Economic

(Monotonic and Convex) In the lecture 2, we considered preferences where a person only cares about the sum of the amounts of goods in the bundle, in particular bundle (x1, X2) Z ()1, y2) if and only if X1 +x2 2 /1+12 These preferences are often referred to as perfect substitutes since it is as if any amount of one good can be substituted for the other without changing welfare of the decision maker. (a) Are these preferences monotonic? (b) Are these preferences strongly monotonic? (c) Are these preferences convex? (d) Give two distinct utility representations of these preferences