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Q1. (Behavioral Distinctions) One would hope that two agents with different psychology can always be distinguished through their behavior. While they sometimes can, it is not always the case. This question explores this. (a) Suppose that an agent is offered money: she can choose any dollar amount upto $M. We see that she chooses C({0, 1, ..., M}) = {M}. Show by example that this choice can be explain equally well by (i) utility maximization with diminishing marginal utility for money, and (ii) utility max- imization with increasing marginal utility for money. (b) Consider an agent who has to choose how many donuts to eat. He exhibits the choices C((1, 2}) = {1, 2} and C({1, 2, 3}) = {2,3}. Can these choices be explained by (i) maximization of a complete and transitive preference? (ii) satisficing? (iii) regret aversion? (c) Suppose now that the donut-eating agent exhibits the following choices: C({1, 2}) = {1} and C({1, 2,3}) = {2}