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 ψ ( t ) = ∆( t + t 1 ) ∆( t ) and note ψ ( t ) > ψ (0) • ψ ( 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 − ρ ( s ) ds • Then ∆ ′ ( t ) = d ln ∆( t ) = d − t ρ ( s ) ds = − ρ ( t ) ∆( t ) dt dt • Standard exponential model ∆( t ) = e − ρs , ρ ( s ) = ρ • Empirical evidence points to ρ ( 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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