This work analyses the equilibrium dynamics of a growth model with public finance where two different allocations of public resources are considered, namely "institutional" spending and “traditional” core productive spending. Both components of government expenditure are complementary with private production. The model we propose simultaneously determines the optimal proportion of consumption, capital accumulation, taxation and composition of the two different public expenditures which maximize a representative household's lifetime utility in a centralized economy. The model supplies a closed-form solution. Moreover, with one restriction on the parameters (a = s) we fully determine the solution path for all variables included in the analysis and establish the conditions for balanced growth.