Time Inconsistent Preferences CR Self o's utility is u(c1+u(c2) CR Self 1's utility is u(1+ Bu(c2 CR Self o believes that self 1's utility l(c1)+B(c2) B≤B≤ perfect sophistica tion: B=B complete naivety:B=1  Self 0’s utility is u(c1 ) + u(c2 )  Self 1’s utility is u(c1 ) + βu(c2 )  Self 0 believes that self 1’s utility Time Inconsistent Preferences 1 ˆ complete naivety : ˆ perfect sophistica tion : 1 ˆ ( ) ˆ ( ) 1 2 = =   + β β β β β u c βu c