This paper establishes a novel mathematical model to analyze the effects of government education and health expenditures on the economic growth. Based on the Cobb-Douglas production function, the analysis of education and health expenditures is conducted using the two-stage least square method and applying the Gaussian mixture model as the estimation method. The results provide not only the long-term relationship between education and economic growth, but also between health expenditure and economic growth. In addition, they show that both education and health expenditures have different contributions to economic growth, resulting in unbalanced development in various districts. We also compare the per capita public health and education expenditures and their economic effects in different regions. We conclude that the district with relatively less contribution may not necessarily increase their expenditure; hence, effective management may be more important. In accordance with the regional contribution divergence, the government should formulate corresponding policies to improve the allocation of education and health resources and ensure rational capital flow among regions.