Consider an individual with utility function U=(C 1 ) 3/4 (C 2 ) 1/4 who is aliv
ID: 1094661 • Letter: C
Question
Consider an individual with utility function U=(C1)3/4(C2)1/4 who is alive for two periods and has an income stream(m1, m2). At some point the government decides to intervene in the economy: in the first period the individual has to pay a fraction 0<t<1 of its income as taxes, and in the second period he receives a transfer equal to q as pension.
(a) What is the value of q that makes the present value of income the same before and after the government intervention?
(b) Use the value of q obtained in the previous question and the effect of the government intervention on the savings of the individual. Differentiate the case when the individual is initially a saver and the case when the individual is initially a borrower.
Explanation / Answer
a) suppose r denotes rate of interest
then value of q = fraction of income taken by goverment* income stream for first period*(1+r)
=m1*q*(1+r)
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b) if he was a borrower he will be borrower but if he was a saver its difficult to tell because it depends on how much he saved
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