handout2 - Handout 2 (Solving the two-period problem) Let...

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Unformatted text preview: 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 0 is c 0 then your consumption at t 1 is c 1 0 1 - c 0 , and your choice of c 0 is between 0 and 0 1 . Case 1: Uc 0 , c 1 c 0 1 - c 1 , 0 1 Now consuming c 0 at t 0 and c 1 0 1 - c 0 at t 1 gives you utility in the amount of fc 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: Uc 0 , c 1 ln c 0 1 - ln c 1 , 0 1 Now consuming c 0 at t 0 and c 1 0 1 - c 0 at t 1 gives you utility in the amount of fc 0 ln c 0 1 - ln 0 1 - c 0 . Here we can rule out corner solutions, so c 0 is optimal if f c 0 0, where f c 0 c 0 - 1 - 0 . 1 -c Case 3: Uc 0 , c 1 c 0 1 - c 1 , 0 1 Now consuming c 0 at t 0 and c 1 0 1 - c 0 at t 1 gives you utility in the amount of fc 0 c 0 1 - 0 1 - c 0 . Here we can rule out conrer solutions, so c 0 is optimal if f c 0 0, where f c 0 2 - c0 2 0 1 - 0 1 - c 0 . ...
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