Economists don't like protectionist unions. Who determines a "living wage"? Should someone working as a cashier in Walmart be able to afford an apartment in Manhattan?
Someone working as a cashier in Walmart should be able to afford shelter, food, and necessary non-emergency medical expenses. A 'living wage' is just that -- I work for you, you pay me at least enough to survive employment. What that amounts to, obviously, depends on the standard of living in any particular area.
If it's impossible to survive in (or on, whatever) Manhattan for less than that, then yes. But I suspect there's a more flexible reality to the market than your question implies, given that people there already work for less than that and aren't dying in the streets as a result.
A minimum wage just means you can't decide one day that sales are down and now everyone makes 2 cents an hour to cover costs [1]. It means there should be an implicit minimum cost to maintaining a human workforce, because people need to eat.