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Standard economic theory (i.e., the Heckscher-Ohlin model) provides the sharp prediction that with perfect factor mobility, gains to trade flow to the abundant factors, such as unskilled labor in developing countries. (source: a paper by economist Petia Topalova)

I am having a hard time parsing this sentence. It seems to me it should be a clause after "with perfect factor mobility". Is "gain" a noun here? And is "gains to trade" the subject of that clause? If so, why is the preposition "to" used instead of "of" or "in"? I have looked at dictionaries and found sentences that use "gain in" and "gain of" but not "gains to".

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to can express an attribute relation.

This is the key to that door.

You could paraphrase here as "gains in trade" or "gains in respect to trade".

The preposition can also express the notion of accrual.

When Microsoft closely coupled their software products to their operating system, they saw significant gains to their market share.

That is, the market share accrued unto itself significant gains, i.e. it grew.

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