To begin with, justice makes people feel happy and fair in the community. if people are treated equally no depending on which social group they come from, how wealthy they are, they feel satisfied and relaxed with their living community. For example, in job interview, candidates feel good if evaluation process focus on the what knowledge, skills and practice they acquire rather which clothes they wear. Otherwise, people, particularly youth, tend to lose their hope for future and feel desperate with their life.
Well, it is not clear that how maintaining the justice would help reduce the gap between rich people and the poor. You need to give some reason that well justifies your opinion and therefore that reason must be very relevant to the topic. You've got to maintain a better alignment between your writing and what your prompt requires.
Furthermore, acquisition of education is the best way to create a happy society and get rid of a huge difference of income among individuals. It is a fact that high level of education lead to high income. When poor people are encouraged to gain vocational education to find a job, poverty rate will be decreased and thus the there will be no anger about earning gap among people.
Your prompt does not ask how this gap can be reduced. I feel you have gone off track in this essay.