210ahomework1_fall2011 - s represents the saving(or...

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Econ 210A: Macroeconomic Theory I Problem Set 1 University of California, San Diego - Fall 2011 Giacomo Rondina Version 1.1 RLN stands for Rody Manuelli’s Lecture Notes on Discrete Time Economies: The Growth Model (available from the class website). The solutions are due Wednesday October 5 in class. Enjoy! Exercise A Solve Exercise 16 on page 12 of RLN. Exercise B Solve Exercise 17 on page 13 of RLN. Exercise C: A Two-Period Model with Linear Utility Consider a household that is facing the following maximization problem max c y ,c o ,s c y + βc o subject to the following constraints c y + s e , c o Rs. The maximization is over ( c y ,c o ) 0 and s . The subscript y stands for “young”, and o stands for “old”. This model can be interpreted as representing the consumption/saving decision of a household over its lifetime, which, for simplicity, is divided in two periods, young and old. Assume that e 0 ; e represents the endowment the household is given at the beginning of the “young” period. The variable
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Unformatted text preview: s represents the saving (or borrowing if negative) decision of the household when young. R is the gross interest rate that is applied to the saving (or borrowing) between period young and old. (i) Write the Lagrangean associated with the household maximization problem. Make sure to specify all the constraints which the maximization is subject to. (ii) Suppose that e > . Can you apply the Kuhn-Tucker results (KT.1) and (KT.2) that we have seen in class to characterize the solution to the maximization problem? Suppose now that e = 0 . Would your answer change? 1 (iii) In answering this question assume that e > . Describe the solution to the household optimization problem as carefully as you can. In particular, make sure to consider whether the solution changes under the following cases: β − 1 < R , β − 1 = R and β − 1 > R . 2...
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210ahomework1_fall2011 - s represents the saving(or...

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