We present a tractable model of Artificial Intelligence (AI) as self-learning capital: Its productivity rises by its use. An AI sector and an applied research (AR) sector produce intermediates for a final good firm and compete for high-skilled workers---while benefitting from mutual spillovers. The economy displays a sequence of four tipping points: First, entrepreneurs and second, high-skilled workers drive the accumulation of self-learning AI. This is reversed in two subsequent tipping points. In the steady state, AI accumulates autonomously due to spillovers from AR. By characterizing the social planner's selection of tipping points, we obtain that suitable subsidy/tax policies induce socially optimal movements of workers. In particular, we provide a macroeconomic rationale for an AI-tax as soon as AI becomes mature and benefits strongly from its learning ability. Moreover, we observe an increasing income divergence due to the rise of AI.