Yes, if people are payed more for jobs that require self-improvement, they would want to do what is necessary to get the jobs. That doesn't mean that the lowest paying jobs should not provide a living wage. As long as big corporations are allowed to pay less than that, we, the taxpayers will be subsidizing them through food and rent subsidies financed by our taxes. 
CEO's who make hundreds of times more money than their low wage workers (and who have had their taxes reduced regularly) are one of the reasons that poverty is increasing so much. They should at least pay a fair share of taxes. Their corporations could receive tax breaks if they pay living wages, but they should be heavily taxed if they don't.
Those taxes could go to pay for projects that provide necessities, such as food, clothing, and shelter, to the needy.