From 2021 to 2035, China will be in a rapid growth period of the elderly population, and the growth of the demand for pension funds will accelerate. Under the condition of ensuring that the income level of the elderly population and working age population does not decrease, the minimum expected level of economic growth should be considered in the “14th Five-Year Plan” and the long term goal of 2035. In this context, using the method of numerical simulation, based on the extended endogenous economic growth model, this paper studies and identifies the minimum level of economic growth expectation that can ensure that the income level of the elderly and working age population does not decrease in the future rapid growth period of the elderly population, and puts forward and tests the optimization effect of scientific and technological progress caused by the improvement of knowledge production efficiency. The results show that: 1) During the period of rapid growth of the elderly population, the lower limit of economic growth rate is around 4. 4% in order to ensure that the income level of the elderly and the working age population does not decrease. 2) From 2021 to 2035, the growth of the elderly population will increase in associaton with the level of pension spending, and every 1% increase in the level of pension expenditure will affect the economic growth rate by about - 1. 3 percentage points. 3) In order to achieve sustainable economic growth and the goal of not reducing the income level of the elderly and working age population, one of the best paths is to improve the efficiency of knowledge production and promote the progress of science and technology. It is preliminarily estimated that for every 1% increase in the growth rate of knowledge production efficiency, the growth rate of knowledge storage and capital will increase by about 4. 0%. This not only makes up for the negative impact of population aging on economic growth, but also raise the per capita pension income and per capita labor income by about 40 percentage points.
