Economics question

1. Give an explicit example of an economy with two consumers and two commodities having each initial endowment vector equal to (1,1) such that every feasible allocation is Pareto optimal. (Assume that each consumer's consumption set is the closed first quadrant in the plane.) [35 points total] (a) To do this, you should explicitly give a utility function for each consumer. These utilities (and the underlying preferences) may be the same or different. [17 points] (b) For each consumer (if you suggested different utility functions), identify (yes or no) whether the underlying preference relation represented by the utility satisfies the following properties and explain your reasoning (which should make clear that you know and understand the definition of each property) very briefly: [18 points or 2 points each] (1) Reflexive. (2) Transitive. (3) Complete. (4) Monotone. (5) Strictly (or strongly) monotone. (6) Convex. (7) Strictly (or strongly) convex. (8) Locally nonsatiated (Ins). (9) Nonsatiated