(FYI though I think we've chatted about several new varieties issues that I think could come up in the event of a big change in "growth mode", and this post is just about one of them.)

No worries, good to hear!

Thanks! People have certainly argued at least since Marx that if the people owning the capital get all the income, that will affect the state. I think more recent/quantitative work on this, e.g. by Stiglitz, has generally focused on the effects of inequality in wealth or income, rather than the effects of inequality via a high capital share per se. But this isn't my area at all—ask your favorite LLM : )

The reference point argument is also about consumption inequality rather than what gives rise to it. My guess would be that if we all really get radical life extension and a huge quantity of amazing goods and services, that will probably for most people outweigh whatever jealousy comes with the knowledge that others got more, but who knows.

In any event, my guess would be that even if the marginal product of labor stays high or rises following full automation, most people's incomes will eventually come not from wages, but from interest on whatever investments they have (even if they started small) or from redistribution. And full automation could well trigger so much redistribution that income inequality shrinks, since it will remove one motivation for letting income inequality remain high today, namely that unlike with robots, taxing productive people too much can discourage them from working as much.

Great to hear, thanks!

As for the prediction—fair enough. Just to clarify though, I’m worried that the example makes it look like we need growth in the new good(s) to get this weird slow GDP growth result, but that’s not true. In case that’s the impression you got, this example illustrates how we can have superexponential growth in every good but (arbitrarily slow) exponential growth in GDP.

Here's an example in which utility is additively separable, $u_n(.)$ is identical for all goods, the productivity and quantity of all goods grow hyperbolically, and yet GDP grows exponentially.

Ok, fair enough--thanks for getting me to make it clearer :). So I guess the disagreement (if any remains, post-retitling/etc) is just about how plausible we think it is that the technological advances that accompany full automation will be accompanied by further technological advances that counterintuitively slow GDP growth through the "new-products-Baumol" mechanism illustrated here. I don't think that's so implausible, and hopefully the note I'll write later will make it clearer where I'm coming from on that.

But this post isn't aiming to argue for the plausibility, just the possibility. It seems to me that a lot of discussion of this issue hasn't noticed that it's even a theoretical possibility.

not being on track to produce Good 2 only happens in your model specifically because you define automation to be a thing that takes Good-2 productivity from 0 to something positive... Automation is usually understood to be something that increases the productivity of something that we could already produce at least a little of in principle

Okay, I'm happy to change the title to (a more concise version of) "the ambiguous effect of a technological advancement that achieves full automation, and also allows new goods to be introduced on GDP growth" if that would resolve the disagreement. [Update: have just changed the title and a few words of the body text; let me know.]

On the second point: in practice I don't think we have additively separable utility, and I don't know what you mean by "extracting this from our utility function". But anyway, if I'm understanding you, that is wrong: if your utility function is additively separable with an upper bound in each good, say $u\left(x\right)={\sum }_{n}max(0,1-1/x_n)$, a technological shift can yield superexponential growth in the quantity of each n but exponential GDP growth. I'll write up a note on how that works this evening if that would be helpful, but I was hoping this post could just be a maximally simple illustration of the more limited point that Baumol-like effects can slow growth even past the point of full automation.

Right, I’m just not taking a stand here. 

I might be more pessimistic than you about wages on balance, since I would argue for the importance of the “reallocation of capital from labor-augmenting to non-labor-augmenting uses” point, which if strong enough could lower wages through a channel other than the DRS+PS one you focus on. 

Hey Jess, thanks for the thoughtful comments.

On whether "this is still basically Baumol"

If we make that one tiny tweak and say that good 2 was out there to be made all along, just too expensive to be demanded, then yes, it's the same! That was the goal of the example: to introduce a Baumol-like effect in a way so similar to how everyone agrees Baumol effects have played out historically that it's really easy to see what's going on.

I'm happy to say it's basically Baumol. The distinction I think is worth emphasizing here is that, when people say "Baumol effects could slow down the growth effects of AI", they are usually--I think always, in my experience--pointing to the fact that if

1. AI dramatically speeds productivity growth on most goods but leaves some that only humans can produce (say, artisanal handicrafts), and
2. consumers see those goods as not very substitutable for the goods we're getting way more productive at,

then GDP growth won't speed up much. This then invites the response that, when we look around, there doesn't seem to be any human-only good strongly satisfying (1) and (2). My point is that the existence of a human-only good satisfying (1) and (2) is unnecessary: the very same effect can arise even given true full automation, not due to a limitation of our ability to fully automate, but due to the fact that a technological advance can encompass full automation and go beyond yielding a world where we can produce way more of everything we would ever produce without the advance, by letting us produce some goods we otherwise wouldn't have been on track to produce at all. This has not been widely appreciated.

On whether there is any reason to expect the productivity acceleration to coincide with the "kink in the utility function"

Here I think I disagree with you more substantively, though maybe the disagreement stems from the small framing point above.

If indeed "good 2" were always out there, just waiting for its price to fall, and if a technology were coming that would just replace all our existing workers, factory parts, and innovators with versions that operate more quickly in equal proportion--so that we move along the same paths of technology and the quantity of each good produced, but more quickly--then I agree that the past would be a good guide to the future, and GDP growth would reliably rise a lot. The only way it wouldn't would be if the goods we were just about to start producing anyway were like good 2, featuring less steeply diminishing marginal utility but way slower productivity growth, so that the rise in productivity growth across the board coincidentally turned up at the same time as the "utility function kink".

But if the technological advances that are allowing us to automate the production of everything people would ever be able to produce without the advances are also what allow for the invention of goods like good 2, it wouldn't be a coincidence. I.e. presumably full automation will coincide with not only a big increase in productivity growth (which raises GDP growth, in the absence of a random "utility function kink") but also a big change in the direction of productivity growth, including via making new products available (which introduces the kind of "utility function kink" that has an arbitrary effect on GDP growth). The idea that we're soon producing very different products than we otherwise ever would have, whose productivity is growing at very different rates, seems all the more likely to me when we remember that even at 30% growth we're soon in an economy several orders of magnitude bigger: the kink just needs to show up somewhere, not anywhere near the current margin.

To reiterate what I noted at the beginning though, I'd be surprised if the ambiguous second effect single-handedly outweighed the unambiguously positive first effect. And it could just as well amplify it, if "good 2" exhibits faster than average productivity growth.

Great! I do think the case of constant returns to scale with different uses of capital is also important though, as is the case of constant or mildly decreasing returns to scale with just a little bit of complementarity.