William Frazier, MD, FACS

Yes, the larger the treatment area, the more you will pay.  Most physicians will work with you to package treatments for lower cost with a percentage off when you purchase several at once.  Remember, too, that sessions are scheduled several weeks apart which gives you a little more time to spread out payments if you are paying each time you come in.  Do you have good credit? Ask whether your physician has a credit plan to spread out payments. (For instance Care Credit is offered by many physicians).
You will want to look at the overall picture--are you going to pay a small amount for 30 sessions or pay a little more for the top of the line laser treatment that will do the job in a handful of sessions?  Consider, too, there is a "cost" in travel time, healing or "down" time, and time that you must take out of your schedule for appointments.  
The great thing about treatment with a PicoSure laser is that the laser pulses are so strong that they break up tattoo ink incredibly faster than older technology.   With Pico, we are seeing tattoo removal in a handful of sessions as compared to the 20-30 sessions that removal used to take.  
When considering price, too, you might want to consider booking with a physician trained to care for skin and pain control.     People want as little pain as possible.  That's why the Picosure laser is really neat because each treatment generally takes just minutes.   At our office,  we inject local anesthetic and use ice packs after most treatments to lessen post-treatment pain and swelling.  Be sure to ask your physician or consultation specialist all the questions you have about how they care for the area after treatment.
Finally, one last note: you mentioned your half sleeve tattoo.  To lessen swelling, we generally recommend doing only a portion of the "sleeve" at each session, but since yours is black a Picosure laser should knock it out in 4-6 sessions for each area.    

Like many plastic surgeons, our practice charges for the PicoSure laser treatments--one of the newest lasers in the medical field today-- based on square inch size. Many physicians give discounts based on number of treatments or special discounts such as to military recruits so be sure to ask about any packages or specials.
 
You should consider the overall picture when looking at your best options for removal costs.  Many tattoo removal lasers using older technology may require a large amount of treatments spaced over a large period of time.  Be sure to ask about the average time for clearance.  With PicoSure, four to six treatments are average spaced about four to six weeks apart.