This paper studies the equilibrium dynamics of a growth model with public spending. The model considers negative production externalities by explicitly including them as unfavorable effects in the production function. Differently from conventional analysis here government spending along with private production, also generate negative externalities. The model simultaneously determines the optimal shares of consumption, capital accumulation, taxes and composition of the two different public allocations, which maximize the representative household's lifetime utilities in a centralized economy. Moreover, with one restriction on the parameters we fully determine the solutions path for all variables of the model and determine the conditions for balanced growth. Given the active role the government has in determining the level of production, the higher the externalities compared to the optimum, the lower the tax rate.