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Unformatted text preview: EC 323 Practice Questions December 7, 2009 Q1. Suppose that an agent has a complete and transitive preference over dated rewards, and moreover, in any given period prefers more to less, that is, for any t he satis&es the following moreisbettercondition (called Monotonicity ): m > m = ) ( m; t ) & ( m ; t ) : The agent also exhibits the following preferences: Receiving $100 now is as good as receiving $200 in 6 months. Receiving $80 now is as good as receiving $200 in 1 yr. Receiving $120 in 6 months is as good as receiving $200 in 1 yr. Receiving $15 now is as good as receiving $20 in 6 months. (a) Prove that this agent would prefer to get $200 sooner than later. (b) Show that this agent must exhibit a Preference Reversal. Q2. The agent has to decide whether to play or study today, and whether to play or study tomorrow. His grade on the exam day after tomorrow depends on whether the agent takes the exam, and if he takes the exam his grade depends on the number of days studied. If he plays today and tomorrow, he gets on his exam if he takes the exam, but gets q if he does not take the exam (for instance, q reects the shame attached with being a quitter). Suppose that the following information is known about preferences at time : ( p; s; 10) & ( s; s; 20) & ( s; p; 10) & ( p; p; q ) & ( p; p; 0) ; and at time 1 , if the agent consumed s yesterday then ( p; 10) & 1 ( s; 20) 1 and if he consumed p then ( p; 0) & 1 ( p; q ) & 1 ( s; 10) ; and at time 2 , if the agent consumed p in the &rst two periods, then q & 2 (a) Is the agent dynamically consistent? (b) If the agent is naive in every period, what will an observer observe him choosing over time? (c) If the agent is sophisticated in every period, what will an observer observe him choosing over time? (d) Suppose the agent is sophisticated in every period. Does he exhibit a preference for commitment?...
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