Our founders certainly had a good idea of the things that Government may be more effective at, as indicated in the specifically enumerated powers of A1S8 of the constitution.
There are cases, in general where, government may have a role ( when goods are non rival and nonexclusive- education, national defense). Or when there are external effects, example: you and I engage in voluntary exchange and harm a 3rd party. However, the existence of 'public goods' or 'externalities' alone does not guarantee that government will offer any improvement.
Past posts related to the function of government:
Type I and Type II Errors
Type II Error Bias -the FDA
Type II Error Bias and Hurricane Katrina
The Tragedy of The Commons
Our Commons Our Choice
Public Choice Theory
The Median Voter Theorem
The Coase Theorem
Tragedy of the Anticommons
Public Choice Recapitulation
Public Choice and the Constitution