In my state we have been slowly increasing the minimum wage. It's now at $12/hour and it is working out great. The economy seems to be doing fairly well (although there are obviously other factors at play there). So controlling wages isn't too hard.

Food prices have mostly remained static, with minor increases to help pay the new wages. Nothing that I would even call noticable beyond regular inflation. So controlling those costs isn't exactly a priority if you increase minimum wage to the point where people can afford food.

The biggest problem is still housing costs. Where housing is cheap, jobs are scarce. In and around the cities where jobs are plentiful, rent is through the roof. This is probably the hardest cost to control, because all the fixes are extremely expensive (such as building low-income housing or increasing public transportation to more affordable areas).

Let's not pretend that controlling this costs is beyond our grasp as a society. We just need politicians willing to push legislation to fix the problems.