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What happens then?
The price will stop going up…
No, price is driven by supply and demand, when all bitcoin have been mined, supply will no longer increase, while the demand will (in theory).
The Bitcoin price is fundamentally driven by the cost of electricity: if you're a miner, you can spend $40K on electricity (on average) to mine a new coin, or if existing coins cost less money to buy, you can simply buy them instead (and make a profit in the process).

The goal of miners it to acquire coins, and they can either buy electricity and compute machines and "trade" that expense for coins, or they can buy coins directly. Either way, miners will do whatever is cheapest to get new coins.

What happens when the price is so high that it cannot be used to purchase food? I guess it could buy a higher echelon of assets. But what demand is going to drive the price if the currency cannot meet basic needs? Can demand drive price if a commodity is entirely illiquid?
You can divide one Bitcoin into very small parts, the smallest 1/100000000 part of one.

The bigger problem is that the transaction fees are much too high to buy small things.

That's a good point that I didn't articulate and understanding of in my comment. I guess I meant more so that if the price gets higher and remains high, then its holders will not or are not selling, and I wonder if how long this illiquidity could sustain the price of bitcoin.
Miners will only make money from transaction fees.

Currently, when a miner solves a block, they collect the block reward and the transaction fees for transactions included in that block. The block reward gets cut in half on a schedule based on the block number. Eventually, the block reward hits zero once it can't be divided any further, so only the transaction fees are the reward. Of course, at some point between now and then, the transaction fees will exceed the block reward, so it'll be moot.

By that time, a single Bitcoin will either be worthless, or it will be worth millions.

What happens after 2140??

Excerpt:

As of Monday morning, 90% of the total bitcoin supply of 21 million has been mined, according to data from Blockchain.com.

The remainder is not expected to be mined until February 2140. Until then, miners can continue to earn bitcoins.

Bitcoin operates on a proof-of-work model, which means that miners must compete to solve complex math problems to validate transactions. It’s not an easy process — reaching the 90% milestone took 12 years.

Newly minted Bitcoin (a new blocks coinbase reward) is just one way to earn Bitcoin. The other is a reward of the sum of the transaction fees included in said block.
"The remainder is not expected to be mined until February 2140. Until then, miners can continue to earn bitcoins."

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