Maria has (beta, delta)-preferences: U^T (u_1, u_2,...,u_T) = u_1 +beta sigma_t=
ID: 1210357 • Letter: M
Question
Maria has (beta, delta)-preferences: U^T (u_1, u_2,...,u_T) = u_1 +beta sigma_t=2,...,T delta^t-1 u_t, as discussed in class. She likes movies. This weekend she has time to go once. Her options and their values are as indicated in this table: Suppose beta = 1/2, delta = 1, and that Maria is sophristicated (i.e, at any time she understands how her preferences may change in the future). When will she go? Friday Saturday Sunday She randomizes uniformly between her three options She'll go on Friday with probability 5/22, on Saturday with probability 3/11, and on Sunday with probability 1/2.Explanation / Answer
E She'ill go on friday with prob. 5/22 on friday
AS Maria is sophisticated, So ˆ =
When t = 1,She prefers movie on friday than on saturday and sunday
2: c + 1 2 · 0 > 0 + 1 2 ( 3 2 c) She also prefers moovie on sunday than on saturday: 0 + 1 2 (0 + 3 2 c) > 0 + 1 2 (c + 0) However, when t = 2, her preference reverses, and She prefers on saturday than on sunday: c + 1 2 · 0 > 0 + 1 2 ( 3 2 c)
Time-inconsistency: Maria is willing to delay gratification in the future, but not today. So when the moment arrives, he changes her decision
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