E. Cerive the intertemporal optimality condition. Hint: What is the MRS = MU/MUC? (a) Hint 1: A higher capital income tax rate 7, induces the household to consume more in period 1 relative to the 2nd period. (b) Hint 2: A higher consumption tax rate in period 1 Te, must induce the household to consume less in period 1 relative to the 2nd period. (c) Hint 3: A higher consumption tax rate in period 2 Te must the household to consume more in period 1 relative to the 2nd period.
E. Cerive the intertemporal optimality condition. Hint: What is the MRS = MU/MUC? (a) Hint 1: A higher capital income tax rate 7, induces the household to consume more in period 1 relative to the 2nd period. (b) Hint 2: A higher consumption tax rate in period 1 Te, must induce the household to consume less in period 1 relative to the 2nd period. (c) Hint 3: A higher consumption tax rate in period 2 Te must the household to consume more in period 1 relative to the 2nd period.
Chapter17: Capital And Time
Section: Chapter Questions
Problem 17.1P
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Transcribed Image Text:E.
Derive the intertemporal optimality condition. Hint: What is the MRS =
MUC₂/MUC₁?
(a) Hint 1: A higher capital income tax rate 7, induces the household to consume
more in period 1 relative to the 2nd period.
(b) Hint 2: A higher consumption tax rate in period 1 Te₁ must induce the household
to consume less in period 1 relative to the 2nd period.
(c) Hint 3: A higher consumption tax rate in period 2 Te must the household to
consume more in period 1 relative to the 2nd period.
![Let's incorporate the labor-leisure trade-off and capital
income taxes in the two-period model. Let c₁, c₂ be consumption in two periods, I the number
of hours worked, Te Te the proportional taxes on consumption in 2 periods, s the saving
rate, w the wage rate, b pension in the 2nd period, and 7, the tax on savings (capital income
tax). The household's maximization problem in this case is: given by maxe₁,e2,8,1-1 log(c₁) +
log (1-1)+5log (c₂) such that (1+T₂) C₁+8 = (1-7)wl and (1+T₂)C₂ = [1+r(1-Ts)]s+b,
where measures how the household values leisure vis-a-vis consumption.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2962072d-3853-4de7-a7f9-f8e46fcd50e2%2F0daa9641-4324-4ebe-9225-f9f45a90018b%2Fcu633wp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let's incorporate the labor-leisure trade-off and capital
income taxes in the two-period model. Let c₁, c₂ be consumption in two periods, I the number
of hours worked, Te Te the proportional taxes on consumption in 2 periods, s the saving
rate, w the wage rate, b pension in the 2nd period, and 7, the tax on savings (capital income
tax). The household's maximization problem in this case is: given by maxe₁,e2,8,1-1 log(c₁) +
log (1-1)+5log (c₂) such that (1+T₂) C₁+8 = (1-7)wl and (1+T₂)C₂ = [1+r(1-Ts)]s+b,
where measures how the household values leisure vis-a-vis consumption.
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