In any first year macroeconomics course, students are introduced to the concept of the quantity theory of money. The quantity theory of money can be expressed as an intuitive and basic formula.
M * V = P * Q
M = Money supply (measured in $)
V = Velocity of money (a constant)
P = Price level ($)
Q = Quantity of goods sold
Generally, P * Q is the final demand for goods and services sold in an economy in a year (C + I + G + X – M). So, V, the velocity of money, is the usually measured as the ratio of the size of the liquid monetary base relative a country’s nominal GDP – the final goods and services consumed by consumers, governments, businesses, or exported net of imports.
A higher velocity means that money changes hands faster in an economy.
For complex economies, there can be many ways to measure the money supply. The narrowest definition is M0 – the value of currency in circulation. Obviously, the deposits in chequing and savings accounts are also as liquid currency. M1 is the sum of all currency in circulation and demand deposits or checking accounts at financial institutions.
In the U.S., the current velocity of M1 is about 7. That is, the nominal GDP of the U.S. is about 7 times greater than the amount of money available in currency and held in chequing and demand deposit bank accounts.
So, what is the velocity of Bitcoin?
MB * V = (P * Q)B
One can easily convert this into $U.S. by multiplying both sides by the exchange rate
MB * eUS/B * V = (P * Q)B * eUS/B
In my last post, I estimated that the value of goods and services bought with Bitcoin was between $62 million and $116 million U.S in the last year.
Currently, the Bitcoin market capitalization is valued an astronomical $1.88 billion!
So, if $1.88 billion * V = $62 million to $116 million
The current velocity of Bitcoin is about 0.032 to 0.062.
On average, Bitcoins are changing hands for final goods and services at a rate 110 to 210 times slower than U.S. dollars. A year ago, the velocity was nearly a factor of 10 higher. In April 2012, the final demand for goods and services in the past year was $28.3 million compared to a market capitalization of $44 million. The velocity of Bitcoin was 0.64. Clearly, the amount of Bitcoin hoarding, which was already high, has gone illogically parabolic as speculators flood into the market.
With some modifications, the M * V = P * Q formula can actually be used to determine what the exchange rate of Bitcoin will be if suddenly people stop hoarding and return to the relatively stable market of last April.
Let’s assume that the velocity of Bitcoin returns to 0.65. To use this method, we have to also assume that the number of Bitcoins in existence does not influence the demand for goods and services. I think this is a very sound assumption. There is no Bitcoin economy interest rate that can fall with growth of the monetary base. Demand for Bitcoin goods is based entirely on the fact that Bitcoin transaction fees are lower and that it provides some anonymity in transactions. Basically, there is no reason to suspect a real-financial linkage in the Bitcoin economy.
(P * Q)B * eUS/B = (P * Q)$U.S.-> The final demand in U.S. dollars is the final demand expressed in Bitcoin multiplied by the exchange rate.
So, if MB * V = (P * Q)B then,
MB * V = (P * Q)$US / eUS/B
Right now, MB is about 11 million, I’m assuming that a more appropriate V is 0.64, and that the current final demand for goods and services in U.S. dollars is up to $116 million.
Substituting in my assumptions,
11 million * 0.64 = $116 million / eUS/B
eUS/B = $116 million / (11 million * 0.64)
eUS/B = $16.4 U.S.
Now, this assumes that the velocity can return to 0.64, this might be troublesome. Recent speculative activity might cause many Bitcoins to be effectively destroyed – either deleted, forgotten or lost. According to Blockchain.info, in the past year the number of Bitcoin days destroyed – a proxy for the amount of Bitcoin effectively out of circulation – has nearly doubled.
Even then, if the velocity of Bitcoin were halved to 0.32 as a result of lost/destroyed Bitcoin, the exchange rate should be around $32.8 U.S. per Bitcoin and nowhere near the currently absurd level of $190 U.S.
Of course, there are other factors I haven’t considered. After such a huge crash the amount of goods and services (whether legal or illegal) people want to buy in Bitcoin could collapse as well. This would drag the exchange rate even lower.