Cost of Mini Lift for Under the Chin ?

This is a great question and a lot of surgeons hate answering this question because there are a wide variety of surgical and nonsurgical options and combination procedures. Additionally, it really depends on which areas are bothering you specifically.  Is it just the neck? Also the jowls?The prices also vary widely depending on what part of the country you're from. The usual range is anywhere from a few thousand dollars for non-board-certified plastic surgeons to up to $50,000.
A Neck Lift in our office is $4000.  Our price includes all surgical fees, private transportation, 3 scar laser treatments after surgery, and post op massage therapies to help you heal quicker and optimally .More definitive pricing can be provided after a private consultation in our office.
I would recommend that you see a board-certified plastic surgeon in your area that is a member of both ASPS & ASAPS and performs a lot of facelifts & neck lifts but also offers all the nonsurgical options such as injectables and laser treatments. Go over your concerns with them and make sure above all, you walk out of there with several options and an idea of the pros and cons to each of them as well as realistic expectations. 
I hope this helps you. If my answer helps, please take a moment to up vote this answer on the “respond” button on the top right.  Have a great day.

"For a double chin, InMode FaceTite with VASERlipo would give you the best result.

With significant neck sagging you would need a facelift / neck lift with muscle tightening (platysmaplasty). At the same time, I would recommend lasers (Fraxel, CO2, Halo, or Erbium) and microneedling RF (Fractora, Morpheus8, PiXel8, Intensif) to improve the crepey skin and wrinkles. Overall, the neck can be treated with a combination approach:

1. Microneedling and laser treatments for texture
2. Botox, Dysport, Xeomin or Jeuveau to help platysmal bands
3. Intensif, Fractora, PiXel8, or Morpheus8 microneedling RF for crepey skin and lifting
4. Injectable fillers like Belotero, Restylane Silk, Versa, and Juvederm Volbella to improve lines and folds
5. Face/neck lifting if sagging is prominent or premature, with or without platysmaplasty (muscle tightening)
6. Renuvion (J-Plasma), ThermiRF, and InMode FaceTite/AccuTite for internal tightening
7. Ultherapy and Thermage for external tightening
8. Regular Venus Legacy, Exilis Ultra, or InMode Forma treatments with facials to maintain tightness
9. PDO NovaThreads or Silhouette InstaLift cone threads for lifting and long-term collagen production

See an expert for a formal evaluation and to develop a personalized treatment plan based on your individual situation and goals. Best, Dr. Emer"

Skin under the chin can be deceiving to many people.  Most people think they can get a mini neck lift or necklift alone for this area.  In reality, most people need a combination of a minifacelift with or without volume to address this.As we age, we lose volume in the face which causes skin to 'pool' under the chin; we also lose elasticity in the face and neck which causes the skin to sag in this area.  Depending on your age and the way you have been aging, you may need one or both to address.