This study assuming that the consumers were self-interested under the given tax system, constructs an intergeneration model by using Bernoulli utility function to explore consumers' purchasing plan of optimal long-term care (LTC) insurance for maximizing their expected utility. We find that (1) if the children are willing to provide care giving and the after income-tax wage rate were less than after-legacy-tax the premium for LTC insurance, then the expenditure of LTC insurance is positively relative to the amount of care giving. If the children aren's willing to provide care giving, others being equal, then the expenditure of LTC insurance is negatively relative to the amount of care giving. (2) If the after-income-tax wage rate were higher than after-legacy-tax the premium for LTC insurance, then the results are just opposite to the findings above. Meanwhile, if parents know well of children's behavior, the benefit from higher expenditure of LTC insurance would be smaller than the cost incurred when the children increase the amount of care giving and the deductible decreases. Then, a corner solution was found. Otherwise, the relationship is ambiguous.