Some evolutionary genetic models that assume pleiotropic constraints among care for old parents and care for infants are developed, in order to examine the evolution of care for the elderly within a population, in which population aging coupled with a tendency toward a decrease in population size is in progress. Not only does this study suggest that high levels of care for old parents could evolve within the population if the cost of care of the elderly is not too heavy, but it also suggests that, if younger generations experience a high cost of elderly care, this behavior might be eliminated from the population, resulting in the loss of high levels of care for infants. It is also suggested that the benefit of the help from the elderly is essential, not only for the behavior of care for old parents to be maintained within the population, but also for population growth, even though there may be a high cost of elderly care. Based on the results obtained, some social issues that some countries, such as Japan, are now, or will be, faced with are discussed.