually, I think the problem with gold is that it suffers from the same problem that bitcoin has recently – people treat it both as an asset and as a means of exchange, and a good currency should only be a means of exchange.

  70. 70 70 Harold

    #69 – gold is also chemically pretty inert. It won’t rust away.

  71. 71 71 Daniel

    @ AJ V,

    “Actually, I think the problem with gold is that it suffers from the same problem that bitcoin has recently – people treat it both as an asset and as a means of exchange, and a good currency should only be a means of exchange.”

    Why aren’t dollars used as both an asset and as a means of exchange? I would argue because of stable inflation rates artificially (in a good way) created by federal reserves. Sometimes they fail at it, like now when inflation is too low, but without them, there’s no way to create a stable inflation rate that I can think of.

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