China has entered an aging society and will likely become the fastest-aging country in the world. The demand for aging care services has greatly increased. In recent years, the model of mutual aid for aging care has met the needs of older adults, especially those in rural areas. In this case, how much time should be spent on mutual aid for the older adult in terms of time and how much influence the size of the group has in terms of space are two very important questions when studying mutual aid for aging care.
An overlapping generations model is built in this article, which includes representative agents, representative enterprises, the endowment insurance system constructed by the government, and the behavior of representative agents in mutual aid for aging care under the background of active aging.
In the base case, the optimal proportion of time to participate in the mutual aid group is 9.31%, and the optimal proportion of time is influenced by the benchmark time of care and the size of the care group. With the increase in the benchmark time of care, the optimal proportion of time increases correspondingly, but the increase is decreasing. With the increase in the size of the care group, the optimal proportion of time decreases, but after the size reaches 4 or 5, the impact becomes very small. When parents' psychological preference coefficient changes from 0.1 to 0.9, that is, when parents change from introverted to extroverted personalities, the optimal proportion of time and parents' utility will also change.
For children who usually take care of their parents for a long benchmark time, the optimal time to participate in the mutual aid group based on personal utility maximization is also long. Second, as the size of the group increases, the time for representative agents to participate in the mutual aid group gradually decreases. In addition, the model of mutual aid for aging care is highly correlated with parents' personalities, and extrovert parents benefit more from this model.