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Sample exchange
I got this wrong: a $0.40 tax raised the price by $0.30. Why does that tell me demand is inelastic?
Because of who absorbed the rest. The tax was $0.40 and consumers only saw $0.30 of it, so producers ate $0.10 — three quarters to consumers, one quarter to producers.
A tax lands more heavily on whichever side is less able to walk away. Consumers took most of it, so consumers were the ones who kept buying anyway. That is what inelastic demand means.
Try this one: if the price had risen by only $0.10 of the $0.40, which side would be inelastic then?