Experimental evidence suggests that AI tools raise worker productivity, but also that sustained use can erode the expertise on which those gains depend. We develop a dynamic model in which a decision-maker chooses AI usage intensity for a worker over time, trading immediate productivity against the erosion of worker skill. We decompose the tool's productivity effect into two channels, one independent of worker expertise and one that scales with it. The model produces three main results. First, a decision-maker who fully anticipates skill erosion still rationally adopts AI when front-loaded gains outweigh long-run skill costs, lowering long-run productivity. Second, when the decision-maker and the worker are misaligned, through short-termism on either side or private returns to skill that the deployment ignores, this loss becomes an augmentation trap that leaves the worker worse off than without AI. Third, when AI productivity depends little on worker expertise, the model can generate permanent divergence, with high-skill workers reaching their potential and low-skill workers deskilling to zero. The decomposition sorts deployments into five regimes, separating beneficial from harmful adoption.

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