2. Bart lives for two periods: young and old. He can supply labor when he's young, earning $1 per hour. His utility function is given by u (C₁, 11, C₂) = log c₁01+3 log c₂ where c is consumption at period t, l₁ is the labor supplied, 3 = ₁1 € (0,1) is the time discount factor, and p is time preference. There is an asset market that individuals can save and borrow at interest rate (1 + r). (a) Solve for the optimization problem (ci, c₂, 4) of Bart. (b) Suppose that the government imposes capital and labor income taxes, TK and TL. Define the life-time budget constraint of Bart with taxes. (c) Solve for the optimization problem with taxes. Does your answer differ from part (a)? Explain.
2. Bart lives for two periods: young and old. He can supply labor when he's young, earning $1 per hour. His utility function is given by u (C₁, 11, C₂) = log c₁01+3 log c₂ where c is consumption at period t, l₁ is the labor supplied, 3 = ₁1 € (0,1) is the time discount factor, and p is time preference. There is an asset market that individuals can save and borrow at interest rate (1 + r). (a) Solve for the optimization problem (ci, c₂, 4) of Bart. (b) Suppose that the government imposes capital and labor income taxes, TK and TL. Define the life-time budget constraint of Bart with taxes. (c) Solve for the optimization problem with taxes. Does your answer differ from part (a)? Explain.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
![2. Bart lives for two periods: young and old. He can supply labor when he's young, earning $1 per hour.
His utility function is given by
u (c1,l1, c2) = log c1 – 0l7 + B log c2
where c is consumption at period t, 1 is the labor supplied, ß = , € (0,1) is the time discount
factor, and p is time preference. There is an asset market that individuals can save and borrow at
interest rate (1+r).
(a) Solve for the optimization problem (cj, cž, l4) of Bart.
(b) Suppose that the government imposes capital and labor income taxes, TK and TL. Define the
life-time budget constraint of Bart with taxes.
(c) Solve for the optimization problem with taxes. Does your answer differ from part (a)? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febf6118f-5341-447a-a50d-9a02b2f4de8f%2Ff79c730d-a0bf-4975-8f13-82c7c11d4201%2Fqgkpnb_processed.png&w=3840&q=75)
Transcribed Image Text:2. Bart lives for two periods: young and old. He can supply labor when he's young, earning $1 per hour.
His utility function is given by
u (c1,l1, c2) = log c1 – 0l7 + B log c2
where c is consumption at period t, 1 is the labor supplied, ß = , € (0,1) is the time discount
factor, and p is time preference. There is an asset market that individuals can save and borrow at
interest rate (1+r).
(a) Solve for the optimization problem (cj, cž, l4) of Bart.
(b) Suppose that the government imposes capital and labor income taxes, TK and TL. Define the
life-time budget constraint of Bart with taxes.
(c) Solve for the optimization problem with taxes. Does your answer differ from part (a)? Explain.
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