Definition 1: For any preference relation _ on X and any A E , max( A, ) is the set of all -maximal elements in A, that is, max( A, _) = {x E A : x _ y for all y e A\\ {x}}. Note that max(., ) is a choice correspondence on ., that is, max(., _) C A for each A E . Definition 2: For a given choice correspondence C : 2 -> X, the revealed preference relation ~* is defined by x _* y if re C(A) for some A E o with z, y E A. Definition 3: B(p, m) is the Walrasian Budget set for given m E R+ + and p E RT; that is , B(p, m) = {xER"| > pix.