Rapid technological progress in artificial intelligence (AI) has been predicted to lead to mass unemployment, rising inequality, and higher productivity growth through automation. In this paper we critically re-assess these predictions by (i) surveying the recent literature and (ii) incorporating AI-facilitated automation into a product variety-model, frequently used in endogenous growth theory, but modified to allow for demand-side constraints. This is a novel approach, given that endogenous growth models, and including most recent work on AI in economic growth, are largely supply-driven. Our contribution is motivated by two reasons. One is that there are still only very few theoretical models of economic growth that incorporate AI, and moreover an absence of growth models with AI that takes into consideration growth constraints due to insufficient aggregate demand. A second is that the predictions of AI causing massive job losses and faster growth in productivity and GDP are at odds with reality so far: if anything, unemployment in many advanced economies is historically low. However, wage growth and productivity is stagnating and inequality is rising. Our paper provides a theoretical explanation of this in the context of rapid progress in AI.