Abstract: 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.

Key words: positive feature vector, carbon emission, economic growth, consistency