ec3332Sem20112012HW1Soln (1)

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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

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.

Page1 / 5

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online