本文在人力資本內生增長模型的基礎上引入二氧化碳排放,并將二氧化碳作為環境質量引入效用函數,利用最優控制理論求得穩態時經濟增長速度、二氧化碳增長速度,分析了穩態時實現經濟增長和二氧化碳減排雙重目標的條件,證明人力資本可以克服物質資本邊際報酬遞減和二氧化碳排放帶來的負效用,實現經濟增長和二氧化碳減排。通過比較靜態分析、參數校準等方法研究了穩態時各增長率的變動趨勢。隨后本文考察引入二氧化碳排放后內生增長模型的動態性和穩定性,筆者分別通過相位圖、數值模擬的方法研究了系統的動態過程,證明了系統的穩定性。

Based on endogenous growth model of human capital,carbon dioxide emissions are introduced into the model according to the relationship of energy and carbon dioxide emissions provided by IPCC,in addition,carbon dioxide is introduced into utility functionas the environmental quality.The optimal control theory is used to obtain the steady economic growth and the growth rate of carbon dioxide,and the conditions of achieving the double targets on economic growth and carbon dioxide emission reduction in the steady-state are analyzed.It is proved that human capital can overcome the decreasing marginal utility of physical capital and disutility of carbon dioxide emissions in order to achieve economic growth and carbon dioxide emission reduction.By comparing static analysis and parameter calibration,the changing trend of the growth rate in steady state is studied.The method of numerical simulation and phase diagram is used to examine the dynamic path and stability of system.Finally the constant quantity relation in steady state is simulated by parameter calibration method,proving the model conclusions.The inspiration of this paper includes three aspects:First,the consumption level of the whole society should be improved and the economic growth should be stimulated through consumption,rather than through saving investment;Second,the training of human capital should be strengthened and the overall quality of human capital should be improved,in order to make human capital become the new motive force and " new dividend" of China’s economic growth;Third,the awareness of environmental protection and energy saving,as well as environmental legislation and environmental law enforcement should be strengthened.On the whole,the paper can help the researchers and the government to get the relationship of economic growth and carbon dioxide emissions and get the enlightenment that how to keep economic growth when reducing carbon dioxide emissions.Besides,the paper gives us a new perspective that we can research the relationship of economic growth and carbon dioxide emissions through endogenous economic model.