We propose a dynamic non-cooperative framework for long-term-care (LTC) decisions of families and use it to evaluate LTC policy options for the US. We first document the importance of informal caregiving and economic determinants of care arrangements. We then build a heterogeneous-agents model with imperfectly-altruistic overlapping generations to account for the patterns we find. A key innovation is the availability of informal care, which is determined through intra-family bargaining. This opens up a new margin in response to policy and allows for informal insurance through home-production of care. Our calibrated model captures the observed care arrangements well. We study the implications of non-means-tested informal-care and formal-care subsidies as well as changes to means-tested Medicaid. We find that informal care responds strongly to these policies. An informal-care subsidy substantially reduces reliance on Medicaid, the reduction of tax revenues due to lower labor supply by caregivers being modest. There are large welfare gains from a combination of informal-care and formal-care subsidies, even when combined with a reduction of the Medicaid program.