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Want to afford a house? Move to Ohio.

The middle class's incomes have stagnated in recent years, and there's no sign of recovering. Still, there is a place where there is hope for the middle class, and it's called the Midwest. At least when it comes to affording the roof over your head, a new analysis from real estate site Trulia shows that Midwestern cities — particularly ones in Ohio — are where homes are the most affordable for people in the middle of the income distribution.

Houses middle class cities

(Source: Trulia)

The blue dots represent cities where the largest share of homes on the market are affordable for that metro area's median income, whereas red shows the lowest share. ("Affordable" here means that the monthly payment is no more than 31 percent of a given metro area's median income.)

Topping the list is Dayton, Ohio, where 85 percent of homes are affordable to the middle-class. Following close behind are Rochester, N.Y., and Akron, Ohio.

What's maybe most striking here is that the cities where people are the richest — New York City, San Jose, San Francisco — are also the least affordable.

There are two big reasons for that, writes Trulia Chief Economist Jed Kolko. One is that the rich people have made houses unaffordable in those more expensive cities.

"High-income households bid up home prices, and high prices push out lower-income households," he writes.

In addition, new homebuilding has tended to be slower in these more affluent cities. Less supply and the same level of demand equal higher prices.