# a blog about things that I've been thinking hard about

# How Bitcoin Could Reach US$100,000 per Bitcoin

4 April, 2013
If Bitcoin became a major world currency, then each bitcoin would have to be worth US$100,000, or thereabouts. Even as a minor world currency, bitcoins would be worth much more than what they are worth now.
by Philip Dorrell

## Theories About the Value of Money

There are various theories of the how the value of money is determined, including the Quantity Theory of Money, the Cambridge Cash-Balance Approach and Keynes's theory of Liquidity Preference.

Economists seem to argue a lot among themselves about what is the best way to explain changes in the value of money.

For the purposes of this article, I will state a very simple theory of the value of the money, which is:

For any particular type of holding of any particular currency, the total value of that type of holding is equal to the the total demand for that type of holding.

This theory assumes nothing at all about how much money moves around in transactions – it only considers how much money people want to have, in total, at any point in time. (Which I think is closer to the Cambridge approch than to the other two theories given above.)

With typical national fiat currencies, there are different types of holding we can consider, such as cash, or on-call bank deposits. With Bitcoin there is really only one type of holding, i.e. you are either the owner of a bitcoin or you aren't, which simplifies things a bit.

If Bitcoin as a system operates as designed then the number of bitcoins will eventually reach a maximum of 21,000,000 bitcoins.

In order to reach a value of US$100,000 per bitcoin, it would be necessary for the total value of bitcoin holdings to be US$2,100,000,000,000. Which would require the total demand for bitcoin holdings to be US$2,100,000,000,000, i.e. US$2.1 trillion.

This is comparable to US$2.472 trillion for M1 in February 2013 as given in this document from the US Federal Reserve.

How much is US$2.1 trillion per person?

If there are 7 billion people in the world, then US$2.1 trillion is US$300 each. Which doesn't seem like so much. But there are probably many people who don't even have US$300 of cash or savings to their name in any currency. If we consider the world's richest 1 billion people, then that would require an average holding of US$2100 worth of bitcoins.

We can also compare US$2.1 trillion to the total value of gold in the world, which according to this Wikipedia article is about US$10.4 trillion – only some of which is actually held for monetary purposes.

(And if you read an article somewhere suggesting that the demand for bitcoins has somehow affected the price of gold, you can see that this is very unlikely, because the current total value of Bitcoin is very tiny compared to the total value of gold.)

## The Enormous Upside of Bitcoin

Even if Bitcoin only ever becomes a minor world currency, the price will still go much higher than what it is now. If demand for bitcoin holdings reaches only 10% of current US$ holdings, then the price will rise to more than US$10,000. If the demand only reaches 1%, the price will still rise to more than US$1000.

It would seem crazy for anyone with spare cash not to buy bitcoins.

Of course these calculations assume that nothing bad happens to Bitcoin.

## What Could Go Wrong?

There are various reasons why Bitcoin could fail:

- An error could be found in the design of Bitcoin which cannot be remedied, which allows hackers to steal bitcoins, or to double-spend (or something else).
- Governments may declare Bitcoin to be illegal, and successfully destroy it as a working system.
- The increasing value of Bitcoin may stress the system of peer-to-peer trust in a manner that undermines the trustworthiness of Bitcoin.
- Someone invents a new digital currency somewhat like Bitcoin, but obviously better, and everyone migrates to the new currency instead.

Even if Bitcoin as a whole does not fail, an individual's investment of bitcoins may fail:

- The investor may have their computer or their online Bitcoin account hacked and they lose their bitcoins.
- A Bitcoin exchange may be hacked to such a degree that it can not make up losses to its account holders.

## Only Two Possible Directions for the Bitcoin Price: Up or Down

If Bitcoin fails in any significant manner, it is likely that the price will decrease all the way to zero.

If it doesn't fail, then almost certainly the price will rise to a much higher value than what it is now.

There is no plausible in-between scenario.

## Hyperdeflation

If you surf around the internet reading critiques of Bitcoin, most of them list one or more of the possible failure scenarios I've listed above.

One specific critique that deserves further analysis is that Bitcoin is suffering hyperdeflation, which makes it unuseable as a currency, and therefore supposedly of no value.

It is true that if a currency is deflating rapidly, then people will prefer to hold it rather than use it for transactions, somewhat analogously to what happens when a currency is inflating rapidly, which is that people prefer not to hold it, and also don't use it for transactions.

Given my analysis above, Bitcoin hyperdeflation is inevitable.

But there is one difference between hyperdeflation and hyperinflation, which is that hyperinflation can go on without limit until a currency becomes worthless, whereas hyperdeflation has to stop somewhere, because there is a limit as to how much value anyone can afford to hold in the form of money.

When a deflating currency stops deflating, then the value is constant, and it becomes useful as a means of exchange, which creates a non-zero demand for holdings of that currency.

(There may be a bit of bouncing up and down from a maximum value before it settles down into an equilibrium state, but such an equilibrium will eventually be reached.)

## Conclusion: Bitcoin May Crash, But It's Not A Bubble

There are reports and opinions on the Internet that there is a "Bitcoin bubble". (There's too many to list, I'll let you Google for them.)

Now it is possible that the price has risen sharply due to recent economic events.

To fully understand any market, you have to know the private motivations and thoughts of all the buyers and sellers. Which is impossible for anyone to know.

A "bubble" is when the price is only held up by people buying because they think other people want to buy, but those other people only buy because they think the price is going to continue rising.

But as I have explained here, as long as Bitcoin is usable in the long run as a medium of exchange, the so-called fundamentals of Bitcoin are very strong.

Bitcoin may fail, for one the technical reasons I have listed, but it won't fail just because it's a "bubble".

Update (5 April): I have deleted the section I wrote on partial bitcoins, where I had cast some doubt on the successful operation of Bitcoin when most transactions are partial, because, as various commenters pointed out, my understanding of partial bitcoins was wrong. (I was wrong in the direction of making Bitcoin seem less viable as a currency system, so this correction strengthens the argument in favour of the proposition that bitcoins will be worth much more in the future than they are now.)
I have also added a link to the "Seeking Alpha" article about Bitcoin and gold.
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