My own feeling is that minimum wage does not matter when economy is at full employment like it is now. But when the economy is in a downturn a minimum wage of €13.50 will stop some employers from hiring at all.
Many have forgotten but the troika forced Ireland to cut the national minimum wage from €8.65 to €7.65 in late 2010 when unemployment was 14% but it was the first thing that the incoming FG-Labour coalition reversed when it come into office a month or two later.
Personally I think minimum wage legislation should have in-built flexibility to provide for a reduced rate during tough economic times but not many politicians have the courage.