Very unlikely you will ever get a logical answer to this. Of course the minimum wage should be livable, nobody should have to work 2 or 3 jobs just to get by.
Firstly, there are numerous problems with the minimum wage.
1) Living costs dramatically vary from place to place.
2) The supply of labour can vary from place to place.
3) The availability of work can vary from place to place.
It is absolute hubris to think you can distil all these complexities and regional differences into one number, which you call the living wage.
Secondly.
It really is about understanding how the concept of the price of something is determined. Contrary to what your buddy Marx says, prices are not determined by how much work you put into providing a good or a service. They are determined by what someone else is willing to pay for said good or service and what someone is willing to sell said good or service for. If prices are not determined like this, you get severe economic problems. Like unemployment, inflation caused by the lack of production.
The only proven way of helping those on the lower end of the economic scale is to have a free economy that produces high economic growth. That growth then allows workers to be more picky about which jobs they can pick as the burden then shifts to employers to look for lower cost labour.