Bitcoin Price Napkin Math – $15,882


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Economist 1, “Look, there is a $20 bill on the ground!”

Economist 2,  “Can’t be. If there was a $20 bill on the ground, somebody would have already picked it up.”

It’s an old joke, not exactly very funny, but it does illustrate how economists think.  Economists have the luxury of making assumptions.  If the government decreases taxes, all things equal, people will spend more money.  Economists also create economic models.  These models are to make complicated ideas easier to understand.  The following is a simple economic model of cryptocurrency and the output it services.  There are lots of assumptions here and it’s not supposed to be taken literally.  But it can give us an understanding of bitcoin’s relationship in a complex, crypto-world.

The Equation of Exchange

Previously, I wrote about the equation of exchange here:

Essentially, the equation of exchange is an economic equation that showcases the relationship between the money supply, the velocity of money, the price level and real output. The equation was derived by John Stuart Mill 150 years ago and is a staple in any Macro or Monetary Theory class.


M=money stock

V=velocity of money

P=the overall price level

Q=real output.

We can first apply this to the US economy and apply some real-world numbers to this equation.

PQ= Fourth quarter, nominal US GDP in 2017 was 19.73.  This is the 2017 price of goods and services produced within the country during 2017.

Next, how much money is needed to service that GDP?

M=According to the St. Louis Fred database,, we use 13.82 trillion dollars to service the 19.7 trillion dollars of output.  They are using M2.  Go way back to your college days and remember M1 is more or less cash and checking accounts and M2 is more or less your savings accounts.

Since we have these numbers it’s easy to find the velocity of money. Remember velocity is how fast money changes hands. We divide the nominal GDP, 19.7 by the money stock, 13.82.  This comes out to 1.42.  This is exactly what the St. Louis Feds’ velocity number is as well.

That was easy.  Our US dollar equation of exchange looks like this:

M(13.82) V(1.42)=PQ(19.7)

Applying to Bitcoin

Ok, since we plugged in all the numbers with the dollar, let’s do the same with bitcoin.  Now we need to define PQ in the bitcoin ecosystem.  Q is the real-world output that people purchase using bitcoin.  There are 2 identifiable groups of people who would derive utility out of using bitcoin:  those who want to get off the grid and those who want to get on the grid. Internet gamblers, people trying to send money abroad from economically unfree societies and a multiple of other people who use it for illegal activities.

In addition, there are people that have no access to the world financial system. These are people from war-torn countries like Afghanistan, Syria or Iraq or people in countries where the monetary and financial authorities have let them down, like Zimbabwe or Venezuela.  They will be allowed to get on the grid with use and access to bitcoin.

PQ=Umm? Oops.  There is not a reliable number that can give us a PQ. The dark web and Zimbabwe are not exactly transparent with their financial numbers.  Being economists, we have to make assumptions here.  With all the hype and publicity of cryptocurrency lately, it’s not absurd to assume that crypto could service 1% of world GDP in the next 3 years.

According to Statista, world nominal GDP was 79.28 trillion dollars in 2017.  Now we have a number for our PQ, which is our nominal world GDP that crypto would service.  1% of 79.28 trillion or 792 billion dollars.

So our equation now looks like this: MV=792 billion dollars.  Once again, the PQ (792 billion) represents the goods and services produced that are being purchased with cryptocurrency.

Next is V.  This number is quite dark as well because we can’t easily divide PQ by M.  According to Woodbull charts, bitcoin’s velocity is 1.2.

This doesn’t seem too absurd. Bitcoin’s velocity would be definitely lower than the dollar because it’s being used as a store of value (M2)  more than a medium of exchange (M1).

M*V(1.2)=792 billion

Solving for M, we divide PQ by V.  PQ/V, or in napkin math, 792/1.2= 660 billion.  With this velocity and ratio, the world would need a crypto stock of 660 billion dollars to service 1% of world GDP.

Let’s switch out the M for C. C representing the world’s crypto money stock. CV=PQ

C(660 billion)V(1.2)=792 billion

The next step on our napkin would be to isolate bitcoin’s share of the M stock.  According to, bitcoin’s share of the crypto market is 40.8 percent.  This works out to a 269 billion dollar bitcoin money stock.

Bitcoin’s Equation of Exchange

Our final equation of exchange for bitcoin looks like this:

B(269 billion) V(1.2)=PQ (322.8 billion)

269 billion dollars of billion being spent 1.2 times will service a world nominal GDP of 322.8 billion.

The last step on the napkin is to figure out what each bitcoin is worth.  Presently, there are 17 million bitcoin out there (up to 4 million may be lost forever) with a cap of 21 million.  Let’s use the 17 million.  269 billion/17 million bitcoins.  This comes out to $15,882 per each bitcoin.  This is not at all out of the range we have been in in the last 6 months.


Economists make assumptions and create models to simplify complex concepts and ideas.  According to this simple model, each bitcoin is worth $15,882, which is approximately 46% higher than current valuation.  This was not at all a literal take on the exact price of bitcoin but it can help us get an understanding of the relationship between crypto, bitcoin and the output that it services.   Clearer numbers on V and PQ in the future will help us become more accurate at determining bitcoin’s price and help us digest the complexity of this new asset class and money stock.

Which assumptions were right?  Which assumptions were wrong? Comment below.

Disclosure: I spend, invest and save with cryptocurrencies.

All price and ratios were based on March 2, 2018.

Featured image from Shutterstock.

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