When it comes to Bitcoin, there are two schools of thought on how the economic system should work. The first one of these is that Bitcoin should be a wealth transfer system in which low-frequency, high value transactions occur, so that the fees are proportionately low, and Bitcoin can compare with other methods of settlement like transporting gold, wire transfers or Western Union. This is the economic "policy" being advocated for by the Bitcoin Core team. The second economic model of Bitcoin is one in which Bitcoin is a peer-to-peer electronic cash system, and individual transactions have low fees, but there are more transactions happening on the network to compensate for it. A lot of people think that this economic model is unsustainable, and won't be enough to subsidize the entire network, but I disagree, so I decided to do the math to see how it would work out!
Before making any calculations on the economic model of Bitcoin and Bitcoin Cash, this model is going to be based on a few assumptions:
A blocksize limit of 8,192,000,000 bytes by 2036 (doubling every two years, and following the increases set out originally by Bitcoin XT)
Blocks are half full, and therefore 4,096,000,000 bytes in size, so the market regarding blocksize isn't distorted
Each transaction on average is 450 bytes
The average transaction fee is $0.005 (consistently under a penny)
Now taking the math into consideration, Bitcoin currently earns (and yields), $3,000,000,000 from the current block reward subsidizing. Assuming that Bitcoin Core decides to raise the blocksize limit to 8MB in the future (this is assuming with SegWit), and transaction fees are $10 for every on-chain transaction, the total yield of such a system (assuming that people will actually be willing to pay such high transaction fees) will be $9,344,000,000 a year. So far the math checks out in terms of replacing the block reward subsidy. This is effective in replacing in the block rewards (at current rates) 3 times over.
At first glance, this would seem to work, but it's working on a false assumption: That people will be willing to pay $10.00 in fees every time they want to transact on the Bitcoin network when there are other cryptocurrencies that are far faster and cheaper. Realistically, I can't see this economic model being sustainable because other cryptocurrencies are starting to take out of Bitcoin's share, and there is no incentive for people to pay high fees when they can just use those other currencies. It seems like Bitcoin mostly wants to compete with wire transfers, but realistically, there are other cryptocurrencies that can do that for cheaper . If a currency can function as peer-to-peer cash, then it can also replace the international bank transfer system, however the inverse is not true.
Now let's contrast this with the economic model of Bitcoin Cash. The Bitcoin Cash community wants to have high transaction volumes, but with low fees, so miners can earn from fees, AND people can transact without worrying about how much money they are going to lose. With the blocksize at 8,192,000,000 bytes, and the actual usage at 4,096,000,000 bytes of transactional data, this would mean that ~9,100,000 transactions are happening per block, which roughly equates to 15,170 transactions per second, and 1.3 billion transactions per day. If we take this figure, and multiply it by the average $0.005 transaction fee, the entire network will make $2.4 billion per year. This is with the conservative estimate of ~4GB blocks, which isn't where Bitcoin Cash is stopping. Double that figure to 8,192,000,000 bytes of usage, and now the network is earning ~$4.4 billion per year in fees. That seems pretty manageable, given that this supposed to be a global network for payments.
Now let's take this a step further: What if we want full global adoption? Currently around 2.5 billion people own a smartphone. Assuming that they will do ~10 transactions per day on average (at peak), that would mean 25 billion transactions per day, or almost 290,000 transactions per second. At this rate, the network would earn a total of ~$45 billion per year. Of course, this would require ridiculously large blocks (~80 GB), but this is not going to happen to any cryptocurrency anytime soon. Even looking at the statistics now, it's technically doable, as we have the tech to do so, but it would be extremely expensive to run a full node. You would have to have a 50 gigabit connection, which would only be available if someone is running a specialized server farm for mining.
TL:DR; Running Bitcoin as a global payment system with low fees and high transaction volume is not only sustainable, it also makes sense. If there are lots of transactions, each with low fees, people get great security, and at a lower individual cost.
At some point the network will either become unusable and expensive, or grow in size to the point where regular people can't run nodes, and only specialized server farms can. Assuming that there are even 450 server farms at global adoption levels (25 billion transactions per day), that would make the gross earnings for each farm $100 million on average. Even at current costs for storage, bandwidth, and technology, such a server would cost a few hundred thousand dollars per year (including labour costs), which is fairly negligible to the gross earnings that these servers will be making.
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