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 up to $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 maximization with increasing marginal utility for money.

be original, and explain clearly written out plsss.