I don't think Jeeps ever came with 3.83. depending on your motor transmission combo, you might have either 3.07, 3.54, 3.73, 4.10
as for running 31" tires again, depending on your motor transmission combo, you should not be seeing a difference in milage that much. 30" tires were factory on many 4.0 equipt vehicles.
going down in gearing would not make a noticable difference. I would consider adding some type of cold air intake, some better spark plugs, electric cooling fan and a free flowing exhaust as a means of increasing milage. Assuming you can stay out of the accelerator all the time, you should yield better milage, maybe 1 mpg increase can be expected.
one of the hugest issues to your milage will be did you lift the jeep, if so, that will contribute to poor milage (more than a tire size increase). Also remeber, a jeep is about as aerodynamic as a brick.