Unrestricted immigration would reduce global income inequality. I don't judge the worth of individuals by their nationality, so it is global inequality that I must be concerned about, if income inequality is my concern.
According to the ILO (UN labour organisation) [1], in PPP dollars global average wage is 1480$ per month. So for the US equality would mean that 50% of working age people earn less than that. This is only counting wage-earners. No freelancers, children, elderly or anything like that are collected.
In the US, average wage for employed individuals is about 42000 [2]. Since there are 300 million Americans and 6.7 billion non-Americans, America should shift almost entirely to the average to get income equality. This will mean the equivalent of a 55% across-the-board pay cut for every American, provided prices do not go down. Your rent will stay the same, but your income should go down 55%.
(This is in fact happening, but is manifesting as uneven inflation without corresponding wage rises, so you'd experience an 81% rise in average prices, rent, food, restaurants, ..., while seeing your wage stay the same)
Also note that average worldwide unemployment is at least a factor of 3 higher than in the US. So it would not just take a massive pay cut, but also firing close to 20% of all workers, to bring the US into the worldwide average.
This is why socialists are (or should be) against immigration, and should be pro-isolationist. I think that if you want to improve the conditions of the American working class, that would be the correct attitude to have.
In reality the period of 1950-today has been a very exceptional period in history where not only incomes were higher, by most measures, than ever before, but income inequality was far lower than the vast majority of economic history.
I think unrestricted immigration can really disrupt the social cohesion in a country, I think this is what we're currently experiencing in Europe. Immigration also seems to put huge economic pressure on the welfare state.
I think it's better to try to help people in their own country, so their local economy is improved instead of allowing just anyone to emigrate to your own country.
> Immigration also seems to put huge economic pressure on the welfare state.
One of the ironies of income-redistribution schemes. People are happy to soak the 1% to pay for benefits for our lower/middle-classes, but if poorer people come along it's a strain, never mind that they almost certainly need it more.
As for helping people in their own country -- it is unfortunate but (barring conquest) there's only so much you can do in places ruled by kleptocrats, rife with corruption, and with only weak protections of the rule of law.