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Unformatted text preview: Problem 1: Optimal Choice in the ConsumptionSavings Model When Bor rowing is Constrained (A &Credit CrunchÂ¡): Consider a twoperiod economy (with no government and hence neither government spending nor taxation), in which the representative consumer has no control over his income. The lifetime utility function of the representative consumer is u ( c 1 ; c 2 ) = ln c 1 + ln c 2 , where ln stands for the natural logarithm. We will work here in purely real terms: suppose the consumer&s real income in period 1 is y 1 = 10 and the consumer&s real income in period 2 is y 2 = 22 . Suppose that the real interest rate between period 1 and period 2 is ten percent (i.e., r = 0 : 10 ), and also suppose the consumer begins period 1 with real net wealth (inclusive of interest) of (1 + r ) a = 2 . Set up the lifetime Lagrangian formulation of the consumer&s problem, and use it to answer parts a, b, and c. Show all steps in your logic/arguments. a. (8 points) Is it possible to numerically compute the consumer&s optimal choice of consumption in period 1? If so, compute it; if not, explain why not. b. (8 points) Is it possible to numerically compute the consumer&s optimal choice of consumption in period 2? If so, compute it; if not, explain why not. c. (6 points) Is it possible to numerically compute the consumer&s real asset position at the end of period 1? If so, compute it; if not, explain why not. 1 Intermediate Macroeconomic Analysis d. (6 points) Is it possible to numerically compute the consumer&s level of borrowing or savings (be explicit about the sign) during period 1? If so, compute it; if not, explain why not. For parts e and f of this problem, suppose that lenders to this consumer impose credit constraints on the consumer. SpeciÂ¡cally, they impose the tightest possible credit con straint Â¢the consumer is not allowed to have any debt at all at the end of period one, which means that the consumer&s real wealth at the end of period one must be nonnegative , that is, a 1 & ....
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This note was uploaded on 03/08/2011 for the course ECON 602 taught by Professor Chugh during the Spring '11 term at Johns Hopkins.
 Spring '11
 chugh

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