4. Consider an individual with utility function U (C₁, C₂) = (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 find the effect of the gov- ernment intervention on the savings of the individual. Differentiate the case when the
4. Consider an individual with utility function U (C₁, C₂) = (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 find the effect of the gov- ernment intervention on the savings of the individual. Differentiate the case when the
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![=
4. Consider an individual with utility function U(C₁, C₂) (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 find the effect of the gov-
ernment 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e289a05-dba5-4c4f-9914-e3515c1b1e3d%2Fa1b6506f-fa59-4f0b-8315-d963befdadff%2Fed8map_processed.jpeg&w=3840&q=75)
Transcribed Image Text:=
4. Consider an individual with utility function U(C₁, C₂) (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 find the effect of the gov-
ernment 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.
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