1 x 1 > 1 x P(payment)
Your claim amounts to the idea that giving someone a loan at 0% interest can be profitable. It can't.
Disclosure: I have no stake in the success or failure of bitcoin. I'm interested in knowing if you do, just so I know to stop wasting my time?
Loaning someone an asset at 0% is always worse than holding the asset. The value of the loan is P(repayment) x value of asset in future. The value of the asset today = value of asset in future + option value. There is no escaping this mathematical identity. Provided P(repayment) < 1, you are better off holding the asset, regardless of the rate of return on the asset.
If you were correct, then you could make a profit by loaning out shares of SPY or other security with a positive expected rate of return at 0%. You can't.
If you disagree with this, please express your disagreement in math.
I don't own any bitcoins, and have no stake in it. I think it's a good idea that might solve the current mess of payment systems, however.
Exactly. My previous reasoning was indeed a bit muddied, but what you're saying now clarifies it. I don't disagree with your math.
There are so many logical contradictions in the concept, which is why I end up making silly assertions that you correctly pointed out. Instead, the argument should simply be that the rate of return on bitcoin, due simply to built-in deflation, and expressed in dollars, may or may not be so high that it always makes sense to hold the asset rather than use it as currency to buy other assets. In which case it can't function as a currency: contradiction.
Of course, I do believe the BTC USD exchange rate will be the dominant factor in determining prices expressed in BTC in the long term, but I'm sure plenty of people would disagree. If that does happen, a lot of this becomes theoretical - the worsening exchange rate will take care of the deflation.
Note I'm not necessarily for or against bitcion. Thanks for the discussion.
Nit: if the carry cost of the asset is zero. This is _not_ true for dollars (at least at large corporate/pension fund/hedge fund scale) and various government securities have occasionally sold at negative nominal interest rates.
(It is, essentially, true for BTC, which is why your analysis is largely correct here, but there certainly are cases where one would reasonably lend USD or the like at 0%.)
I don't have any interest in bitcoin, I'm a spectator. Edit: I realized that's not entirely true, I got 1.5 namecoin from a fountain a couple of years ago.