I mostly agree with your overall statement (eg, there are better ways to accomplish the goal than to increase the minimum wage, and EIC may be one of those). However, I have some nitpicks (or devil's advocacy, or whatever).
First, your paragraph on efficiency wage theory shows how the two of us might know the same fact and yet our assumptions about how well the market works lead us to two different conclusions. You see that paying a higher wage than the market-clearing rate yields benefits to businesses, therefore you assume that businesses indeed pay that higher wage. Whereas I assume that in many cases businesses do not take advantage of efficiency wages, and therefore there may be some room for "no-regrets" legislative increases in wages. (Of course, half the time I'm the economist who doesn't pick up the $20 bill on the sidewalk because if it was real it would have been picked up already... but half the time I'm not)
Also, for some anecdotal evidence read this Nytimes article.
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First, your paragraph on efficiency wage theory shows how the two of us might know the same fact and yet our assumptions about how well the market works lead us to two different conclusions. You see that paying a higher wage than the market-clearing rate yields benefits to businesses, therefore you assume that businesses indeed pay that higher wage. Whereas I assume that in many cases businesses do not take advantage of efficiency wages, and therefore there may be some room for "no-regrets" legislative increases in wages. (Of course, half the time I'm the economist who doesn't pick up the $20 bill on the sidewalk because if it was real it would have been picked up already... but half the time I'm not)
Also, for some anecdotal evidence read this Nytimes article.