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jonny@neuromatch.social ("jonny (nonvenomous)") wrote:

Sure, yeah, assuming perfect substitution of AI and human labor for a task such that the only place they differ is their price is a totally fair assumption

Each task instance can be produced by labor or by capital: 𝑦𝑖 ,𝑑 = 𝐴𝑑 𝛼𝐿,𝑖 ,𝑑 ℓ𝑖 ,𝑑 + 𝛼𝐾 ,𝑖 ,𝑑 π‘˜π‘– ,𝑑 , (2) where ℓ𝑖 ,𝑑 and π‘˜π‘– ,𝑑 are labor and capital per instance, 𝛼𝐿,𝑖 ,𝑑 and 𝛼𝐾 ,𝑖 ,𝑑 are task-specific factor productivities, which AI shifts over time, and 𝐴𝑑 is the stock of ideas, which augments labor on every task and is taken as given in this section. The labor-augmenting structure for 𝐴𝑑 facilitates a balanced growth path in our model in the absence of AI; letting it augment both labor and capital has only small effects in what follows (though it would have larger effects over longer horizons). Capital and labor are therefore perfect substitutes within a task and, since 𝜎 < 1, gross complements across tasks. Once each instance is assigned to a factor, the technology in Equations (1)–(2) is a constant-returns aggregate of total capital 𝐾𝑑 = Í𝑖 π‘˜π‘– ,𝑑 and labor 𝐿𝑑 = Í𝑖 ℓ𝑖 ,𝑑 .