The government sometimes provides public goods because

The government sometimes provides public goods because they are non-rival in market and non-excludable in their consumption.

Public goods commonly face a free rider problem due to their nature.

A free rider is a person who benefits from something without contributing their fair share.

Some examples of public goods include: Police services, lighthouses and street lighting.

more people will not obey the law or vice vice versa

explanation: the answer really speaks for itself if the number of prisoners are going up then that means that more people will not obey the law and if less people are going to prison then that means that more people are obeying the law.