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(x)=∑nmax(0,1−1/xn), 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.
Oh yea, I didn’t mind the title at all (although I do think it’s usefully more precise now :)
Agreed on additively separable utility being unrealistic. My point (which wasn’t clearly spelled out) was not that GDP growth and unit production can’t look dramatically. (We already see that in individual products like transistors (>> GDP) and rain dances (<< GDP).) It was that post-full-automation isn’t crucially different than pre-full-automation unless you make some imo pretty extreme assumptions to distinguish them.
By “extracting this from our utility function”, I just mean my vague claim that, insofar as we are uncertain about GDP growth post-full-automation, understanding better the sorts of things people and superhuman intelligences want will reduce that uncertainty more than learning about the non-extreme features of future productivity heterogeneity (although both do matter if extreme enough). But I’m being so vague here that it’s hard to argue against.
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.
Here’s an example in which utility is additively separable, un(.) is identical for all goods, the productivity and quantity of all goods grow hyperbolically, and yet GDP grows exponentially.
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(x)=∑nmax(0,1−1/xn), 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.
Oh yea, I didn’t mind the title at all (although I do think it’s usefully more precise now :)
Agreed on additively separable utility being unrealistic. My point (which wasn’t clearly spelled out) was not that GDP growth and unit production can’t look dramatically. (We already see that in individual products like transistors (>> GDP) and rain dances (<< GDP).) It was that post-full-automation isn’t crucially different than pre-full-automation unless you make some imo pretty extreme assumptions to distinguish them.
By “extracting this from our utility function”, I just mean my vague claim that, insofar as we are uncertain about GDP growth post-full-automation, understanding better the sorts of things people and superhuman intelligences want will reduce that uncertainty more than learning about the non-extreme features of future productivity heterogeneity (although both do matter if extreme enough). But I’m being so vague here that it’s hard to argue against.
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.
Here’s an example in which utility is additively separable, un(.) is identical for all goods, the productivity and quantity of all goods grow hyperbolically, and yet GDP grows exponentially.