Baloth Cage Trap
Instant — Trap
If an opponent had an artifact enter the battlefield under their control this turn, you may pay 
rather than pay this spell's mana cost.
Create a 4/4 green Beast creature token.
Austin Hsu
Modern Masters 2017 (MM3)
• #120Rulings
You may ignore a Trap’s alternative cost condition and simply cast it for its normal mana cost. This is true even if its alternative cost condition has been met.
(wotc • 2009-10-01)
Casting a Trap by paying its alternative cost doesn’t change its mana cost or mana value. The only difference is the cost you actually pay.
(wotc • 2009-10-01)
Effects that increase or reduce the cost to cast a Trap will apply to whichever cost you chose to pay.
(wotc • 2009-10-01)
Rulings
You may ignore a Trap’s alternative cost condition and simply cast it for its normal mana cost. This is true even if its alternative cost condition has been met.
(wotc • 2009-10-01)
Casting a Trap by paying its alternative cost doesn’t change its mana cost or mana value. The only difference is the cost you actually pay.
(wotc • 2009-10-01)
Effects that increase or reduce the cost to cast a Trap will apply to whichever cost you chose to pay.
(wotc • 2009-10-01)