I agree it correlates and is evidence, but I still think that the exact claim is easy to counterexample.
In particular, I think the argument you make ignores substitutes. E.g., suppose that quinoa because 1000x cheaper in all regions (cheaper than even current transportation costs). I think quinoa as a fraction of GDP would grow massively despite quinoa currently being a small fraction of GDP.
Sorry for handwaving some details away: I agree you can construct toy models in which the claim is not true. I think in pretty much any realistic CES production function you construct (and trivially in Cobb-Douglas functions), the substitution effect will not be strong enough to outweigh this consideration for minerals. The essential quantity here is the elasticity of substitution, and more specifically, how substitutable the item is for other things in the economy.
Minerals are not great substitutes for lots of things in the economy: they can’t be eaten, they can’t be used as fuel, they can’t substitute for labor etc. As they become more abundant, I expect the income effect and substitution effect will roughly cancel out, causing their contribution to GDP to neither rise nor fall by much.
I asked GPT-4 to demonstrate the precise effect on total utility of a good falling in price by a factor of a million in two separate toy models, if you’re interested (the conversation is here). But ultimately I agree my language was a bit sloppy and you’re right to point out that there are worlds in which the claim I made is technically not true. (I guess I should have stated it less confidently too.)
Sorry for handwaving some details away: I agree you can construct toy models in which the claim is not true. I think in pretty much any realistic CES production function you construct (and trivially in Cobb-Douglas functions), the substitution effect will not be strong enough to outweigh this consideration for minerals. The essential quantity here is the elasticity of substitution, and more specifically, how substitutable the item is for other things in the economy.
Minerals are not great substitutes for lots of things in the economy: they can’t be eaten, they can’t be used as fuel, they can’t substitute for labor etc. As they become more abundant, I expect the income effect and substitution effect will roughly cancel out, causing their contribution to GDP to neither rise nor fall by much.
I asked GPT-4 to demonstrate the precise effect on total utility of a good falling in price by a factor of a million in two separate toy models, if you’re interested (the conversation is here). But ultimately I agree my language was a bit sloppy and you’re right to point out that there are worlds in which the claim I made is technically not true. (I guess I should have stated it less confidently too.)