Okay, let's see what we've got here.

Assuming 1 childless worker, got a list of things here (would like to know more about how these numbers were arrived at, but I'll take them at their word).

Food, medical, housing, transportation, civic (apparently this is recreation etc.) Internet/mobile, and "other" (saving?)

I looked up an area near me. They give annual values, but I, like most Americans I imagine, can relate more easily to monthly costs, so I divided everything by 12. So here's what MIT says a "living wage" should pay for, per month:

Food: $406. That seems like a LOT for a single adult. My roommate and I spend less than this for the both of us and we buy groceries together, so I know how much our combined cost is.

Medical: $276. Can't really comment in either direction about this, fact is that medical costs vary SO much from person to person, and even for the same person at different stages of life, that I'll just give the benefit of the doubt that that's the correct cost on average.

Housing: $1615. My rent is less than this, and I'm talking about the actual rent, not just the 50% of it I pay (as I said, roommate). I could see this being more or less accurate for my area for someone just moving in someplace, though.

Transportation: $897. What the fuck? If you have shitty credit AND you financed an expensive car for a shitty rate, then maybe you could get here, not that requires a series of bad decision making. NOBODY should be paying anything close to this a month for a car, even if you get gas weekly.

Civic: $251. That's significant, $60+ every week? Doing/buying what?

Internet/mobile: $117. That sounds fine, assuming middle of the road Internet and standard mobile plan.

Other: $368. Well, what can you really say about "other"?

So, other than a few of those categories being WAY out of proportion imo, the biggest issue I see here is that MIT is giving different, separate "living wages" for 3 categories of people (1 alone, 2 with 1 working, and 2 with both working (why isn't this just the first category doubled?)), and for 0 to 3 children. So, some issues I'm seeing:

1. It's one thing to force a company to pay a worker more if they have a kid(s), and/or live with someone who doesn't work, but you can't force a company to hire these people. Considering that the value of the labor itself obviously does not increase based on those things, this seems like it'd obviously create massive direct (there's likely some that's indirect, but the fact is that your boss is not entitled to know anything about your living situation) incentive against hiring anyone other than single childless individuals.

2. Typically an employer is not even entitled to know such personal details about a worker/applicant in the first place. But if we put these into effect, they would have to, in order to know which category you fall into, which leads back into 1 above.

3. There is a LOT of work that does not generate nearly that amount of value (in the case above, around $27/hour assuming 40hr work week) for the business, but are things the business can't function without. It's easy to say "if you can't afford to pay every single one of these positions at least this living wage, then you can't afford to be in business", but the fact is that this would place huge obstacles in the way of a small business getting up and running to any real degree. Megacorporations have pockets deep enough to eat the cost though, and so they'll become even better at driving small business to extinction than they already are, and hasten us toward a society where they're the only real game in town. And I shouldn't have to list the reasons that an 'employer monopoly' is a REALLY bad state of affairs for the working population.

"Just increase the minimum wage to a living wage" is not the 'duh, just do it' obvious solution it's made out to be.

The classic definition is the wage needed to cover the basic needs of the family including things like rent

Rent where? Rent costs vary wildly.

childcare

What sort of childcare, and how many children is it meant to support? Or do you get $X per child? And if so, is there a maximum number of children, where having more won't get you more money?

transportation

Over what distance? And how, owned vehicle or public transportation? If owned vehicle, what kind of vehicle? Used/new? Price ranges for vehicles also vary wildly.

I would go one further and say that the family needs to not be living paycheque to paycheque.

That entails what amount of extra money? And what do you do about people who willfully choose to spend it instead of saving it? Are you aware that in the US, 1 in 4 of people earning $150k or more live paycheck to paycheck? Just because one has money to save doesn't mean they're going to do it.

go out once in a while

Again, far too vague. How often? And how much money does 'going out' cost? You'd have to figure both of those out, and multiply them by each other, to ensure this goal is met.

educate their children

Taxpayer-funded public school already covers this. Unless you feel everyone should be entitled to the cost of private schooling?

save and pay for university

University tuition is another massive variable, so you'd need to decide how much is given for tuition. Also, if someone does not go to college, do they not get that part of the money?

and advance themselves.

The vaguest criterion yet. It's pretty much impossible to say if a given minimum wage satisfies 'everyone can advance themselves'.

As anyone can see, this "classic" definition is still full of major holes, and not nearly complete enough to even conceptualize a goal such that progress toward it can even be measured. Just saying "living wage" over and over will never get anyone anywhere.