minimum wage

The Guardian - How much is an hour worth? The war over the minimum wage
and for a little background info about the minimum wage from the US department of labor

i quickly googled it, but didn't find it easily so my main questions remains: how is minimum wage determined anyway? and how did they arrive at the $15 an hour for the new minimum wage?

the Guardian article keeps referring to economic studies and theories, but is that the only field of study that matters in the fight for or against a minimum wage? I feel like we should also be consulting psychologists and sociologists, and more. certainly the economy affects everyone, but in what feels like a very indirect way. it'll be harder to find a job, or you'll get a bigger year-end bonus, but generally things are pretty stable, even prices of apartments and milk. 

what does a living wage mean to people? what to they spend their extra money on? are there fewer deaths somehow (since people can now afford preventative health care rather than "I'm literally on my deathbed where's the nearest hospital" kind of care) is there less crime? more college graduates? more babies being born?

there's a widely quoted factoid: "When affordable is defined as comprising up to 30% of a renter’s budget, a full-time worker earning the federal minimum wage [$7.25 per hour] cannot afford rent on the average two-bedroom apartment anywhere in the country." not sure why they went with two bedrooms. maybe cause many people have dependents? I think a one-bedroom apartment might be a more realistic expectation. all the couples I know share a one bed-room,  unless they have roommates in the another bedroom. the singles are either in studios, or also have roommates. only those that are in their 40s are living alone, without roommates, in their one bedrooms. 

I think there should be a federal minimum wage, and, likely a higher one for most states. it should be determined based on a number of factors like average price of a one bedroom apartment, cost of gallon of gas, and maybe cost of a dozen eggs. cost of living, basically, which is why each state would have it's own minimum wage. it's true that cost of living can vary wildly across each state, but I think it maybe too much to do city minimums. possibly counties might be better.