> One of your assumptions is that we will start from 1 robot per year.
Not per year, total. And it's not really an assumption, just a demonstration of how fast exponential growth is.
> I assume robots will be similar to high end cars in regards to the complexity of manufacturing.
Agreed. This is also the framing Musk uses for Tesla's androids.
> Once a company develops a prototype with AGI
I don't think it needs a complete solution to AGI, as other people use the term. First, all three letters of that initialism mean different things to different people — by my standard, ChatGPT is already this because it's general over the domain of text, and even if you disagree about specific definitions (as almost everyone reading this will), I think this is the right framing, as you'd "only" need something general over the domain of factory work to be a replacement factory worker, or general over mining and tunnels to be a miner, or general over the domain of roads and road users to be a driver.
This isn't to minimise the complexity of those domains, it's just that something as general as ChatGPT has been for text is probably sufficient.
> The first million will be built by humans. The initial robots will take over the manufacturing only later.
Perhaps, perhaps not. The initial number made by humans is highly dependant on the overall (not just sticker-price) cost and capabilities, so a $200k/year TCO robot that can do 80% of human manual labor tasks is very impressive, but likely to be limited to only a few roles, probably won't replace anyone in its own factory; while one which has total costs of $80k/year and can do 90% might well replace most (but not all) of the humans in its own factory; and one costing $20k/year all-in and which can do 95% might well replace all the factory workers but none of the cobalt miners or the truck drivers.
"Fully general" is the end-state, not the transition period. But with fully-general, which is a necessary condition for nobody having any more work, we get a very fast transition from the status quo to having one robot per human.
> Setting up manufacturing that will be able to produce a million units in 2-3 years is possible. Let's say 5 years for a more plausible situation for a million robots to be built.
Agreed on both.
> Also there is no reason to believe it will be 2^n, it can also be 3^n or 1.1^n or any arbitrary number.
It's a definitional requirement of exponential growth, 2^n units after n doubling periods. I anchored on a the doubling period being a year just by reference to the cost of an example existing robot, and using that dollar cost as a proxy for equivalent human labor, and I specifically noted that the other poster's estimate corresponded to a 5-8 week doubling period which didn't seem unreasonable to me. Some robot can do each specific task 4.2 times slower against the wall clock and still be just as fast as a human overall because it's working 24/7 rather than 8/5.