Paul Krugman argues that a decrease in the minimum wage would increase unemployment. This goes against what others advocate, which is a decrease in the minimum wage to decrease current unemployment.
Here’s how the fallacy works: if some subset of the work force accepts lower wages, it can gain jobs. If workers in the widget industry take a pay cut, this will lead to lower prices of widgets relative to other things, so people will buy more widgets, hence more employment.
But if everyone takes a pay cut, that logic no longer applies. The only way a general cut in wages can increase employment is if it leads people to buy more across the board. And why should it do that?
But proponents of decreasing the minimum wage (abolishing it altogether is best) aren't arguing for "a general cut in wages," they are looking for a change in (abolishing it, actually) legislation that bars businesses from hiring the least skilled among us. Unemployment is currently heavily concentrated among younger people without a high school diploma, and especially among blacks. A decrease in the minimum wage would lower the relative cost of hiring lower skilled people, not cause a cut in the general wage level.
BTW - Given Krugman's reasoning, he must certainly then agree that an increase in the minimum wage at any time is ineffective since it results in an increase in the overall price level and does nothing to increase the relative wages of the least skilled.
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