How are dividends determined?

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When the railroad is producing large profits, dividends are automatically declared and paid to shareholders. How large do profits have to be before dividends are paid? What determines the amount of dividends paid? Is it possible to adjust the amount (e.g. zero dividends or extraordinary large dividends)?
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Dividend Basics
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Images: João Rabelo, Andrea Piacquadio, Andrea Piacquadio, Marcus Aurelius