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Unformatted text preview: at the end of period 2. Their lifetime utility function is U ( c 1 ; c 2 ) = u ( c 1 ) + &u ( c 2 ) ; where subscript t; t = 1 ; 2 ; denotes period t: Further suppose that u ( c 1 ) = ln ( c 1 ) and u ( c 2 ) = ln ( c 2 ) : Both Mr A and B can borrow and lend freely at a real interest rate of r . They are each endowed with 50 units of consumption goods in both the ²rst and second periods. ( i ) Show that u ( c t ) > and u 00 ( c t ) < , t = 1 ; 2 , for c t > : ( ii ) Draw the ²rst period utility function u ( c 1 ) . Does it matter that for values of c 1 from 0 to 1 that the utility function takes on negative values? Why? 1 ( iii ) Without any computation, tell me what Mr A and B &s optimal consumption and savings choices ( c & 1 ; c & 2 ; s & 1 ; s & 2 ) are. ( iv ) Explain the intuition for your result in part ( iii ) . 2...
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- Spring '11