Should I tell my boss about a morale problem?

Due to company downsizing and people being afraid of being fired, my fellow employees are forming factions and basically stabbing each other in the back to make themselves look good. Rather than working as a team, people are working against one another. If my boss is aware of it, he's doing nothing. If he's not aware of it, I feel it is my duty to let him know so that he can do something to improve morale and get everyone working together. Should I say anything or just keep my mouth shut?