We build an equilibrium model of the market for nursing home care with decision-makers on both sides of the market. The nursing home demand arises as a result of stochastic dynamic optimizations by households heterogeneous in age, health, wealth; and the cost of home-and-community-based care. On the supply side, locally competitive nursing homes decide prices and care intensity. The government pays for the long-term care of the poorest. We estimate the model parameters using Health and Retirement Survey and simulate the model to quantitatively evaluate the effects of long-term care policies on prices, intensities, care allocation, and welfare.