No, this is incorrect. GDP is a proxy for production in nominal terms. If it were just a proxy for local price level, then every place would have the same real income and would differ solely by relative prices. That the U.S. has a a GDP/capita that is 4x times some other nation does not mean that prices are 4x lower in the other nation.
GDP is a measure of production in nominal terms. It’s a rough proxy for labor prices (the kind of price I was talking about). That’s because a dominant component of GDP is personal incomes.
It's a rough proxy of production. Even assuming constant labor shares and working hours (which are not all constant), wages are higher in A than in B because workers produce more per hour in A than they do in B, and then there is a relative price effect. But it's not all a relative price effect, it's not a proxy for the relative price effect, and for large multiples, productivity dominates relative price effects for most occupations.
When you are asking "how much would it cost to do something in B than in A", workers in B might be paid 4x more than in A, but you may also need 1/4 of the workers to do the same job. So the issue isn't wages, it's output per unit work, primarily because of accumulated human and physical capital, as well as things like infrastructure, legal system, needing to pay bribes or efficiency wages, etc.
No, this is incorrect. GDP is a proxy for production in nominal terms. If it were just a proxy for local price level, then every place would have the same real income and would differ solely by relative prices. That the U.S. has a a GDP/capita that is 4x times some other nation does not mean that prices are 4x lower in the other nation.