Imperial Bux are used to speed up many processes throughout the game. You can get more through microtransactions and completing various affiliate actions outside the game.
What in game actions allow you to earn Imperial Bux?
What actions earn Imperial Bux
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Best Answer
Starting to build a new level.
Hiring a bitizen to work in their dream job shop.
Performing any of the "Find a Bitizen" flavor missions.
On a bitizen's birthday, you will earn a bux.