This is exactly right. I'm surprised that so many people, who are otherwise highly educated and intelligent, struggle with this concept.
There's no universal rule of "fairness" saying how much a company should pay you. It's not dictated by COL calculations and logical questions of value.
The company looks at you and your competitors (alternative candidates), and puts forward a number they think is high enough for you to accept, but not so high that they could snag an "equivalent" candidate for a lower price.
You win that battle not by whinging about COL adjustments, but by eliminating your alternatives (metaphorically speaking, of course). If the company truly needs what you do, and you're the only one who can do it, then you set the terms.
There's no universal rule of "fairness" saying how much a company should pay you. It's not dictated by COL calculations and logical questions of value.
The company looks at you and your competitors (alternative candidates), and puts forward a number they think is high enough for you to accept, but not so high that they could snag an "equivalent" candidate for a lower price.
You win that battle not by whinging about COL adjustments, but by eliminating your alternatives (metaphorically speaking, of course). If the company truly needs what you do, and you're the only one who can do it, then you set the terms.