Each task instance can be produced by labor or by capital: 𝑦𝑖 ,𝑡 = 𝐴𝑡 𝛼𝐿,𝑖 ,𝑡 ℓ𝑖 ,𝑡 + 𝛼𝐾 ,𝑖 ,𝑡 𝑘𝑖 ,𝑡 , (2) where ℓ𝑖 ,𝑡 and 𝑘𝑖 ,𝑡 are labor and capital per instance, 𝛼𝐿,𝑖 ,𝑡 and 𝛼𝐾 ,𝑖 ,𝑡 are task-specific factor productivities, which AI shifts over time, and 𝐴𝑡 is the stock of ideas, which augments labor on every task and is taken as given in this section. The labor-augmenting structure for 𝐴𝑡 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 𝐾𝑡 = Í𝑖 𝑘𝑖 ,𝑡 and labor 𝐿𝑡 = Í𝑖 ℓ𝑖 ,𝑡 .