The key element is that demand curves slope downward. That is, the higher the price or cost of anything, other things equal, the less anyone will buy. This is only a matter of common sense, which seems to fly out the window when minimum wages are discussed.

Senator Bernie Sanders wants to make tuition free at public universities. Does he think this will encourage or discourage people from attending them? Of course, the former: the lower the price of education, they more students will buy it.

New York City Mayor Di Blasio wants people to smoke fewer cigarettes. So, he raises their price through taxation. He also believes in a downward sloping demand curve: the higher the price, the less will be consumed.

Nor are these examples limited to tuition and cigarettes. They apply to encouraging people to eschew plastic bags, to buy local (tariffs on foreign goods). This understanding even applies to the labor market in areas other than minimum wages.