Hmm, I'll check out why the 2nd arrow doesn't show up, even if a Department from the 2nd page is unlocked.
The first 3 Departments have a hidden 2nd effect: they increase your Favor, Gift/ and/or Blessing gain by 0.0001% of their revenue (you can check the current revenue by going to Settings -> UI Settings -> Number Notation -> Income per Tick.
So if the production revenue is 1M, your Favor, Gift and/or Blessing Gain doubles.
I really need to put this somewhere, not even the manual mentions it :D