You say: I’ll use “capital” to refer to both the stock of capital goods and to the money that can pay for them.
It seems to me that this aggregates quite different things, at least if looking at the situation in terms of personal finance. Consider four people who have the following investments, that let’s suppose are currently of equal value:
Money in a savings account at a bank.
Shares in a company that owns a nuclear power plant.
Shares in a company that manufactures nuts and bolts.
Shares in a company that helps employers recruit new employees.
These are all “capital”, but will I think fare rather differently in an AI future.
As always, there’s no guarantee that the money will retain its value—that depends as usual on central bank actions—and I think it’s especially likely that it loses its value in an AI future (crypto currencies as well). Why would an AI want to transfer resources to someone just because they have some fiat currency? Surely they have some better way of coordinating exchanges.
The nuclear power plant, in contrast, is directly powering the AIs, and should be quite valuable, since the AIs are valuable. This assumes, of course, that the company retains ownership. It’s possible that it instead ends up belonging to whatever AI has the best military robots.
The nuts and bolts company may retain and even gain some value when AI dominates, if it is nimble in adapting, since the value of AI in making its operations more efficient will typically (in a market economy) be split between the AI company and the nuts and bolts company. (I assume that even AIs need nuts and bolts.)
The recruitment company is toast.
All the infra for fiat currency exists; I don’t see why the AIs would need to reinvent that
Because using an existing medium of exchange (that’s not based on the value of a real commodity) involves transferring real wealth to the current currency holders. Instead, they might, for example, start up a new bitcoin blockchain, and use their new bitcoin, rather than transfer wealth to present bitcoin holders.
Maybe they’d use gold, although the current value of gold is mostly due to its conventional monetary value (rather than its practical usefulness, though that is non-zero).