Satisfying the growing care demands of the elderly has become a major policy issue under the trend of rapidly aging of the population, especially in developing countries. Although the market-oriented transformation on the supply side is a sustainable way to cope with the pressing demands of elderly care in the long term, the conflict between private and public interests seriously impedes the transformation process in its early stage. From the perspective of maximizing social welfare, this study took the specific situation of China as an example and applied a Stackelberg game model to explore the optimal transformation policy that can balance such conflict of interests. By comparing the effects of two forms of subsidy in China, the results first theoretically verified the importance of subsidy in stimulating the private supply of elderly care, and then emphasized that the size of the gap between supply and demand is the fulcrum of differentiated subsidy, which determines the optimal policy for the development of the elderly care market (ECM) in each aging region. Additionally, the study showed that in the process of market-oriented transformation, the government’s positive response to the demands and preferences of the public, the establishment of market supervision measures, and the increase in the elderly’s affordability all play important roles in improving social welfare. These findings not only have policy implications for the marketization of elderly care in China, but also provide meaningful references for other developing countries in the word that are experiencing or about to experience elderly care problems.