Problem 5. Suppose X = R, and Joy = {B(p. m)lp = (P1, P2) > 0 and m > 0}. Suppose a choice function C : > > X satisfies WARP. Suppose that C' is strictly monotonic; that is, C(B(p, m)) # (11, 12) if there is (r), I'2) E B(p. m) such that (1,, 12) > ($1, 2). a) Suppose C(B((5, 5), 100)) = (10, 10). Then is it possible to have C(B((6, 6), 180)) = (0, 30)? b) Suppose C(B((1, 3), 60)) = (18, 14) and C(B((3, 1), 60)) = (12, 24). Determine all possible C(B((2, 2), 80) ) .Definition 2: For a given choice correspondence C : & - X, the revealed preference relation * is defined by x * y if r EC(A) for some A E & with r, y E A. Definition 3: B(p, m) is the Walrasian Budget set for given m E R+ + and p E R7 ; that is , B(p, m) = (x ER"> pixi m}