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While "Spell Economics" is active, you don't have to pay Life Points to activate a Spell Card (place it face-up on the field), but to activate an effect of a Spell Card, like "Archfiend's Oath", you still have to pay.
Only the controller of "Spell Economics" gets its effect.
You have to pay for "Chain Energy" even if you control "Spell Economics".
You pay the 500 Life Points to restore "Horn of Light" to your Deck even if "Spell Economics" is on the field.