Do lower wages in Country A necessarily imply that jobs will flow to that country?
No. Since workers cannot move to other countries, international trade has no effect on jobs whatsoever.
No. Lower wages imply lower productivity per worker. Some jobs will flow there, but not all jobs
Yes. Firms try to maximize profits and thus will always outsource to where the lowest wages are paid
Yes. Wages are arbitrary and firms will chase the lowest wages possible
