The LA County Federation of Labor has released a document that shows that life in Los Angeles is expensive -- something we've always known. http://launionaflcio.org/thefightforgoodjobs/
According to the leaflet "What does it take to live in Los Angeles?" a single person requires an income of $28k to live "modestly" in Los Angeles.
According to Craigslist, however, the $843 rent and utilities for a small apartment underestimates the rent by around $100, unless you're looking for a very small studio with free electricity. http://losangeles.craigslist.org/lac/apa/
And $1,200 for a 1 or 2 bedroom? Good luck. Maybe in extremely modest parts of South Central LA.