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Lumifer comments on Political Debiasing and the Political Bias Test - Less Wrong Discussion
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Never mind resource constraints. Suppose a billion plumbers move to the US. By your and by "economists'" reasoning, this will not drive down the price of hiring a plumber at all, since although competition will reduce the price, the economy is not fixed, and more plumber jobs will be available, compensating for this.
Furthermore, if adding more people doesn't reduce the number of or the pay for jobs, then it necessarily follows that removing people shouldn't increase the number of or the pay for jobs. Do you seriously believe that if half the plumbers dropped dead, the price of hiring a plumber wouldn't go up, and the remaining plumbers wouldn't find it easier to get jobs?
I think the two words missing in this discussion are "short-term" and "long-term".
The question about immigration specifies that immigrants arrive each year, not that there is a one time influx of immigrants that ends. So it's a continuous stream of short-term effects. The long term equilibrium that happens once society adjusts to the immigrants is never reached because there are always new immigrants to which society hasn't adjusted yet.
There's an important difference between effects caused by a surprising change (sudden influx) and the results at equilibrium (ongoing expected rate). The long run is just the sum of the short runs, but the some of those short runs include reactions to previous short runs and expectations of future short runs.
Perhaps "immediate reaction to a change" and "equilibrium" are better terms than "short-term" and "long-term".
In the equilibrium / long-term, there are very few plumbers who remain solely plumbers throughout their lives. Many will switch roles according to demand and aptitude. So the question isn't about influx of plumbers, but of humans who can change and adapt.
If you're continually adding plumbers at a constant rate, you will get an equilibrium. But the equilibrium you get will be different from the one you'll get if you had a one-time influx of plumbers and the market compensated for that. You'll get an equilibrium where the influx of plumbers continually drives the prices down and the compensating factors continually drive the price back up. Exactly where this equilibrium falls will depend on the relative rates of each part, and it may, in fact, be a net downwards effect.