Abstract: Based on the principle of balanced income distribution, this paper constructs a “complementary substitution” mathematical model for the income distribution of family support and individual pension, and estimates appropriate levels for both family support and individual pension. This paper also studies the optimization of economic structure of family support and individual pension from the theoretical and empirical perspectives. The results show that: (1) the income distribution of family support and individual pension substitutes each other while they are complementary under the condition of prolonging working age; (2) the equilibrium time point of the replacement of family support and individual pension is 2 children, and the marginal substitution efficiency of family support pension and individual pension decreases; (3) with the increase of life expectancy, the family support income distribution structure changes, the family support coefficient decreases, and the rise of individual pension coefficient is faster than the drop of family support coefficient; (4) the “complementary and substitution” effects between family support and individual pension follow an invertedV curve, and the turning point is close to the replacement level of total fertility rate of 2.1.

Keywords: Family Support, Individual Pension, Balance Distribution of Lifecycle, Moderate Level

摘要： 依据生命周期均衡收入分配原理，构建家庭子女养老和个人养老收入分配适度水平及其“互补替代”数理模型，从理论和实证角度研究家庭子女养老和个人养老经济结构优化。研究发现：（1）家庭子女养老和个人养老收入分配存在“替代”关系，而在退休年龄延长的条件下，二者存在“互补”关系；（2）家庭子女养老和个人养老替代的均衡点是家庭有2个子女，随着子女数量的增加，家庭子女养老与个人养老边际替代率递减；（3）伴随老年人寿命的延长，家庭子女养老收入再分配系数下降，个人养老收入分配系数上升且上升幅度大于前者下降幅度；（4）家庭子女养老与个人养老之间的“互补替代”效应呈现为“倒V形”曲线，且其替代的均衡点与总和生育率2.1的更替水平存在契合效应。

关键词: 家庭子女养老, 个人养老, 生命周期均衡收入分配, 适度水平