Why might markets fail? Can and should the government intervene if the market fails?

Markets can fail for a number of reasons but the three largest are market power, asymmetric inflation, and externaities. Usually in the first and third government can and sometimes should intervene. In the second the problem is harder because getting parties to have equal information is extremely difficult and can't be solved through legislation alone.

When determining if the government should intervene you must look at how large the market failure is. The government shouldn't for example subsidize deodorant because smelling better has a positive externality. The government though should get involved when a factory is greatly reducing the quality of air of a town or a monopoly is having a large negative impact on the daily lives of your citizens.