This study introduces the spillover effect of public goods and the heterogeneity of jurisdictions to the capital tax competition literature using a two-period economy. A clear result is that the private capital tax rate used by the hyperopic jurisdictional government in the first period significantly depends on the relative size of the income and spill-in effects in the second period. The relative size of the two effects, which work in opposite directions, is determined by the tastes and endowments of the jurisdictions, the form of their production functions and the degree of spillovers, among other factors. This research verifies that the jurisdiction with the less efficient production technology may choose to tax private capital in the first period, assuming that a lump-sum tax is available to it, and receive substantial spillover benefits from the other jurisdiction with more efficient production technology in the second period when the jurisdiction is hyperopic and benevolent, which is quite different from the literature.