Prepare your favorite pie crust recipe for a 10" double crust. Prepare apples; heat apple juice concentrate in saucepan and add apple slices. Cover and simmer until almost tender. Stir in cornstarch (made into a paste with a little water) or the tapioca. Add cinnamon, nutmeg and vanilla. Pour apple mixture into unbaked pie shell. Dot with butter or margarine. Cover with top crust and crimp edges. Bake 15 minutes at 450 degrees. Then lower temperature to 350 degrees and bake additional 30 minutes. NOTE: You may use 1 teaspoon instant tapioca pudding instead of cornstarch. Use undiluted frozen apple juice.