If a company chooses to outsource production to a cheaper country, what would be the external costs? I believe pollution in the new country would be, but how about the job loss in the initial country?

HI,
It's hard to do some research, without knowing the specific type(s) of job(s).
The job loss in the initial country, like America, doesn't seem to be important to large corporations or companies outsourcing jobs to other countries. They are mainly interested in profits... the bottom line.
The costs to the new country would not override the new jobs they would obtain, and the profits they would make. Otherwise, they would not take on the jobs.