So, first of all, that’s an economics formula: they tend to be extreme simplifications to demonstrate a relationship between variables. Of course, that means they’re often wrong or useless. Sort of like if all physics formulas were “cow diameter=(food-waste)/2” or “car velocity=gas pedal depth-brake pedal depth.” Sometimes economists jokingly call it the “dismal science”; what they don’t mention is that the term came from a paper arguing that slavery was superior to abolition - an argument made with many of the same reasoning errors, oversimplifications and lack of perspective that clouds modern economics. Our modern sciences are not quite as evolved as we would like to believe.

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Now, to your question: this is an oversimplification, but most money that’s not in a mattress somewhere is being lent out (invested.) If I have $500 in a bank account, my bank will turn around and lend my $500 to Bob’s Construction Corp or to Mary for a car loan or whatever. In practice things are a lot more complex, but the portion of money that’s sitting still in a mattress or a vault is fairly small. This means that if I get a dividend, money is moved from one bank account to the next, and the amount of investment doesn’t change.

To explain the sibling that came in accounting jargon, money by its very nature only exists by lending. You can't have your number on your savings account if it wasn't lent to somebody first.

I also did not understand this. It seems that “consumption” has different meanings on either side of the equals sign.

Every liability is an asset on another ledger.