Arturo loves chocolate mousse but he is concerned about eating too much sugar. He would like to indulge himself eating as many mousses as possible as long as he keeps daily sugar consumption under 100 grams. Consider the following two choice rules: • Rule 1: After eating N mousses, if he is offered an additional mousse, he would eat it if the mousse contains less than 25 grams of sugar. If instead he is offered a fixed number of daily mousses in advance, he would accept them only if the total sugar content does not exceed 100 grams, otherwise, he would choose not to eat any mousse. • Rule 2: Choose in advance a fixed number of mousses to eat each day that does not exceed 100 grams of sugar content in total. (a) If each mousse contains 21 grams of sugar, Which rules (if any) satisfy IIA? Justify your answer. (b) Can you find a utility function that is maximized by Rule 1? How about Rule 2?
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Arturo loves chocolate mousse but he is concerned about eating too much sugar. He would like to indulge himself eating as many mousses as possible as long as he keeps daily sugar consumption under 100 grams. Consider the following two choice rules:
• Rule 1: After eating N mousses, if he is offered an additional mousse, he would eat it if the mousse contains less than 25 grams of sugar. If instead he is offered a fixed number of daily mousses in advance, he would accept them only if the total sugar content does not exceed 100 grams, otherwise, he would choose not to eat any mousse.
• Rule 2: Choose in advance a fixed number of mousses to eat each day that does not exceed 100 grams of sugar content in total.
(a) If each mousse contains 21 grams of sugar, Which rules (if any) satisfy IIA?
Justify your answer.
(b) Can you find a utility function that is maximized by Rule 1? How about Rule 2?
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