a& We claim that for some condition, TC Solution is equivalent to Precommitment Solution o Method: Evaluate marginal returns to Pf denoted by L, at R=1 with tight CIA Check ( 1 can+be sustained by+er= Pe / →L=(1-x (1-x) For the right derivative L+, i.e. Pf> pe, we have c=1/P, from Cia constraint. m has been normalized to (4) Differentiating(2)yields 1-C1-C2C1C1 Here we use the following equation dIp!/p p f dP 复9大学经学院 since we evaluate derivative at Pe= PI=P and PI P=P❖ We claim that for some condition, TC Solution is equivalent to Precommitment Solution. ❖ Method: Evaluate marginal returns to Pf , denoted by L, at R = 1 with tight CIA. Check if R = 1 can be sustained by Pf = Pe . • For the right derivative L + , i.e. Pf > Pe , we have C1 = 1/P1 from CIA constraint, M has been normalized to 1. /  ' ' ' ' 1 ' ' ' ' 2 1 2 2 2 1 1 1 2 1 2 2 2 1 1 C C C C C C C C C C C C C C C L + = + − − − + = + − ( ) ( ) (3) ' ' 1 ' ' 1 2 2 1 1 2 2 1 1 2 1         = − +          = − + C C C C C C C C C C L   (4) 1 ' 1 ' 1 1 1 2 1 1 C P C P C  −   = − − = − • Differentiating (2) yields (5) ' 1 1 ' 1 1 1 1 1 1 1 2 2 2 C C C C C C C C P C − − − − − =  Here we use the following equation: ( ) ( ) P P P P dP d P P f f f   = − − = 2 2 2 2 / 1 since we evaluate derivative at Pe = Pf = P and P1 = P2 = P