Re: To put it simply....
"Wages don't go up with increased productivity: they go down, as you need less workers, and there is more offer of workers than need."
Only if you assume that output is fixed and, well, it isn't. What actually happens is each worker produces more and output increases. As I say, the simple point is that if you want to have more stuff (i.e. increase wages across an economy) you have to make more stuff.
"You have to increase the company productivity in order to be able to pay more, and that is different from paying more. Completely different."
I'm not quite sure what you mean here, but if one company doesn't keep up with the productivity increases of its competitors then it will go bust. The economy will discard it and march on.
"You just pay as little as possible, and sell for as much as you can, that is the basics of a good deal.. there is no reason to pay more if you can pay less. Not only you have no reason, but it is bad management to do so."
Yep. Absolutely right. It's competition in the labour market that drives up wages. The more investment you have, the greater the ability (through increased productivity) to pay higher salaries and the greater the competition for labour forcing you to pay higher salaries. That's the transmission mechanism.