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Workers in California and New York recently celebrated their home states' decision to raise the minimum wage to $15 an hour. For those who live in major cities, however, that joy may be short-lived.

That's because the cost of living varies widely even within individual states, particularly big, diverse states like California and New York. The purchasing power of $15 an hour could be above average for a small, rural town, but insufficient in a major metro areas, according to research from the Pew Institute.

In order to study this phenomenon, the Pew Institute examined data on regional price parities (RPPs), a concept developed by the Bureau of Economic Analysis to measure local price levels in big cities and non-metro areas alike, relative to the overall national price level. It found that Illinois had the greatest gap in RPPs, with Chicago's price levels amounting about 34.6% above those in Danville, a small city that ranks as the second-cheapest place to live in the United States.

Illinois is followed in the rankings by California and New York, which both recently voted to raise their minimum wage to $15. The Golden State's most-expensive metro, San Jose, has price levels 33.2% higher than the least-expensive place in the state, El Centro. In New York, New York City's price levels are 31.9% higher, respectively, than those in Utica-Rome. Meanwhile, the states with the smallest price gaps—among them, Idaho, Wyoming and Vermont—are generally rural states with few major cities.

It's worth noting that some states, including New York, have attempted to address these regional differences in their minimum wage legislation. While the increase to $15 will phase in fully by 2018 in New York City and by 2021 in Westchester County and Long Island, it is only guaranteed to reach $12.50 in cheaper upstate areas by 2021.

Oregon, which was ranked as the area with the 12th-smallest gap in price levels, also raised its minimum wage in geographic tiers: By 2022, the minimum wage will be $14.75 in Portland and $12.50 in rural areas.