ec3332Sem20112012HW1Soln (1)

# ec3332Sem20112012HW1Soln (1) - EC3332 Money and Banking I :...

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Unformatted text preview: EC3332 Money and Banking I : Semester I, 2011-2012 National University of Singapore Assessed Homework I Submission Deadline Tuesday, 13 September 2011, 4 p.m. 1. Consider the following overlapping generations model where each generation lives for two periods. The utility function of each generation is given by u ( c 1 ,t ,c 2 ,t +1 ) = c 1- θ 1 ,t- 1 1- θ + β c 1- θ 2 ,t +1- 1 1- θ with θ 6 = 1 , < β < 1 . β is the discount factor. It can also be written as β = 1 / (1 + ρ ) where ρ > is the “rate of impatience,” so that a higher ρ or lower β indicates that the consumer is more impatient and would rather consume when young rather than postpone consumption to when old. Suppose that the endowments of each future generation is ( w 1 ,t , 0), and that there is no population growth in the economy. The consumers can save via an asset (a bond) that gives a net rate of return of r t +1 . Thus, one unit of savings yields 1 + r t +1 next period. Denote the purchase of the asset (savings) as s t . Interpretation : The parameter θ defines the “curvature” of the indifference curve. In particular, 1 /θ is the “intertemporal elasticity of substitution” which gives the percentage change of c 2 ,t +1 /c 1 ,t for a one percentage change in (1 + r t +1 ). Thus, if θ goes to 0, we have a linear indifference curve and the intermporal elasticity of substitution goes to ∞ . For θ = 1, the utility function becomes ln c 1 ,t + β ln c 2 ,t +1 . (a) Write down the period-by-period budget constraints of a consumer in future generation t . By substitution write the life-time budget constraint for the individual. (b) By maximizing utility subject to the budget constraint, derive the savings of the individual. As it will depend on w 1 ,t and r t +1 , this will be a function of these given by s ( w 1 ,t ,r t +1 ). (c) Find out how savings change as the w 1 ,t increases, i.e....
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## This note was uploaded on 01/30/2012 for the course ECON 121 taught by Professor Abi during the Spring '11 term at Abu Dhabi University.

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ec3332Sem20112012HW1Soln (1) - EC3332 Money and Banking I :...

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