Even if an AI costs a million dollars in, say, 2020, it’ll be a thousand in 2030 and one dollar in 2040 (give or take a decade). Why hire a human when you can buy the equivalent for a dollar? One way or the other, the human race is going to take an early retirement in the next few decades.
We already have seen what happens when a large amount of human equivalent intelligence (inside human equivalent bodies) becomes available at a vastly lower price. This is what happened over the last few decades with China and India's workforce becoming strongly connected to the developed world economy. It led to manufacturing outsourcing and information and service outsourcing. The caliber and capabilities of the Chinese and Indian people has been growing as well.
This has also been seen for certain tasks or jobs for automation. Vending machines, automated teller machines, automated telephone dialers, spam advertising email and other machine and software automation.
Most of the benefits accrued to the shareholders and owners of companies that were able to take advantage of the cost savings and other benefits. However, other companies were also able to make the business shift. So margins did not permanently expand.
So the Singularity will be a constant series of waves of more powerful robotic outsourcing. It will not all hit at once. Certain things will be more difficult to outsource. Just as making an expert player of the game of Go is harder and is taking over ten years longer than making an expert player of Chess.
Some tasks have a maximum amount of intelligence that can be applied.
The game of Checkers was solved in 2007. That is all the useful moves were placed into a database and computer software. An analysis of the great checker player Marion Tinsley who only lost 9 games over 45 years shows that he only made about 20 mistakes over decades of play.
So even with super AI a human especially a human that is using a computer aid would be able to perform perfectly. But if the AI is so much cheaper then why ? The reason is that many of the consumers (who are generating the demand) are people. They can choose to want the human interaction. The choice is seen with the use of ATMs or human tellers.
There would also be the situation of prostitution versus super virtual reality.
Another factor effecting how the situation will play out is that people start off (the initial state) with all of the money and controlling everything. So any control that is ceded has to move from people to any artificial systems one project or transaction at a time.
It will be up to people to adapt and ride the waves of change to gather control of more and more resources as the resources become cheaper and stay relevant to the economy of civilization.
Physical labor partially made this transition. The top level physical labor tasks/jobs are where people are paid to operate machines with thousands of horse power. Fly large jets, large ships, trains, trucks, taxis etc... People also operate machines in non-paying situations. However, people can still choose to not use machinery in a perfectly adequate scaled situation. A private gardener does not need to use a tractor.
A possible end state is where a galactic civilization uses all of its stellar energy to support 10^50 human equivalent minds. A non-virtual galaxy could have 10^30 human equivalent minds (every solar system full of people). Deeper into a post-singularity world each person would need to be running their own regular galactic empire equivalent to have their share of per capita real person income.