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 consumemore in period 1 relative to the 2nd period.(b) Hint 2: A higher consumption tax rate in period 1 Te₁ must induce the householdto 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 toconsume more in period 1 relative to the 2nd period. Let's incorporate the labor-leisure trade-off and capitalincome taxes in the two-period model. Let c₁, c₂ be consumption in two periods, I the numberof hours worked, Te Te the proportional taxes on consumption in 2 periods, s the savingrate, w the wage rate, b pension in the 2nd period, and 7, the tax on savings (capital incometax). 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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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.

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Question

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.

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