Yes, I think that it is a duty of the employer to make sure that they treat all of the people that they have working for them in a way that is going to make sure that they are treated fair and that they are not being ripped off in life.
If everyone had a living wage, the economy would shoot through the roof, as would the gdp. There would be more money to tax, so it would be better for the country's revenue. And, also, even the companies paying out these sums would profit. Why? People with money spend money.
While all skilled jobs certainly should and to an extent a lot of unskilled ones too, it is financially not possible to make every job one that can support an adult on its own. While I feel for people dealt a hand in life that makes them clock decades at a McDonald's, the fact of the matter is those jobs were created with the intent of giving a kid some pocket money, not provide for a household.
I believe that you should only be paid based on the amount of value you are giving to your employer, I don't believe someone working a part time job is providing enough value at their job to justify a dramatic pay raise to a living wage, in the end all that will happen is that businesses will pass on the cost to consumers increasing the prices on all products and services.
While most jobs should meet a minimal living wage there are some exceptions. Some jobs are so part time that a basic living wage is not possible, but it would provide a second income for someone or some extra cash for a student. Certainly any full time job should meet basic living standards for our people.