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Yes, it would take time to run out, but running out will happen. The BitCoin will not inflate due to supply issues because no one will ever know that money has been lost in the system. As far as people will be more careful:
Scenario:
You make a transaction worth 1 Million BitCoins from selling something doesn't matter. You walk outside to celebrate, and die of a heart attack. Your money is gone. It is lost into the system. Now if you used a holding company (escrow) account and leave the funds there there would be away for relative to retrieve the money. Or are you going to tell your wife ahead of time, she wouldn't need a lawyer to get your money, she could just take it.
Or any number of scenerio's
The proposal is the same type of system the Suisse offers on password accounts. BitCoin's deposited into a password account, you are provided with a Key. In order to withdraw money you must have the Account #, the password, and the Key. Anybody can deposit into the account with just the account #, only a select one or few could withdraw. It would work the same as the IRL Suisse Bank with the exception that the bank never needs to meet you.
Trust is the issue. But just like the Real Suisse accounts, if the bank stole everyones money no one would use them. And every bank knows the real money is not the holding and storing of it but the flow of it. It is the "Transaction Fees", not the 5 BitCoins.
The biggest difference is even if "someone" want the records of accounts, anything that could provided an identity, there would not be one. IRL the Suisse charge a lot of money for that privilege but even you must show up to open the account and then to withdraw, because IRL the "Key" is a small gold bar with numbers on it but they can use another "Key" of your choosing. One has to be present to use the Key, know the password, and account # before withdraw.
In the Online version, the "Key" is probably something electronic, password, and account# would still be used. The Trust would have to be earned by the bank, but that is usually done with a financial backing. (Investment Funds). If a bank wants to handle a $10 transaction but hast a $1 billion dollars you can usually trust them. If they do the same and have only a .01¢, you can't. It is a natural credit system.
The whole idea is a method of preventing attrition. BitCoins must have a way of being reclaimed. Out of curiosity, I will find out what the natural attrition rate is on IRL Money, apply it to BitCoins, and see how long it would be before we would run out. Taking into account you wouldn't need to run dry because as BitCoins become inactive there would be less and less transactions. The breaking point is probably somewhere around 60% when there would not be enough BitCoins left to effectively keep a market going. I will have to factor in some X factors like what if "Bill Gates" lost his wallet.
I know it will take a long time, but it would happen. Just curious.
As far as running an economy off of 1 BitCoin, correct me if I am wrong, there are only 8 places to the right (0.00000001) so the lowest possible BitCoin unit would be ( $00,000,000.00000001) So 1 BitCoin could only have 100,000,000 million people holding each BitCoin but there are 5 Billion people. An the Maximum would be 2,400,000,000,000,000 quadrillion BitCoins. Now if we are a share the wealth type of society, that would give everybody evenly split 480,000 BitCoins each. Which should go to prove, there will always be poor people.