Toyota Repair: 1997 Toyota Camry caliper question, toyota camry, rear brakes

Question
I have a 97 Toyota Camry w/120k miles on it.  When the brake pedal is pressed down, the pedal has dead air for most of the throw then it engages and the brakes work pretty well.  The pads are fine and a rep. shop installed a new master cyl. and adjusted out the rear brakes but neither fixed the problem.  Another shop has suggested that the pistons or pins? are sticking in the calipers thus loading up one side and causing a piston to go all the way out before it engages hence the dead air in the pedal.  Does this make sense and how much should a shop charge for a new set of front calipers installed?  Thank you

Answer
The sliding caliper pins hanging up makes the most sense, in all the years I have worked on toyotas I have never had to replace a caliper because a piston was sticking, have them remove the caliper pins and have them cleaned and lubricated and see if that helps.