14127_lec9_hypbo

14127_lec9_hypbo - 14.127 Behavioral Economics. Lecture 9...

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Unformatted text preview: 14.127 Behavioral Economics. Lecture 9 Xavier Gabaix April 8, 2004 1 Self Control Problems 1.1 Hyperbolic discounting Do you want a small cookie u s now ( t 0 = 0 ) or a big cookie u b later ( t 1 = 1 week)? Many people prefer ( u s , 0) to ( u b , t 1 ) Denote by ( t ) the discount factor applied to time t Then (0) u s > ( t 1 ) u b . At the same time many people prefer ( u s , t ) to ( u b , t + t 1 ) where t = 1 year, and t 1 = 1 day. ( t ) u s < ( t + t 1 ) u b . Thus, ( t + t 1 ) > u s ( t 1 ) ( t ) u b > (0) Denote ( t ) = ( t + t 1 ) ( t ) and note ( t ) > (0) ( t ) 1 t 1 = 1 ( t ) ( t + t 1 ) ( t ) t 1 1 ( t ) ( t ) Thus ( t ) is increasing. ( t ) t Let us write ( t ) = e ( s ) ds Then ( t ) = d ln ( t ) = d t ( s ) ds = ( t ) ( t ) dt dt Standard exponential model ( t ) = e s , ( s ) = Empirical evidence points to ( t ) decreasing In comparison of today and tomorrow emotions are silent, of 1000 days from now and 1001 days cognition takes over....
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14127_lec9_hypbo - 14.127 Behavioral Economics. Lecture 9...

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