No Set Gauge has a great essay on Capital, AGI, and Human Ambition, where he argues that if humankind survives the Singularity, the likely result is a future of eternal stagnant wealth inequality.
The argument: post-Singularity, AI will take over all labor, including entrepreneurial labor; founding or working at a business will no longer provide social mobility. Everyone will have access to ~equally good AI investment advisors, so everyone will make the same rate of return. Therefore, everyone’s existing pre-singularity capital will grow at the same rate. Although the absolute growth rate of the economy may be spectacular, the overall wealth distribution will stay approximately fixed.
Moreover, the period just before the Singularity may be one of ballooning inequality, as some people navigate the AI transition better than others; for example, shares in AI companies may go up by orders of magnitude relative to everything else, creating a new class of billionaires or trillionaires. These people will then stay super-rich forever (possibly literally if immortality is solved, otherwise through their descendants), while those who started the Singularity without capital remain poor forever.
Finally, modern democracies pursue redistribution (and are otherwise responsive to non-elite concerns) partly out of geopolitical self interest. Under capitalism (as opposed to eg feudalism), national power depends on a strong economy, and a strong economy benefits from educated, globally-mobile, and substantially autonomous bourgeoisie and workforce. Once these people have enough power, they demand democracy, and once they have democracy, they demand a share of the pie; it’s hard to be a rich First World country without also being a liberal democracy (China is trying hard, but hasn’t quite succeeded, and even their limited success depends on things like America not opening its borders to Chinese skilled labor). Cheap AI labor (including entrepreneurial labor) removes a major force pushing countries to operate for the good of their citizens (though even without this force, we might expect legacy democracies to continue at least for a while). So we might expect the future to have less redistribution than the present.