Purpose – Recent research supports the role of productive government spending as an important determinant of economic growth. Previous analyses have focused on the separate effects of public investment in infrastructure and on investment in education. This paper aims to introduce both types of public investment simultaneously, enabling the authors to address the trade-offs that resource constraints may impose on their choice. Design/methodology/approach – The authors employ a two-sector endogenous growth model, with physical and human capital. Physical capital is produced in the final output sector, using human capital, physical capital, and government spending on infrastructure. Human capital is produced in the education sector using human capital, physical capital, and government spending on public education. The introduction of productive government spending in both sectors yields an important structural difference from the traditional two-sector growth models in that the relative price of human to physical capital dynamics does not evolve independently of the quantity dynamics. Findings – The model yields both a long-run growth-maximizing and welfare-maximizing expenditure rate and allocation of expenditure on productive capital. The welfare-maximizing rate of expenditure is less than the growth-maximizing rate, with the opposite being the case with regard to their allocation. Moreover, the growth-maximizing value of the expenditure rate is independent of the composition of government spending, and vice versa. Because of the complexity of the model, the analysis of its dynamics requires the use of numerical simulations the specific shocks analyzed being productivity increases. During the transition, the growth rates of the two forms of capital approach their common equilibrium from opposite directions, this depending upon both the sector in which the shock occurs and the relative sectoral capital intensities. Research limitations/implications – These findings confirm that the form in which the gove rnment carries out its productive expenditures is important. The authors have retained the simpler, but widely employed, assumption that government expenditure influences private productivity as a flow. But given the importance of public investment suggests that extending this analysis to focus on public capital would be useful. Originality/value – Two-sector models of economic growth have proven to be a powerful tool for analyzing a wide range of issues in economic growth. The originality of this paper is to consider the relative impact of government spending on infrastructure and government spending on human capital and the trade-offs that they entail, both in the long run and over time.