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Unformatted text preview: Handout 2 (Solving the twoperiod problem) Let the twoperiod 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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 Fall '07
 MBIEKOP
 Macroeconomics

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