101A_lec12 - Economics 101A(Lecture 12 Stefano DellaVigna...

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Unformatted text preview: Economics 101A (Lecture 12) Stefano DellaVigna March 3, 2009 Outline 1. Time Consistency 2. Time Inconsistency 3. Health Club Attendance 1 Time consistency • Intertemporal choice • Three periods, t = 0 , t = 1 , and t = 2 • At each period i , agents: — have income M i = M i + savings/debts from pre- vious period — choose consumption c i ; — can save/borrow M i − c i — no borrowing in last period: at t = 2 M 2 = c 2 • Utility function at t = 0 u ( c , c 1 , c 2 ) = U ( c )+ 1 1 + δ U ( c 1 )+ 1 (1 + δ ) 2 U ( c 2 ) • Utility function at t = 1 u ( c 1 , c 2 ) = U ( c 1 ) + 1 1 + δ U ( c 2 ) • Utility function at t = 2 u ( c 2 ) = U ( c 2 ) • U > , U 00 < • Question: Do preferences of agent in period 0 agree with preferences of agent in period 1? • Period 1 . • Budget constraint at t = 1 : c 1 + 1 1 + r c 2 ≤ M 1 + 1 1 + r M 2 • Maximization problem: max U ( c 1 ) + 1 1 + δ U ( c 2 ) s.t. c 1 + 1 1 + r c 2 ≤ M 1 + 1 1 + r M 2 • First order conditions: • Ratio of f.o.c.s: U ( c 1 ) U ( c 2 ) = 1 + r 1 + δ •...
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This note was uploaded on 09/05/2009 for the course ECON 101a taught by Professor Staff during the Spring '08 term at Berkeley.

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101A_lec12 - Economics 101A(Lecture 12 Stefano DellaVigna...

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