I think this is only true in a closed system. In an open, globalized world like we have today, the price of the output doesn't have to go up if another place with cheaper labor can produce the same output for cheaper. Thus is many cases you end up with a situation where you can't raise the price of your output because your customers will just buy the foreign-produced version.

Unless that cost was "digestible" by the system, but had simply been previously going to C-level and board members' salaries. Then companies which continue to pay execs exorbitantly, and companies which give their execs a 0.001% pay cut or otherwise reduce inefficiencies to absorb the cost increase will compete.