The conventional model indicates a relationship between the degrees of spillover arising from local public goods and the optimal revenue-matching grant rates from central government to local government. In the model, an increase in local public goods only impacts utilities. Therefore, we expand the model in this paper to include general public goods, general public capital, and public goods with the characteristics of local public capital. We examine the relationship between the degree of spillover effect and the optimal revenue-matching grant rates, and consider the external effect of both consumption and production. Thus, we obtain a more generalized conclusion and provide a new perspective.