When I analyze minimum-wage legislation with my freshman economics students, I always emphasize the fact that the analysis itself cannot determine if such legislation is good or bad. Such a determination is not in the province of science. Economic analysis can reveal only the likely consequences of a minimum wage. Assessing the merits or demerits of these consequences necessarily involves value judgments. And because minimum-wage statutes, like nearly all government interventions, have both upsides and downsides – in popular parlance, they generate some ‘winners’ and some ‘losers’ – value judgments cannot be avoided when considering how to weigh the benefits reaped by the ‘winners’ against the losses imposed on the ‘losers.’ Science cannot tell us the maximum amount, if any, of a loss the ‘losers’ can suffer in order for the policy nevertheless to be justified.We have stuff like Hicks-Kaldor or Scitovsky welfare criteria for that. As far as the policy itself, if you get the pay raise, you're happy, but if you're let go (or, more commonly, don't see the hiring that doesn't take place) you're not.
Economic analysis reveals convincingly that a minimum wage very likely reduces the employment options open to low-skilled workers, including stripping some of them of jobs altogether. But this analysis also reveals that a minimum wage results in some other workers being paid wages higher than they’d be paid without a minimum wage. Most people today assess the first consequence as a cost and the second consequence as a benefit.Thus, the reductio wipes out an important part of the trade-off: nobody gets the pay raise. The serious work takes place in the neighborhood of where we currently are, with some people seeing pay raises and others seeing frustration. It might be that on balance, the losers from the policy might be able to bribe the potential winners into not making the change, given a sufficiently omniscient planner. That analysis, however, requires a good understanding of the supply and demand elasticities.
In a follow-up post, he notes that it's possible to raise the issue of "how high?" in a way that neither gets into the reductio nor requires understanding of elasticities. “If it’s truly good to raise the minimum wage to $15 per hour, surely it’s even better to raise it to $50 per hour! Given your assumptions about the way economies work, why not do so?!” The assumption he's assuming about his interlocutor is something along the lines of "Business owners are all, like Scrooge McDuck, swimming in money."
That, dear reader, might be why it's useful to introduce economics ab initio with trading for mutual gain, arbitrage, and opportunity cost, before introducing institutions such as business organizations.

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