Should is the keyword. In many cases the increase in pay isn't enough for the increased cost of living. For example, according to Yahoo!'s cost of living index, Boston is 27% more expensive than an average city. However, the minimum wage for Boston (Massachusetts), $8 per hour, is only about 10% more than the federal minimum, which is $7.25. Honolulu is even worse. The cost of living there is a whopping 88% more than average yet they're stuck with the federal minimum wage of $7.25.
Well there's Walmart's minimum wage, then there's professional minimum wage. My friend is an electrical engineer, and he could make $105,000 a year in NYC doing the SAME exact thing he's doing now in Florida for $45,000. My other friend moved to North Carolina to work for Redhat (he was one of the coders for the OLPC
, and he made MORE there than when he worked in St Louis, Missouri at their branch there. Dallas and Houston's salaries are WAY up now too. I dont know why these things occur though