And yeah, that’s fair. One possible SWE-style story I sort of hint at there is that we have preferences like the ones I use in the horses paper; process efficiency for any given product grows exponentially with a fixed population; and there are fixed labor costs to producing any given product. In this case, it’s clear that measured GDP/capita growth will be exponential (but all “vertical”) with a fixed population. But if you set things up in just the right way, so that measured GDP always increases by the same proportion when the range of products increases by some marginal proportion, it will also be exponential with a growing population (“vertical”+”horizontal”).
But I think it’s hard to not have this all be a bit ad-hoc / knife-edge. E.g. you’ll typically have to start out ever less productive at making the new products, or else the contribution to real GDP of successive % increases in the product range will blow up: as you satiate in existing products, you’re willing to trade ever more of them for a proportional increase in variety. Alternatively, you can say that the range of products grows subexponentially when the population grows exponentially, because the fixed costs of the later products are higher.
Thanks!
And yeah, that’s fair. One possible SWE-style story I sort of hint at there is that we have preferences like the ones I use in the horses paper; process efficiency for any given product grows exponentially with a fixed population; and there are fixed labor costs to producing any given product. In this case, it’s clear that measured GDP/capita growth will be exponential (but all “vertical”) with a fixed population. But if you set things up in just the right way, so that measured GDP always increases by the same proportion when the range of products increases by some marginal proportion, it will also be exponential with a growing population (“vertical”+”horizontal”).
But I think it’s hard to not have this all be a bit ad-hoc / knife-edge. E.g. you’ll typically have to start out ever less productive at making the new products, or else the contribution to real GDP of successive % increases in the product range will blow up: as you satiate in existing products, you’re willing to trade ever more of them for a proportional increase in variety. Alternatively, you can say that the range of products grows subexponentially when the population grows exponentially, because the fixed costs of the later products are higher.