Inter-temporal preferences Several periods model For period T-2, when we got (C-2, x-2)then T-2T-2 DR So VI-2(Wr-2)=max u(C-2)+SEVT-WT-2-CT-R CT-2 T-2 The first order condition u(C -2)+SEV(W-R=0 E(w1)(R1-R0)=0Inter-temporal preferences • Several periods model: – For period T-2, when we got then – So – The first order condition: 1 2 2 ( ) w w c R T T T − − − = − 2 2 ( , ) T T c x − − 2 2 2 2 2 1 2 2 , ( ) max ( ) ( ) T T T T T T T T c x V w u c EV w c R  − − − − − − − − = + − 2 1 1 1 0 ( ) ( ) 0 ( )( ) 0 T T T u c EV w R EV w R R  − − −   + =   − =