The cost of a 2 bedroom apartment always costs what someone working for minimum wage makes plus $100. Why? Because landlords don't want people making minimum wage living at their apartments - never mind the (perceived)increased maintenance and crime - people working minimum wage are people that don't have income security and more likely to miss payments or need to be evicted.
If you raise minimum wage, the price of rent just goes up. Now that isn't a argument against raising it more that an argument against renting and an argument for housing reform, but that is a whole different post.