Old people living in the advance aged care service institutions are the retirement pension group whose pension and savings are sufficient to cover the charges of the advance aged care service institutions. As the elderly group continues to grow, the market is “in short supply” and there is a monopoly phenomenon. The elderly are in the relatively disadvantaged position. In order to make the market healthy and protect the basic rights of the elderly, it is necessary to study its pricing mechanism and social welfare. This paper takes advance aged care service institutions of the duopoly as the research object, establishes two Hotelling dynamic game models, compares the pricing mechanism and social welfare of the elderly when they buy “free deposit” insurance and “wholesaling deposit” insurance, finds that no matter how the elderly choose to stay, the aged care service institutions can obtain excess profits, and when the elderly buy the “free deposit” insurance, the profit of the old-age institutions, the welfare of the elderly and the social welfare have increased significantly.