What is the neoclassical “story” of how free markets do not work, and, hence, the economic justification for government?

I want you to explain how the standard economics textbooks explain when competitive free markets do not work and give the justification for government intervention.

Here is a sample outline:

1. Required role for government in a free market system
a. Legal system to protect property rights, enforce contracts for growth

2.  “Market Failure”
a. Public good
b. Non-rival
c. Non-excludability
d. Why private markets won’t produce them in efficient quantities and how the
government gets around that

2a. Externalities
a. Positive
b. Possible role for government
c. Negative
d. Possible role for government

3. Other roles for government
a.Promote competition
b. Promote better information
c. Income redistribution
d. Promote economic stability (fiscal policy and monetary policy)

4. Government failure