It's an unrelated topic that is more dictated by how comfortable people are with shifting demographics.
Statistically immigrants are going to be less of a burden on those items than native born citizens. Moving forward adding consumers is going to me more critical to keep the economy growing than having productive workers.
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I thought the entire premise of this is THERE ARE NO JOBS because robots are doing them all. There is high unemployment, and government is paying people a guaranteed income (along with healthcare, food, etc).
So an additional person comes to the country. THEY HAVE NO JOB. If there were work available, there is a huge oversupply of labor available already - all those displaced fossil fuel workers, those replaced by robots, and those replaced by AI.
But that additional person is a consumer, and adds to the economy you say. That is true - they do. By spending money given to them by the government since they have no job. The economy can get a better boost by having the government simply spend that money on their own.
But there are jobs, but only immigrants can do them you say. All I can think of is you are a racist, believing there is some innate skill or mental capability that one group of people has that another does not, or that there are jobs suitable for one group of people that are not suitable due to their race of the class they were born in to.
I have the opposite view - while individuals have differences, as groups they are largely the same with the same level of physical and mental abilities. There are no "classes" of people, where one "class" has to do work that another "class" does not.
If there are no jobs, adding more people does not help the economy, There are plenty of other arguments to be made to have immigration even if there are no jobs, but it is a BURDEN on the economy.
About 1.2M people immigrate legally every year. In your scenario where there is no work to do because of automation, should we increase that to 12M people every year so they can "add to the economy"?