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# The Real Value of Bitcoin

The recent dramatic increase in the price of Bitcoin has encouraged lots of people to give us their estimates for what the price of Bitcoin really ought to be. These vary by so much that it’s almost worth treating them like engineers handle values that can vary by many orders of magnitude. The common way that engineers handle large dynamic ranges is by looking at a logarithm of a ratio instead of just a number. That’s how we get decibels. Take a sound pressure level of an acoustic wave, divide it by 20 mPa, multiply it by 20, and that’s how many decibels the sound rates. This is a good way to compress both very big and very small values. A range from 0.000001 to 1,000,000 sounds a bit daunting, but a range from -120 dB to 120 dB doesn’t sound as bad.

This could make dramatic differences in Bitcoin prices to sound less dramatic. If we divide by a 1 Bitcoin reference value, a range from 1 Satoshi (0.00000001 BTC) to 1,000,000 BTC gets compressed to a range of just -160 dBBTC to 120 dBBTC, which is easier to understand in some ways than the uncompressed range.

And this makes the recent wild swings in the value of Bitcoin seem not quite as bad. If the value a Bitcoin drops from \$4,000 to \$2,000, that’s not a drop of \$2,000 or 50 percent. Instead, it’s just a drop of 6 dBBTC.

If you studied electrical engineering in college, this probably makes perfect sense. Otherwise…

But because we need to take a logarithm, we get into trouble if we try to handle the value 0, where the logarithm isn’t defined. And a column in the Wall Street Journal on Tuesday, September 19 (James Mackintosh, “What Should Bitcoin Actually Be Worth?”), actually suggested that this what Bitcoin should be worth. So much so that the WSJ changed the online title to “Bitcoin’s wild ride shows the truth: It is probably worth zero.”

This is almost certainly wrong. Bitcoins are almost certainly very overvalued. A careful look at Bitcoin transactions that was done by Stanford researchers found that most Bitcoins are bought and held instead of being used in transactions, and the researchers say that this suggests that most Bitcoin purchases are made by investors instead of by people planning on using them to buy and sell things.

If this is true, the claim that the recent increase in the price of Bitcoin is the result of a speculative bubble may be true. Even Robert Shiller, the winner of the Nobel Prize in Economics and one of the world’s leading experts on speculative bubbles agrees with this assessment.

But even if the price of Bitcoin is purely driven by investors rather than the value of Bitcoin as a replacement for other forms of currency, there are still lots of valuable uses of Bitcoins, and this suggests that Mackintosh’s idea that Bitcoins have a natural value of zero is probably wrong.

The real value of Bitcoin may be that its blockchain is a handy distributed, fault-tolerant, immutable public ledger that other people maintain for you. Lots of start-ups are betting on using Bitcoin’s blockchain for these sorts of things, and you can be fairly sure that the information that they want to store isn’t messages like “Archie loves Betty.”

It’s not clear how valuable these secondary used of Bitcoin’s blockchain are going to be, but I wouldn’t be surprised if they eventually take over the blockchain and replace lower value transactions. Another winner of the Nobel Prize in Economics, Ronald Coase, tells us that this is exactly what we should expect to see happen. The Coase theorem tells us that property always ends up in the hands of the parties that value it the most.

So if today’s Bitcoin start-ups are successful and Bitcoin’s blockchain becomes very valuable, we should expect to see the price for Bitcoin to increase to a level where its value is determined by these high-value uses and routine uses like buying a cup of coffee with it will disappear.

So is Bitcoin currently overvalued? Probably. Does it have significant value that hasn’t been realized yet that will give it a significant value in the long run? Again, probably. But it’s not clear how long that will take and what the value of Bitcoin will end up being.