Y6

Question A1 Let X be the set of alternatives available to a decision maker. a) Define a rational preference relation a. Explain why these conditions may or may not reflect the rationality of a decision maker. [10 marks] to) Suppose that X = lite, that is, the consumption set is the set of nonnegative real numbers. Consider an individual whose attitude towards the alternatives is \"the larger the better"; however. he finds it impossible to determine whether x E X is greater than y E X unless the difference is at least 1. In fact, he will assign x >1 y ifx > y +1 and x~y if Ix yl S 1. Is the indifference relation ~ transitive? If so prove this and if not provide a counterexample. [10 marks]