Generative artificial intelligence (AI) has the potential to both exacerbate and ameliorate existing socioeconomic inequalities. In this article, we provide a state-of-the-art interdisciplinary overview of the potential impacts of generative AI on (mis)information and three information-intensive domains: work, education, and healthcare. Our goal is to highlight how generative AI could worsen existing inequalities while illuminating how AI may help mitigate pervasive social problems. In the information domain, generative AI can democratize content creation and access but may dramatically expand the production and proliferation of misinformation. In the workplace, it can boost productivity and create new jobs, but the benefits will likely be distributed unevenly. In education, it offers personalized learning, but may widen the digital divide. In healthcare, it might improve diagnostics and accessibility, but could deepen pre-existing inequalities. In each section, we cover a specific topic, evaluate existing research, identify critical gaps, and recommend research directions, including explicit trade-offs that complicate the derivation of a priori hypotheses. We conclude with a section highlighting the role of policymaking to maximize generative AI's potential to reduce inequalities while mitigating its harmful effects. We discuss strengths and weaknesses of existing policy frameworks in the European Union, the United States, and the United Kingdom, observing that each fails to fully confront the socioeconomic challenges we have identified. We propose several concrete policies that could promote shared prosperity through the advancement of generative AI. This article emphasizes the need for interdisciplinary collaborations to understand and address the complex challenges of generative AI.