They can compete if the productivity of that cheap labor is "10%, or even 5%" of what it is here. It is the productivity that counts more than the hourly wage.
In some cases, American labor will not be able to compete -- in others, as shown in this article -- it can. Offshoring was a fad. It won't disappear, but there are still advantages to producing many goods in America.
At least until Obama can figure out how to erase them.
Not when the same technology and manufacturing facilities can be established in the cheap labor nation as in the nation where the technology originated.
And the advanced nations with the advanced technology and less than a billion in population are seeking the cheap labor in nations with 3 to 4 billion in population.