ps5_101_2011 - Economics 101 Problem Set 5 Due Tuesday...

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Economics 101 Problem Set 5 Due Tuesday, March 1, 2011 George J. Mailath Please indicate your recitation time/number and recitation instructor on your answer. 1. Suppose Sheila receives an income stream of income ( I 0 ,I 1 ) over two periods. Her preferences over consumption in the two periods are described by the utility function U ( c 0 ,c 1 ) = log c 0 + 1 (1 + γ ) log c 1 . (a) Suppose Sheila can borrow and lend at the same interest rate r . Derive her demand functions for period-0 and period-1 consump- tion. (b) Suppose that financial transactions are subject to a financial ser- vices tax, τ , so that if Sheila saves x , she receives x (1+ r (1 τ )) in period 1, while borrowing x for period-0 consumption, requires her to repay x (1 + r (1 + τ )) in period 1. i. What is her budget constraint? Illustrate in a diagram. ii. Derive her demand functions period-0 and period-1 consump- tion. 2. Suppose Bruce is a wheat farmer who consumes wheat in periods 0 and 1. At the beginning of period 0, has W bushels of wheat, and
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