2. (15 points) Consider the following lexicographic preference relation El on X = R} : X' El x if and only if x'+ '> x1 + x2, or x1 + x'a = x1 + x2 and x', > 22. (i) Verify whether El is transitive and/or complete. (ii) Let the family of budget sets B be the Walrasian budget sets B(p,w) = {x R4 : px 0, P2 > 0 and income w > 0 Find the choice rule C* generated by this lexicographic preference, that is, find the most preferred consumption plan (or demand) for every p and w. 2. (15 points) Consider the following lexicographic preference relation El on X = R} : X' El x if and only if x'+ '> x1 + x2, or x1 + x'a = x1 + x2 and x', > 22. (i) Verify whether El is transitive and/or complete. (ii) Let the family of budget sets B be the Walrasian budget sets B(p,w) = {x R4 : px 0, P2 > 0 and income w > 0 Find the choice rule C* generated by this lexicographic preference, that is, find the most preferred consumption plan (or demand) for every p and w