Right, some claims don't generalize as I've indicated, but most that we actually see, do. I should have perhaps used those examples the first time around.
The most typical one is, "Raising the minimum wage, because it is the law, will mean that employees who previously made $x will make the new wage $y [rather than just be laid off or new jobs not created in anticipation of having to pay $y in the future]." It's clear that this claim -- existing in the economic models in the minds of the typical proponent, is too strong, and thus false. It is thus very appropriate to point out it's too strong by picking an arbitrarily high value for $y and showing that the economy "just doesn't work like that" -- that no law can make someone worth hiring at $y, so the typical need-based ("living wage") argument is wholly irrelevant, much to the frustration of those of us trying to have a serious exchange on the issue.
The implicit model that you gave -- in which the typical min wage worker is underpaid relative to the (appropriately discounted) marginal revenue they produce would indeed imply that raising it will not (typically) mean job loss (or forgone job creation i.e. "outsourcing" work to a new hire).
It's also an extremely unrealistic model. If it were true, that would mean any firm can steal the profits of other firms by bidding up worker income. That they don't, would imply that competition for low-skill labor is weaker than for other labor, when all evidence indicates this is the opposite of the truth.
So yes, the arguments raised by responses to this reductio reveal the weakness of the case for raising the minimum wage. I'd call that a fruitful point, not a strawman.
The most typical one is, "Raising the minimum wage, because it is the law, will mean that employees who previously made $x will make the new wage $y [rather than just be laid off or new jobs not created in anticipation of having to pay $y in the future]." It's clear that this claim -- existing in the economic models in the minds of the typical proponent, is too strong, and thus false. It is thus very appropriate to point out it's too strong by picking an arbitrarily high value for $y and showing that the economy "just doesn't work like that" -- that no law can make someone worth hiring at $y, so the typical need-based ("living wage") argument is wholly irrelevant, much to the frustration of those of us trying to have a serious exchange on the issue.
The implicit model that you gave -- in which the typical min wage worker is underpaid relative to the (appropriately discounted) marginal revenue they produce would indeed imply that raising it will not (typically) mean job loss (or forgone job creation i.e. "outsourcing" work to a new hire).
It's also an extremely unrealistic model. If it were true, that would mean any firm can steal the profits of other firms by bidding up worker income. That they don't, would imply that competition for low-skill labor is weaker than for other labor, when all evidence indicates this is the opposite of the truth.
So yes, the arguments raised by responses to this reductio reveal the weakness of the case for raising the minimum wage. I'd call that a fruitful point, not a strawman.