We build a two-dimensional political economy model to explain income redistribution and public financing of long-term care. Voting agents differ in income and need opening up two conflicts: one sets the poor against the rich with the former preferring heavier income taxation than the latter. The other sets families with needy parents, who are in favor of a public long-term care program, against the ones without such parents who oppose public financing. We show that a structure induced equilibrium always exists and that it is unique if informal care is provided in equilibrium. The equilibrium not only explains the negative association of income inequality and long-term care financing but also allows predictions about how demographic change might impact long-term care arrangements.