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But in general, the answer to this question depends on the airline which you are traveling with. Most airlines will not refund you if the fare goes down on your ticket. However, many times if you contact the airline or booking agent and advise them the fare decreased and express your frustration, they will either offer you a refund or travel voucher. They might even just offer to waive your baggage fees.
If they do not offer a refund and the fare went down substantially you can check to see if you have a refundable ticket. If you have a refundable ticket you can just cancel your current ticket and rebook the lower fare. Please keep in mind that most airlines charge a cancellation fee so the savings could exceed the cancellation fee.