handout2 - 1 − c Here we can rule out corner solutions so...

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Handout 2 (Solving the two-period problem) Let the two-period constraint be in the form of c 0 c 1 / 0 1 . Now if your consumption at t 0is c 0 then your consumption at t 1is c 1 0 1 c 0 , and your choice of c 0 is between 0 and 1 . Case 1: U c 0 , c 1 c 0 1 c 1 ,0 1 Now consuming c 0 at t 0and c 1 0 1 c 0 at t 1 gives you utility in the amount of f c 0 c 0 1 0 1 c 0 1 0 c 0 1 0 1 . If 1 0 0, what is optimal ( c 0 , c 1 ? (Hint: corner solution) If 1 0 0, what is optimal ( c 0 , c 1 ? (Hint: corner solution) If 1 0 0, what is optimal ( c 0 , c 1 ? (Hint: corner solution and something else) Case 2: U c 0 , c 1 ln c 0 1 ln c 1 ,0 1 Now consuming c 0 at t 0and c 1 0 1 c 0 at t 1 gives you utility in the amount of f c 0 ln c 0 1 ln 0 
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Unformatted text preview: 1 − c . Here we can rule out corner solutions, so c is optimal if f ′ c 0, where f ′ c c − 1 − 1 − c . Case 3: U c , c 1 c 1 − c 1 , 0 1 Now consuming c at t 0 and c 1 1 − c at t 1 gives you utility in the amount of f c c 1 − 1 − c . Here we can rule out conrer solutions, so c is optimal if f ′ c 0, where f ′ c 2 c − 1 − 2 1 − c ....
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