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Abstract This paper takes China as an example to quantitatively study the weight relationship between economic growth, social welfare, and environmental quality, and explores the role of social capital in promoting sustainable development. This paper constructs the Hamilton optimization model, the ‘sustainable’ element is introduced on the basis of the traditional utility function, and given China’s economic characteristics of numerical simulation analysis was carried out on the model parameters, to reveal the connotation of Chinese sustainable development from the mathematical, to explore the influence mechanism of social capital in promoting sustainable development. Research has found that sustainable development seeks coordinated economic, social, and environmental development. Setting the weight ratio of economic growth, social welfare, and environmental quality at 1:1.5:1.5 can better explain China’s concept of sustainable development. When social capital accelerates its accumulation, it can effectively control the development and utilization of natural resources, and the ecosystem environment can maintain the stable state of the ecosystem through its own regeneration and restoration ability. Social capital has become a new driving force for sustainable development, achieving a steady and rising trend of China’s economic development level. The research conclusions are helpful to promote the sustainable development, and to enrich and expand the relevant research on social capital.
Zhang et al. (Mon,) studied this question.
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