I once asked my professor about something similar, although not in context of a welfare state (minimum wage, some autonomous consumption guaranteed) so it wasn't about a consumer wanting to consume at least a consumption bundle Q, but about making enough to keep oneself alive. Surely one would try to work as much as possible if that was the only way to keep oneself alive? Well, it's actually difficult to measure via labour market since at superlow wages, the labourer would probably retreat from the labour market completely and revert to something like subsistence farming, begging, stealing, activities that bring income but are not based on offering one's labour on a market. Of course in your case, the minimum wage should eliminate most of this. Yet the problem is that the minimum wage is set at an arbitrary level and therefore acts as a cutoff since as aniari pointed out, you can't distinguish the reservation wages and therefore your sample will contain workers who would "gladly" work for less than minimum wage and their greater income per hour might put them on the backwards bend of their personal labour supply curve, so they will actually work less. So I think your hypothesis won't probably hold on the labour market as a whole, since the mass of workers eliminates the abberations on the lower and higher end. So while a personal labour supply curve might be double bended, resembling the letter S inverted by the y-axis (working more hours near the minimum wage, then working slightly less with increasing wage, then working more, then again working less), an aggregate curve will probably simply show a positive correlation between wage and labour supplied, irrespective of the subset of workers chosen.