Most Cost-effective Procedure for Drooping Mouth Corners?

Dear Droopy
You should be much more concerned about what is right rather than what is cost-effective. Yes, fillers can be fantastic ,but the costs do add up. At your age, it probably makes sense to consider a facelift.
Ultimately, I find that some patients are really not so excited about having surgery. In the long run it is probably more cost effective to have surgery and then use fillers to correct what can't be fixed with surgery. However, it is possible to have great improvement just with fillers.
The dilemma you will have is that most surgeons who offer facelifts, are not enthusiastic users of fillers. Also in the short term, there is more money in performing surgery than in performing fillers. So you have to be careful of economic bias on the part of your consultant.
I would recommend that you seek multiple opinions and in particular, consider seeing a cosmetic dermatologist regarding their take on fillers. You might look on the liquidfacelift.com website for the name of a highly qualified physician who performs these services in your area.
Ultimately do what your are comfortable with and recognized that all of there options are expensive and there are no absolute best ways to approach this.

Droopy mouth corners can be reflective of two different issues.  Sometimes, the muscles that allow us to make a sad frown are too strong, and they can then be weakened with Botox to quickly correct the problem.  Other times – or in conjunction – there can be laxity of the skin that causes what are known as “marionette lines.” For these, filler can be placed in the valley of these lines to plump them up.  In extreme cases, most often seen in patients in their late 40s and onwards, a facelift might be necessary. Many factors can determine the procedure that’s right for you, which is why it’s important to meet with a board certified plastic surgeon who is capable of both surgical and injectable solutions so he or she can properly assess, educate, and direct you.  

Each patient's anatomy is unique. The marionette lines that run from the corner of the mouth down to the jaw line can be improved with a facelift procedure or augmentation of the marionette line with filler injections or other tissue transfer. In a younger patient with a downturned corner of the mouth, a small amount of Botox injected by an expert injector can help to lift the corners of the mouth slightly.
A facial plastic surgeon or plastic surgeon should be able to assess and offer formal recommendations during a consultation.
All the best,