Should the government work to substantially reduce the income gap?

The different governments help the upper class be come more successful with all kinds of deals to get them to do business in their city or state. Why not help reduce the income gap. If nothing else improve the schools and try to counteract what just being poor does to most kids. Spend the money for good technical programs in schools. Pay the teachers in those programs what they would make on the job. Hire instructors that have worked in the field for 10 years not just out of college. The best way to reduce the gap is to find a way to bring even more manufacturing back to the US.