A person like me does not have as much a demand for minimum wage (immediately) since my parents earn $40/hr and pay most of my tuition. I am OK with my job such that if they lower it $3/hr, it will take a while to sink in. Heck, with the stupid union dues, it takes my $5.50 wage down to below that (w/ $7/week union dues). The union dues sinks my wage below minimum wage if I work less than 28 hours that week. I hated unions in high school and don't know why I end up joining them a year later. But I still work at my job because my spending patterns aren't that much (no rent or utilities).
It's best to raise wages indirectly. If rich people put greater fractions of their wealth into the poor regions of the economy (whether it is the global economy or state economy), those poorer regions will be able to develop their economy.
Economy\ (in\ real\ units)=Skills*Working\ Hours
But do not confuse economy with standard of health or education. It is likely that country with highest quality education or health will not be the wealthiest nation. People respond to incentives. For some people the money is the incentive, for other people its the quality of life, for other people its the education. And for people like me, none of the above serve as an incentive (in of itself). Your economy, health, and education is a product of your culture. Do you want it differently?
What is so great about the United States' federal system (and similar federal systems) is the ability to test different parameters in the economy and see how the play out. In the more well-off parts of Houston we have more house for our money than in California, but that is obviously due to large differences in other factors. In the end, the system is democractic. If you really desire to live in a place where the minimum wage is going to be $8/hr, try California. If you're like me, and don't care if you're being paid at federal minimum wage, try a state like Texas (or any other state which provides that). Of course, there are other factors too, such as where your buds are located

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The world would be duller if everything was the same. There would also be fewer incentives. This also means that different places have different ranges of incentives themselves. But it does not have to go too far such as of the likes of the North Korean "economy" :.