This paper extends a two-period Overlapping Generations model of endogenous growth where the interactions between public infrastructure, human capital with R&D activities, and growth are studied. The paper makes two important contributions. First, it accounts for the spillover effect of the stock of ideas on learning which in turn promotes the production of innovative technologies. In doing so, it brings to the fore a two-way interaction between human capital and innovation. The paper then applies various econometric methods which confirm the above theoretical thesis. Second, the solutions of the model emphasise the important role public spending on infrastructure, human capital and R&D can play in promoting economic growth. In order to study the transitional dynamics of the model and to illustrate the impact of public policy, the model is calibrated using the average data for low-income countries and a sensitivity analysis is reported under different parameter configurations. The findings of the numerical analysis show that trade-offs in the allocation of public spending may inevitably emerge. In particular, investment in public infrastructure at the expense of spending on R&D is less likely to succeed in promoting economic growth, whereas it may be more effective to foster growth through an offsetting cut in another productive component, namely, education. In light of these potential trade-offs, governments in low-income countries need to use their limited budgets as part of holistic measures in order to achieve efficient outcomes.