Optimal federal taxes with public inputs

This paper deals with the solution to vertical expenditure externalities in a federation with two levels of government sharing taxes. Under these circumstances, the Nash equilibrium does not satisfy the condition for production efficiency in the provision of public inputs. This vertical expenditure externality is removed when the federal government, behaving as Stackelberg leader, chooses the optimal tax rate on labor income. The sign of this tax rate depends on the elasticity of marginal productivity of the public input with respect to employment. Moreover, the previous result concerning both vertical (tax and expenditure) externalities are independent each other is confirmed here.