在全球化背景下，未来经济增长将更多地依靠制度改进、科技创新和技术进步，因此，调整经济的增长方式和产业结构可以在保证经济稳定发展的同时实现碳排放总量下降。在科技进步不变的情况下，即经济增长与碳排放二者之间仍存在正相关时，从华氏经济增长优化模型出发，给出了碳排放减少优化模型，通过将二者合并得到经济增长与碳排放协调发展的分式规划模型，并给出其求解方法；同时，通过分析和证明经济增长率、Frobenius根的关系、消耗系数、消耗碳排放系数之间关系，得出了经济增长与碳排放的一致性模型和解决方法。
Under the background of globalization, the future economic growth will more rely on the improvement of the system of science and technology innovation and technological progress. Therefore, the adjustment of economic growth and industrial structure can guarantee the stable economic development and at the same time to achieve a decrease in total carbon emissions. When the technology advance is invariant, which means there exists positive correlation between economic growth and carbon emissions, the carbon emission reduction model could be drawn from HUA'S economic growth and optimization model.The fractional programming model could be drawn from the coordinated development of economics growth with carbon emissions, and the method to solve the model is given. At the same time, the consistency between economic growth and carbon emission model could be concluded through the analysis of the relationship among economic growth rate, Frobenius root, consumption coefficient and carbon emission coefficient of consumption.The research result would help government to make decision for increasing economy and controlling carbon emissions at the same time.
[1] Roberts J T, Grimes P E. Carbon intensity and economic development 1962-1991:A brief exploration of the environmental Kuznets Curve[J]. World Development, 1997, 25(2):191-198.
[2] 李明贤, 刘娟. 中国碳排放与经济增长关系的实证研究[J]. 技术经济, 2010, 29(9):33-36.
[3] 张国兴, 张振华, 刘鹏,等. 我国碳排放增长率的运行机理及预测[J]. 中国管理科学, 2015, 23(12):86-93.
[4] 吴振信,谢晓晶,王书平. 经济增长、产业结构对碳排放的影响分析——基于中国的省际面板数据[J]. 中国管理科学,2012,20(3):161-166.
[5] Stiglitz J. Growth with exhaustible natural resources:Efficient and optimal growth paths[J]. Review of Economic Studies, 1974, 41:123-137.
[6] Romer D. A simple general equilibrium version of the Baumol-Tobin model[J]. Quarterly Journal of Economics, 1986, 101(4):663-686.
[7] Ani?a S, Capasso V, Kunze H, et al. Optimal control and long-run dynamics for a spatial economic growth model with physical capital accumulation and pollution diffusion[J]. Applied Mathematics Letters, 2013, 26(8):908-912.
[8] 崔百胜, 朱麟. 基于内生增长理论与GVAR模型的能源消费控制目标下经济增长与碳减排研究[J]. 中国管理科学, 2016, 24(01):11-20.
[9] Samuelson P A. A catenary turnpike theorem involving consumption and the golden rule[J]. American Economic Review, 1965, 55(3):486-496.
[10] 华罗庚.计划经济大范围最优化的数学理论-(Ⅰ)量综与消耗系数方阵[J].科学通报,1984,29(12):705-709.
[11] 华罗庚.计划经济大范围最优化的数学理论-(Ⅱ)消耗系数(Ⅲ)正特征矢量法的数学证明[J].科学通报,1984,29(13):769-772.
[12] 华罗庚.计划经济大范围最优化的数学理论-(Ⅳ)数学模型(矛盾论的运用)(Ⅴ)论调整(Ⅵ)生产能力的上限,表格[J].科学通报,1984,29(16):961-965.
[13] 华罗庚.计划经济大范围最优化的数学理论-(Ⅶ)论价格[J].科学通报,1984,29(18):1089-1092.
[14] 华罗庚.计划经济大范围最优化的数学理论-(Ⅷ)论Brouwer不动点定理[J].科学通报,1984,29(21):1281-1282.
[15] 华罗庚.计划经济大范围最优化的数学理论-(Ⅸ)基本定量的证明[J].科学通报,1985,30(1):1-2.
[16] 华罗庚.计划经济大范围最优化的数学理论-(Ⅹ)生产危机的产生[J].科学通报,1985,30(9):641-645.
[17] 张金水.可计算非线性动态投入产出模型[M].北京:清华大学出版社,2000.
[18] 徐大举, 刘家壮, 陈晓兰.多部门经济平衡增长研究[J].中国管理科学, 2002,10(5):39-41.
[19] 徐大举, 刘家壮, 孔淑兰.华氏宏观经济模型的推广[J].中国管理科学,2003,11(5):16-19.
[20] 沃西里·里昂惕夫.投入产出经济学[M].崔书香,译.北京:商务印书馆, 1982.
[21] 李爱华, 宿洁, 贾传亮, 等, 推广的实用华氏宏观经济增长模型及参数估计[J], 数学的实践与认识, 2009, 39(21):59-64.
[22] 徐大举,尹金生,李爱芹,等.直接消耗系数矩阵特征值的经济意义研究[J]. 中国管理科学,2010,18(01):33-38.
[23] 华罗庚, 高等数学引论(余篇)[M].北京:科学出版社, 1984.
[24] 吴文江, 袁仪方, 实用数学规划[M].北京:机械工业出版社, 1993.
