F. Derive the intratemporal optimality condition; that is, the consumption-leisure trade-off in period 1. (Hint: What is the MRS = MU₁-1/MUC₁?) Interpret. (a) Hint 1: A higher labor income tax rate 7 reduces consumption relative to leisure. (b) Hint 2: A higher consumption tax rate in period 1 Te, reduces consumption relative to leisure.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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F.
Derive the intratemporal optimality condition; that is, the consumption-leisure
trade-off in period 1. (Hint: What is the MRS = MU₁-1/MU?) Interpret.
(a) Hint 1: A higher labor income tax rate 7 reduces consumption relative to leisure.
(b) Hint 2: A higher consumption tax rate in period 1 Te, reduces consumption relative
to leisure.
Transcribed Image Text:F. Derive the intratemporal optimality condition; that is, the consumption-leisure trade-off in period 1. (Hint: What is the MRS = MU₁-1/MU?) Interpret. (a) Hint 1: A higher labor income tax rate 7 reduces consumption relative to leisure. (b) Hint 2: A higher consumption tax rate in period 1 Te, reduces consumption relative to leisure.
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 max₁,02,8,1-1 log(c₁) +
log (1-1)+5log (c₂) such that (1+T₁₁) C₁+s=(1-7)wl and (1+T₂)C₂ = [1+r(1-T)]s+b,
where measures how the household values leisure vis-a-vis consumption.
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 max₁,02,8,1-1 log(c₁) + log (1-1)+5log (c₂) such that (1+T₁₁) C₁+s=(1-7)wl and (1+T₂)C₂ = [1+r(1-T)]s+b, where measures how the household values leisure vis-a-vis consumption.
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