NORTH ADAMS - Economic inequality has grown across Massachusetts, but no one has to tell Mindy Shoestock that.

Laid off several years ago from a $12-an-hour job as a housekeeping supervisor at a ski lodge, she took a job at a local McDonald’s, where she earns just $9 a hour. Cable TV and a phone are luxuries she simply cannot afford; some months she runs out of money to buy food for her two children.

“I feel like I’m going backwards,’’ Shoestock said, hot and tired after a recent shift. “Sometimes I feel like I work just to work.’’

Shoestock, 29, is part of a forgotten economy. While family incomes across Massachusetts have generally risen over the past three decades, the state’s poorest residents have fallen behind. And nowhere have they fallen farther than here in Western Massachusetts, where families in the bottom fifth of the income scale have seen inflation-adjusted earnings drop below 1979 levels, according to a new study by University of Massachusetts economists.

The study paints a stark picture of two commonwealths, in which the gap between rich and poor, east and west is growing. For example, the inflation-adjusted median income of affluent families in Greater Boston has grown 54 percent since 1979, to $230,000 from $150,000 a year, largely due to high-paying technology jobs.

In Berkshire County and the Pioneer Valley, where decades of plant closings have left hollowed-out economies, the inflation-adjusted median income of the poorest families fell 24 percent, from $21,000 a year in 1979 to $16,000 - on par with some of the most impoverished parts of Appalachia.

“No real income growth over three decades is what we’re seeing - no improvement in the standard of living,’’ said Michael D. Goodman, one of the study’s authors. “It’s a lost generation of families.’’

Those families live in places like North Adams, in the shadow of Mount Greylock along the state’s westernmost edge. North Adams’s population has declined every decade since 1950 as mills and other manufacturers disappeared. Rising poverty and the recent recession took another toll when bedrock employers, such as the local hospital and city government, laid off workers.

Mayor Richard J. Alcombright described the financial condition of the city, on a scale of great to horrible, as “just a little below horrible.’’ The unemployment rate here was 9.7 percent in June; by contrast, Waltham, an industrial city near Boston, had a 6.3 percent jobless rate.

One-fifth of North Adams households make less than $20,000 a year, and about half of those earn less than $10,000 annually. One economic bright spot, if it can be called that, is the potential expansion of a Wal-Mart, which could bring about 20 new jobs.