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How the three economists model government services is to imagine that extra users impose congestion costs, so that the more users there are the less satisfactory is service delivery. But even under that seemingly unobjectionable assumption completely unrestricted immigration can be optimal. If your fiscal system lets you distinguish between immigrants and non-immigrants, you can charge immigrants for the extra costs they impose on people already here. In that case, immigration will be self-limiting. If its cost to society really is high, the immigration charge will be high, too, and immigrants won’t come.

If you can’t levy separate taxes on immigrants, however, you may have to re-think open immigration. Key to your updated considerations will be how immigrants affect the labour market. If you’ve got two kinds of workers — higher-skilled and therefore higher-paid and lower-skilled and therefore lower-paid — you may have to control immigration by skill class. If you’re particularly interested in the well-being of lower-paid people, you will want to restrict the immigration of such people. Flooding the domestic market for them will drive down their wages, which defeats your goal of making them better off (and may elect a Trump, though the authors don’t mention that).

If part of your concern for the well-being of the bottom earners expresses itself in redistribution, you may want to encourage immigration by higher-skilled immigrants, since they can pay the taxes that make such redistribution possible. But you’ve got to be careful about the extent of redistribution. Raise your top-end taxes too much and you won’t get any immigration. As the three economists say: “This scenario resembles the experience of the Scandinavian countries. Despite having liberal immigration policies for high-skill workers, the heavy taxes levied on both native and foreign high-skill workers results in very little high-skill immigration to these countries.” There’s also the dilemma of whether you want to be luring high-skilled people from poor countries.

Now, models aren’t always right, economics isn’t everything and doubtless some people who are anti-immigrant really are racists. But deciding the optimal level of immigration isn’t — or at least shouldn’t be — a “you’re evil, look how morally superior I am” kind of argument. There’s plenty of room for disagreement that is civil and respectful, which is exactly what people who say they want to be open and welcoming should favour.