Government spending composition in an endogenous growth model with congestion

We build an endogenous growth model in which government expenditure is divided into public consumption and investment in public capital, and where both components suffer from some degree of congestion. We demonstrate that the socially optimal growth rate is negatively related with the degree of congestion. As regards the optimal share of government spending on infrastructure, we prove that an increase in congestion leads to a decrease in this share and that the optimal share of government spending on output can increase or decrease with congestion. In addition, we compare the social planner optimum with the second-best outcome and show that, in this second case, welfare is lower. In this framework, we derive a necessary condition, that must hold in the second-best equilibrium, involving the income tax-rate and the share of government spending on public investment