Cost for a rear differential gear swap?

Very simply I have a 2012 Ford Mustang V6 with the stock 2.73 gears and I ordered 3.73 gears and I wish to have them installed. My local auto body shop is asking $1000 for the installation + gear oil + engine retune (apparently that s needed when you jump gears like that). Is that a fair price or should I look elsewhere?

Body shop? No go to the dealer service department or a reputable local shop. It shouldn't cost more than $700 in labor.

LOL, they are trying to rip you off.

I had 3.73's put in my 03 GT for $350. I provided the ring an pinion gear set, the gear oil and install/bearing kit. I already had a hand held tuner which allowed changing of the speedometer calibration.

You don't need to tune the engine for a gear swap as the rear axle has nothing to do with the engine. What do you need the change is the speedometer calibration (which will also keep your odometer accurate)

Body shops generally aren't going to be your best bet for this kind of work. A transmission shop (not a chain) will be who you want to talk to.

Way too much - Even half of that would be a lot.