Although New York’s minimum wage has steadily increased over time, its real value has fluctuated. New York's minimum wage has generally hovered at or slightly above the federal minimum wage since its inception. From 1962 to 1981, the state minimum wage went up every one to four years before it stagnated for about a decade during the 1980s. It has struggled to keep up with inflation since then.

The 1960s were a high point for the minimum wage. Barnard College Economics Professor David Weiman said the minimum wage was most valuable in 1968 when the minimum wage was $1.60 per hour, or $10.86 in 2014 dollars. Census data shows the median monthly cost for a New York rental plus utilities was about $886, adjusted for inflation.

“Even though the nominal value (of the minimum wage) may have been lower (than it is now), it was actually higher. So, when folks are talking about wanting $15 and others say, ‘You’re out of your mind,' they can point to this historical experience,” Weiman said.

But the city was rocked by a fiscal crisis in the 1970s, leading to budgetary cutbacks and fewer social services. This marked the first period of decline in real value of the minimum wage. In the wake of these financial troubles, there was no political coalition willing to increase the nominal wage during the 1980s, so the real value deteriorated pretty sharply.The minimum wage in New York and across the nation held at $3.35 an hour from 1981 until 1990. It would have to be $5 an hour to keep up with the cost of living.

James Macklin, who runs The Bowery Mission homeless shelter, says he's a growing number of working people at the shelter since he first arrived in 1987. He thinks raising the minimum wage would help keep working people off the streets.

“Most people would love to be able to have a decent wage so that they can provide for their family and themselves and pay their rent. I don’t think they want to be rich. I think they want to live a well-balanced life,” he said.

Macklin said the area surrounding the shelter is exemplary of the city's growing unaffordability. While the area was once considered New York's Skid Row, gentrification and increasing high rises now mark the area.

“There’s a building right next door that just sold for $35 million, but if you look on the outside, you see people that are destitute, that have nothing. On the next right is a museum that costs $25 million. The mission sits in the midst of all of this,” Macklin said.

Russian immigrant Elena Popova was at the shelter for a school project, but ended up consulting Macklin for investment advice. She said she came to the U.S. five years ago with $500 in her pocket and made minimum wage as a hostess in Bay Ridge to get by. She said she walked dogs, babysat and painted houses on the side. Meanwhile, her family back home was clueless.

"My job was to tell them everything was fine. I didn't want them to worry," she said.

A coalition of local politicians recently proposed a Fair Wage Act, which sets out to create a living wage in the city. It would require large employers and chain stores to pay their employees $15 an hour indexed to inflation. According to the Bureau of Labor Statistics’ Consumer Price Index, New York’s minimum wage is $2 short of what it would need to be to keep up with the cost of living.

“New York’s minimum wage does not go far enough to keep families out of poverty. Large chains, from McDonalds to 7-Eleven, have higher profits and lower costs, yet they still pay their workers poverty wages,” said bill sponsor state Sen. Daniel Squadron.

At issue is what workers are entitled to at the most basic level. The U.S. Supreme Court has already ruled that the federal minimum wage is constitutional, but is it intended to be a living wage? The Fair Labor Standards Act, which established the minimum wage, says its purpose is to correct and eliminate “labor conditions detrimental to the maintenance of the minimum standard of living necessary for health, efficiency, and general well-being of workers.” The 1938 law aims “to provide for the establishment of fair labor standards in employments in and affecting interstate commerce, and for other purposes.” But what’s fair is up for debate.

The gap between the cost of living and the minimum wage has fluctuated but remained. The federal minimum wage was last raised in 2009 and has lost about 5.8 percent of its buying power to inflation. In New York, it's set to go up to $8.75 by the end of this year and $9 by the end of 2015, though Macklin isn't satisfied.

“That’s a very good step, I will not deny that, but we need to keep looking to see how we can improve upon this,” he said.