> So if tier one needs something from tier two I don't think they need to even ask

You mean stealing? I'm assuming no stealing.

> But this also means probably there will be no way way for tier two to extract any of the resources which tier one needs at all bc the marginal cost is determined by tier one

If someone from tier 2 owns an oil field, tier 1 has to pay them to get it at a price that is higher than what the tier 2 person values it, so at the end of the transaction, they would have both a positive return. The price is not determined by tier 1 alone.

If tier 1 decides instead to buy the oil, then again, they'd have to pay for it.

Of course, in both these scenarios, this might make the oil price increase. So other people from tier 2 would find it harder to buy oil, but the person in tier 2 owning the field would make a lot of money, so overall, tier 2 wouldn't be poorer.

If natural resources are concentrated in some small subset of people from tier 2, then yes, those would become richer while having less purchasing power for oil.

However, as I mentioned in another comment, the value of natural resources is only a small fraction of that of goods and services.

And this is still the worst-case, unlikely scenario.

OK let's assume no stealing (which is unlikely). I think the previous argument was a little flawed anyhow, so let me start again.

I mean fundamentally if tier 2 has something to offer to tier 1, it is not yet at the equilibrium you describe (of separate economies). I think it's likely that tier 2 (before full separation) initially controls some resources. In exchange for resources tier 1 has a lot of AI-substitute labor it can offer tier 2. I think the equilibrium will be reached when tier 2 is offered some large sum of AI-labor for those resource production means. This will in the interim make tier 2 richer. But in the long run, when the economies truly separate, tier 2 will have basically no natural resources.

This thing about natural resources being small fraction is current day breakdown. I think in the future where AI autonomously increases efficiency of the loop which makes more AI-compute from natural resources, its fraction will increase to much higher levels. Ultimately, I think such a separation as you describe will be stable only when all natural resources are controlled by tier 1 and tier 2 gets by with either gifts or stealing form tier 1.