Yes, but also don't need maths to know that competition can be controlled with 20 ways (and usually is, e.g. US ISPs), or that you can have tariffs AND internal competition.
Or even that you can have a fine quality product at a good price even without competition at all -- e.g. produced by a single vendor, as long as the vendor is so inclined.
If competition is controlled then there's less competition and one can expect efficiency to drop down ceteris paribus. Now you have to explain why controlling competition could lead into better quality or cheaper prices. (The only thing I see is that it could let governments keep more money, thus more power ?)
fine quality product at a good price even without competition at all
Threat of competition is also a form of competition (for example a software product not protected with patents, anyone could compete so the producer offers good prices)
The US is really big, if there's not a mis-configured regulation, adding overseas competition won't really increase efficiency as the perfectly sperical market in a vacuum equation suggests.
Maths have nothing to do with economics. I said efficiency as a way of comparing market offer from the point of view of customers (you can picture the formula "quality/price" if you want but that doesn't mean that it is objectively & mathematically defined), meaning that prices go down and/or quality increases
mis-configured regulation
Do you have examples of good protectionist regulation ?
And no I gave a specific example with software patents so even if the US is big enough it can benefits from outside products
If we're talking about efficiency from the customer point of view, I can pay full price for American goods on Amazon but receive garbage-cheap Chinese knock-offs in the mail.
I don't even understand what you are trying to prove. That some sellers are not trust worthy ? That there will always be an intermediary taking the profit ?
Or even that you can have a fine quality product at a good price even without competition at all -- e.g. produced by a single vendor, as long as the vendor is so inclined.