All Hail Bitcoin.
If bitcoin is to capture 10% of the U.S. transactions involved with GDP in 15 years, it needs to grow in value at 61%+ per year during that time. I think 15 years is a good amount of time as a rough and ready indication of what can happen on the internet, given that Google is just about 15 years old.
Todays GDP is $15.09 T. The total value of bitcoin is $1B. If bitcoin is to take 10% of the GDP transactions today, the value of bitcoins would need to grow in value to match the total amount, divided by the monetary velocity of bitcoins.
The way to value bitcoins in the future is the same, except we need to account for notional economic growth, and the number of bitcoins in circulation in the future.
To figure out how much bitcoins might appreciate in value, we need to estimate the velocity of bitcoins.
Most people don’t want to buy a pizza with something that will double in value every 17 months, so we can assume the velocity of bitcoins will be quite low, something lower than the current velocity of money. For example, do you think this guy is satisfied today with his 10,000 bitcoin pizza? (Let’s see, I can either buy a pizza today, or a really nice house in 3 years – what should I do? I am pretty hungry right now.) I would imagine few people are going to buy pizzas with bitcoins today or in the future.
Therefore, we can assume a very low real world transaction volume for bitcoins compared to the total supply of bitcoins. The current velocity of money is 1.5. Assume 1.2 for the velocity of bitcoins. I think this is extremely high estimate of the velocity of bitcoins, because I do not think $2.3mm of exchanges of bitcoins for real world goods are happening everyday right now. Most of the transactions are exchanges of bitcoins for another currency, and the bitcoins are then hoarded and not used to purchase real world goods.
It is difficult to tell how many transactions involve real world goods for bitcoins, but the largest site where actual transactions take place with bitcoins is Silk Road. Silk Road is a place where you can easily buy illegal stuff, like MDMA and LSD. There is no way to know exactly how many transactions are taking place, but Silk road was only doing about $2m in transactions per month as of January 2013. That’s about 1/7th of the necessary volume to make bitcoins have a monetary velocity of 1.2 given the value of bitcoins in January.
Transactions for real world goods fall off extremely rapidly after the top few websites, but if we double the single largest site transactions to get the total real world transactions, we still end up with a very low velocity. Using this velocity of .35, bitcoins would have to gain in value by 75% per year, continuously compounded.
Then we need to adjust for future GDP and the number of bitcoins in the future, but this is all pretty simple math, which Wolfram Alpha was kind enough to do for us.
We have bitcoin appreciating at 61%+ per year, and the USD losing 2% per year. I don’t know which one you would prefer to use to purchase a pizza, but if I have a choice between using bitcoins or USD to purchase a pizza, I’d use USD.
The good thing is you can use this math to imagine if bitcoin was very successful and took over 20% of world GDP in 15 years. 2012 world GDP was $83T. 105% per year for the next 15 years, which as far as I know, would be the best investment in human history.
You can see how this is a huge problem with bitcoin. The success of bitcoin relies on it being used in real world transactions, yet if bitcoins actually gets used in real world transactions, a bitcoin rapidly becomes far too valuable to use in real world transactions for things like toilet paper. Let’s see, I can either use bitcoins or USD to buy this toilet paper today. If I use the USD, then I can buy a nice house, a car, and go on vacation in 15 years with exactly the same money. If I use the bitcoins, I’ll regret it for the rest of my life.