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1. What will all of the monster hashing machines do after the last coin is mined?
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I'm not sure why you are concerned about what is going to happen to bitcoin more than 100 years from now.
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For example, suppose that most of the transactions that are happening right now are directly related to individuals using BTC to purchase mining equipment. I don't know if this is a valid assumption but if it is then the number of transactions will decrease substantially once the demand for equipment eases. If the number of transactions decreases will not the fees decrease?
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I'm not sure why you think "that most of the transactions that are happening right now are directly related to individuals using BTC to purchase mining equipment", and I certainly can't understand why you would think that would still be true 100 years from now.
Regardless, I'll play along...
So we get to block number 6,930,000 somewhere around 120 years from now. Suddenly the block subsidy drops from 0.00000001 BTC to 0 BTC. At this point, for some reason, the number of transactions drops off and less people pay less in transaction fees. Some miners find that the costs of running their equipment is greater than the revenue they generate. Some miners shut off their equipment.
This causes the difficulty to drop within the next 2016 blocks. The reduced difficulty means the remaining miners mine more blocks for themselves without having to increase their costs. This brings them closer to profitability as they will get a larger percentage of the transaction fees that are being paid.
If there are still some miners loosing money by running their equipment, they too will shut their equipment off. This will reduce the difficulty even more, bringing the remaining miners even closer to profitability.
This cycle repeats over and over until eventually, enough miners have shut off their equipment to allow the remaining miners to be profitable from the percentage of the transaction fees that they receive. These miners will continue mining, and the rest of the bitcoin network will continue to function.
Seeing that the network has stabilized, people who are holding bitcoins will look far ways to make use of the value that they hold. This will result in new sources of transactions. The increase in transaction leads to an increase in fees. Now mining is becoming more profitable for those who are still mining. This provides an
incentive for additional people to acquire mining equipment and start mining. The increase in mining results in an increase in difficulty.
As you can see, mining will react to whatever is occurring with transactions. As transactions (and transaction fees) increase, the total amount of mining will increase. As transactions (and transaction fees) decrease the total amount of mining will decrease. Eventually the mining reaches an equilibrium with the transaction load at that time.