Generative Artificial Intelligence (AI) tools are rapidly adopted in the workplace and in education, yet the empirical evidence on AI's impact remains mixed. We propose a model of human-AI interaction to better understand and analyze several mechanisms by which AI affects productivity. In our setup, human agents with varying skill levels exert utility-maximizing effort to produce certain task outcomes with AI assistance. We find that incorporating either endogeneity in skill development or in AI unreliability can induce a productivity paradox: increased levels of AI assistance may degrade productivity, leading to potentially significant shortfalls. Moreover, we examine the long-term distributional effect of AI on skill, and demonstrate that skill polarization can emerge in steady state when accounting for heterogeneity in AI literacy -- the agent's capability to identify and adapt to inaccurate AI outputs. Our results elucidate several mechanisms that may explain the emergence of human-AI productivity paradoxes and skill polarization, and identify simple measures that characterize when they arise.

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