It is critical to understand how government policies affect intergenerational mobility and inequality. We study intergenerational mobility and its mechanisms in China, where regional policies have been the source of social controversy for many years. Existing policies concerning education and migration produce inequities in quality of and access to opportunity. We consider three relevant policies. First, decentralized public K-12 education spending implies that richer regions have better-funded public schools. Second, the Ministry of Education allocates more seats at public colleges to richer provinces relative to the number of provincial applicants. Finally, the Hukou, or residential permit, system imposes substantial costs to migrate to rich areas by restricting access to local Hukou, which is required for individuals to access important public resources such as education, subsidized housing markets, and healthcare. These policies drive intergenerational persistence in education and location, leading to intergenerational persistence in income. We calibrate a structural spatial overlapping generations model that encapsulates China's institutional setting and calibrate it to recent Chinese data. We then use the calibrated model to quantify the effects of changing these policies on intergenerational mobility, welfare, education, and the income distribution, with particular interest in outcomes for children born at the bottom of the parental income distribution. We find that lifting Hukou restrictions and equalizing public spending levels increases intergenerational mobility and improves outcomes for the poorest born in poor provinces at the expense of children born in rich provinces. Modifying college allocations to a merit-based or equity-based admissions system has modest aggregate effects, with positive (and negative) effects are largely concentrated among children born to richer parents.