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f09_midterm_ans - Graduate Macroeconomics I Midterm Prof...

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Graduate Macroeconomics I: Midterm Prof. Vollrath Answer Key Problem 1 : β (1 + r ) = 1, so people want c 0 = c 1 , assuming they are not liquidity constrained. A) Type A people have a budget constraint of c A 0 + c A 1 4 / 3 = 4 + 4 4 / 3 = 7 . (1) If unconstrained, then c A 0 = c A 1 , and this would mean c A 0 = 4. As they have 4 in the initial period, this is feasible and so they will consume c A 0 = 4. Therefore s A 0 = 0. B) Type B people have a budget constraint of c B 0 + c B 1 4 / 3 = 1 + 3 4 / 3 = 13 / 4 . (2) If unconstrained, they would choose c B 0 = 13 / 7. But this is greater than first period income (1), so it is not feasible with the liquidity constraint. Therefore c B 0 = 1 and s B 0 = 0. C) Lifetime income is unchanged, meaning that type A people still have 7 and type B people still have 13/4 in resources to spread across the two periods of their life. β (1 + r ) is the same, so people still want consumption to be equal in the two periods. Type A people, because nothing relevant has changed, will consume c A 0 = 4 again, but now will have s A 0 = 5 - 4 = 1, as they save the extra dollar for the second period.
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