Problem 3. 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, Te₂ 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)+Blog (c₂) such that (1+7₁) C₁+8 = (1-7₁)wl and (1+T₂)C2 = [1+r(1-Ts)]s+b, where measures how the household values leisure vis-a-vis consumption. A. B. Explain in English the meaning of the objective function and the 2 constraints. D. 2 What is the intertemporal budget constraint? Hint: Get s in the 2nd con- straint, plug it in the 1st constraint, and simplify. C. Rearrange the budget constraint so that terms with C₁, C2, 1-1 must be on the left-hand side. Hint: Use the fact that 1=1 (1-1). Interpret. What is the Lagrangian function (combining the objective function and the constraint you derived)?

Problem 3. 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, Te₂ 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)+Blog (c₂) such that (1+7₁) C₁+8 = (1-7₁)wl and (1+T₂)C2 = [1+r(1-Ts)]s+b, where measures how the household values leisure vis-a-vis consumption. A. B. Explain in English the meaning of the objective function and the 2 constraints. D. 2 What is the intertemporal budget constraint? Hint: Get s in the 2nd con- straint, plug it in the 1st constraint, and simplify. C. Rearrange the budget constraint so that terms with C₁, C2, 1-1 must be on the left-hand side. Hint: Use the fact that 1=1 (1-1). Interpret. What is the Lagrangian function (combining the objective function and the constraint you derived)?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter16: Labor Markets

Section: Chapter Questions

Problem 16.12P

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