In the recent debate about minimum-wage jobs and living wages, McDonald's (NYSE:MCD), Wal-Mart (NYSE:WMT), and Yum! Brands (NYSE:YUM) have come under fire for not paying enough to help some families make ends meet. But the other main contributor to affordability is the cost of living in a particular place. With the federal minimum wage being the same across the nation, a minimum-wage job goes a lot further in terms of purchasing power in some places than in others. And although some states have set their minimum wages at higher levels than the federal minimum, even somewhat higher pay rates don't always bridge the gap to cover basic living expenses.

One interesting study came from the Massachusetts Institute of Technology, where researchers created a living wage calculator modeled after the Economic Policy Institute's metropolitan living wage tool. With its goal of showing minimum reasonable estimates of the cost of living for low-wage families, the calculator shows some interesting results. Let's look at the five lowest-cost states in the country for a family of four to see how well minimum-wage workers are able to make ends meet.

Cheapest Cost Of Living
Images from U.S. Mint.

5. Kentucky
According to the MIT calculator, you'd have to earn $17.18 an hour full-time to support a family of two adults and two children in Kentucky. The federal-minimum $7.25 an hour that minimum-wage jobs pay there would fall 16% short of that figure even if both adults worked full-time. As you'd expect, major cities were somewhat more expensive, with Louisville residents requiring an extra $0.50 per hour. Construction and repair jobs typically paid enough to meet the minimum, but many jobs, including transportation, food preparation, and personal services, were insufficient to meet basic income needs.

4. Wyoming
Wyoming comes in with a slightly cheaper $16.93-per-hour cost of living, but two-income-earner families would still fall 14% short of that level under the federal $7.25-per-hour minimum. Costs vary widely across the state, though, with the resort area of Jackson requiring a wage almost $3.75 per hour higher to support a family of four. Ironically, most of the jobs in the industries that support those resort services pay well below sustainable income levels.

3. South Dakota
In South Dakota, statewide figures for cost of living point to the need for a job paying $16.75 per hour, leaving two-income families 13% short. With few urban areas, statewide figures point to the need to be in high-paying areas such as technology, engineering, law, and other professional jobs to make ends meet for one-earner families.

2. Montana
Montana's $16.68-per-hour living wage also fails to match up to the $7.25 federal minimum even for two-earner families. The mining and construction industries provide jobs that are sufficient to meet families' income needs, although the typical farming, ranching, fishing, or forestry job doesn't. Areas in the eastern part of the state have benefited from the influx of energy-related jobs, although costs have also increased, making it difficult for residents outside the energy industry to keep up.

1. North Dakota
North Dakota tops the list with a $16.62 living wage that again falls 13% short for families with two minimum-wage earners. Here, MIT's database might not have the latest information, as towns in the Bakken shale play area still show low costs of living despite evidence that the influx of oilfield workers has driven up housing costs. As in Montana, high-paying energy-related jobs are ample to cover costs of living, but more basic jobs such as food preparation and sales are typically insufficient.

Moving toward a sustainable wage
With the four cheapest cost-of-living states in some of the most sparsely populated areas of the country, one might wonder why more people don't move to those locations. Indeed, in areas where energy has taken off, influxes of workers have already occurred. Yet with relatively few jobs available in other areas, those states don't have the capacity to solve the poverty problem on their own.

Fool contributor Dan Caplinger has no position in any stocks mentioned. You can follow him on Twitter: @DanCaplinger. The Motley Fool recommends and owns shares of McDonald's. Try any of our Foolish newsletter services free for 30 days. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.