Well, it depends on what you mean by "cheap." If you are just looking at housing costs, then yeah, there are some pretty inexpensive places to live. But there are a lot of other things to look into besides housing costs. Also, when you compare the cost of renting money (i.e taking out a bank loan) to buy a house versus renting the house/apartment, the cost is fairly equal after taxes and other costs (both implicit and explicit) are taken into account. Regardless, you should also look at job opportunities, availability of education, even health care. You might also want to look at projected growth forecasts because an area may be relatively inexpensive now, but in a few years or so it may completely change. You'll also want to look at utility costs AND the tax rate. Housing might be cheap, but it might also be subsidized by a lot of taxes. Check out the costs of owning/driving a car in an area. Gas prices fluctuate from city to city and state to state. States might be very cheap to live in because no one wants to live there. Alaska is handing out free land, but if you live there you'll not only freeze, but you'll only see the sun about half the year. You might also want to take into consideration commute times, and how that effects your cost of living.
It is the economist in me talking, I know, but there really are almost an infinite number of variable to consider when determining what is "cheapest." It isn't just numbers involved; there is value as well. What person A considers to be tolerably cheap probably isn't going to match person B's idea.
Then again, Arizona doesn't follow DST, so that is a HUGE plus.
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