this is for question 1

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. [1? 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: [13 points or 2 points each] {1} Reflexive. (2] Transitive. [3] Complete. (4] Monotone. (51 Strictly (or strongly) monotone. (6] Convex. [7] Strictly [or strongly) convex. (8] Locally nonsatiated {Ins}. (9} Nonsatiated