In traditional macroeconomics argues that the decision and fluctuation of output level is short-term theory, and the growth of output is a long-term theory. The former is determined by the demand; the latter is determined by the production. No one has questioned why the former is determined by production and the latter is determined by demand. This paper argues that the factors that affect the output are the same in the short and long term, but there is no need to analyze the problem of fluctuation in the long term. Based on the analysis of the growth path in our previous paper, this paper first examines whether our model is applicable to the Pontryagin maximum principle, and then analyzes the difference of the Cobb-Douglas function in the exogenous growth model and the endogenous growth model. Reveal the special role of parameter A in Cobb-Douglas function: as long as A is considered as output-related variables, there is no substantial difference between the so-called exogenous model and endogenous mode. Finally, according to the trend of the growth path and the nature of A, the paper derives the final state of Cobb-Douglas function.