Long-run growth and welfare in a two sector endogenous growth model with productive and non-productive government expenditure

• Growth rate is increasing in the elasticity of substitution but decreasing in the weight of public good in utility.
• Long-run growth rate is increasing in the intertemporal elasticity of substitution.
• The welfare-maximizing tax rate is lower than the long-run growth-maximizing tax rate.
• The results depend on the production technology.

We develop a two-sector model of physical and human capital accumulation, where public goods provide both productive capital (i.e. infrastructures) and utility enhancing services. We analyze the impact of both the level of government expenditure and its composition on growth and welfare, under different production technologies, and derive their respective growth and welfare-maximizing levels. We show that contrary to what happens with welfare, the long-run growth rate is increasing in the intertemporal elasticity of substitution but decreasing in the relative weight of public goods in utility. Furthermore, the welfare-maximizing tax rate is lower than the growth-maximizing tax rate, whereas the welfare maximizing share of productive government expenditure is greater than the growth maximizing share. Finally, we employ numerical simulations to get a better understanding of the model.