📝 Abstract
Generative AI is a directional technology: it excels at some task combinations and performs poorly at others. Knowledge work is also directional and endogenous: workers can satisfy their job requirements with different combinations of tasks. Studying AI adoption by knowledge workers hence requires comparing two vectors.We develop a high-dimensional model of task choice and technology adoption, with otherwise standard neoclassical assumptions. AI is adopted when its direction is aligned with what the worker values at the margin -- the worker's shadow prices, rather than with what the worker actually does -- their activity vector. This yields a cone of adoption that widens as AI capability grows; near the entry threshold, small improvements in capability translate into large expansions in the set of adopted directions. Adoption also has a structured intensive margin: a tool can be worth using but not worth using all the time, generating a region of stable hybrid production between an entry threshold and an all-in threshold. We also show how to derive shadow prices as explicit functions of observable skill and requirement vectors. The framework explains rapid adoption in aligned occupations, heterogeneous adoption elsewhere, and weak correlation with one-dimensional skill measures: the key heterogeneity is directional alignment, not skill level.