For new hires I suppose it's okay but to adjust the pay of an existing worker whose output remains the same afterwards because they relocated is a bit insulting to me. It's a pay cut, not a "COLA".
This is irrelevant, though. You aren't paid based on your output, you're paid based on how much you cost.
Think of how much you pay for water. In place A, you might pay $0.02 per gallon of water. You move to place B, and they only charge $0.01 gallon of water. Are you going to keep paying $0.02/gallon? The value that the water provides to you hasn't changed, but why would you keep paying $0.02 when you could get it for $0.01?
In FB's view, you aren't any different. Even if you provide the same value, there's no reason to keep paying you $300k when they could pay you (or someone who replaces you) $150k.
My experience with these kind of dislocations is that your HR department starts tracking your target number internally based on your new circumstances and you don't see any pay rises until that number exceeds your actual.
