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1. Consider a household in the two-period consumption-savings model with well-behaved preferences over period-1 and -2 consumption given by u(c1, c2). Suppose that interest income in period 2 is taxed at a constant rate of 7. Assuming no initial endowment of wealth, A0 = 0, and the terminal condition A2 0, the household has the following nominal lifetime budget constraint: = Pic+ P2C2 (1+i(1 - Ti)) Y2 = Y₁ + (1+i(1 - Ti)) (a) Using indifference curve analysis, graphically locate the optimal choice (c1, c2). Label slopes and intercepts on your graph. (b) Write down the household's intertemporal optimality condition in terms of the gen- eral utility function. (c) In the United States, interest income received by households is taxed at a positive rate (i.e. > 0) while interest income paid by households is not taxed (i.e. T₁ = 0). Suppose legislators propose complete elimination of this tax. Use economic logic and your answer from part (b) to explain how this policy change would (if at all) affect the optimal level of private saving in period one for the following types of households: i. Net borrowers ii. Net savers for whom the substitution effect dominates the income effect on c₁ iii. Net savers for whom the income effect dominates the substitution effect on c₁

1. Consider a household in the two-period consumption-savings model with well-behaved preferences over period-1 and -2 consumption given by u(c1, c2). Suppose that interest income in period 2 is taxed at a constant rate of 7. Assuming no initial endowment of wealth, A0 = 0, and the terminal condition A2 0, the household has the following nominal lifetime budget constraint: = Pic+ P2C2 (1+i(1 - Ti)) Y2 = Y₁ + (1+i(1 - Ti)) (a) Using indifference curve analysis, graphically locate the optimal choice (c1, c2). Label slopes and intercepts on your graph. (b) Write down the household's intertemporal optimality condition in terms of the gen- eral utility function. (c) In the United States, interest income received by households is taxed at a positive rate (i.e. > 0) while interest income paid by households is not taxed (i.e. T₁ = 0). Suppose legislators propose complete elimination of this tax. Use economic logic and your answer from part (b) to explain how this policy change would (if at all) affect the optimal level of private saving in period one for the following types of households: i. Net borrowers ii. Net savers for whom the substitution effect dominates the income effect on c₁ iii. Net savers for whom the income effect dominates the substitution effect on c₁

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter17: Capital And Time
Section: Chapter Questions
Problem 17.2P
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1. Consider a household in the two-period consumption-savings model with well-behaved preferences over period-1 and -2 consumption given by u(c1,c2). Suppose that interest income in period 2 is taxed at a constant rate of T;. Assuming no initial endowment of wealth, Ao = 0, and the terminal condition A2 = 0, the household has the following nominal lifetime budget constraint: %3D P2c2 Y2 Pịci + = Y1 + (1+i(1 – Ti)) (1+i(1 – T;)) (a) Using indifference curve analysis, graphically locate the optimal choice (cj, cž). Label slopes and intercepts on your graph. (b) Write down the household's intertemporal optimality condition in terms of the gen- eral utility function. (c) In the United States, interest income received by households is taxed at a positive rate (i.e. T; > 0) while interest income paid by households is not taxed (i.e. Tị = 0). Suppose legislators propose complete elimination of this tax. Use economic logic and your answer from part (b) to explain how this policy change would (if at all) affect the optimal level of private saving in period one for the following types of households: i. Net borrowers ii. Net savers for whom the substitution effect dominates the income effect on c1 iii. Net savers for whom the income effect dominates the substitution effect on ci 2. Consider the general period-t nominal budget constraint from the dynamic-consumption savings model, P¿ct + A¢ = (1+ i)Aµ-1+Y;: (a) Derive an LBC for a three-period model, i.e. for t = 1,2,3, assuming a terminal condition of A3 = 0 and an initial condition of Ao = 0. (b) In the two-period model, we typically assume a terminal condition of A2 = 0. Explain why for the three-period model the terminal condition is instead A3 = 0. (c) Interpret the LBC. Does the interpretation differ from the two-period model?
Transcribed Image Text:1. Consider a household in the two-period consumption-savings model with well-behaved preferences over period-1 and -2 consumption given by u(c1,c2). Suppose that interest income in period 2 is taxed at a constant rate of T;. Assuming no initial endowment of wealth, Ao = 0, and the terminal condition A2 = 0, the household has the following nominal lifetime budget constraint: %3D P2c2 Y2 Pịci + = Y1 + (1+i(1 – Ti)) (1+i(1 – T;)) (a) Using indifference curve analysis, graphically locate the optimal choice (cj, cž). Label slopes and intercepts on your graph. (b) Write down the household's intertemporal optimality condition in terms of the gen- eral utility function. (c) In the United States, interest income received by households is taxed at a positive rate (i.e. T; > 0) while interest income paid by households is not taxed (i.e. Tị = 0). Suppose legislators propose complete elimination of this tax. Use economic logic and your answer from part (b) to explain how this policy change would (if at all) affect the optimal level of private saving in period one for the following types of households: i. Net borrowers ii. Net savers for whom the substitution effect dominates the income effect on c1 iii. Net savers for whom the income effect dominates the substitution effect on ci 2. Consider the general period-t nominal budget constraint from the dynamic-consumption savings model, P¿ct + A¢ = (1+ i)Aµ-1+Y;: (a) Derive an LBC for a three-period model, i.e. for t = 1,2,3, assuming a terminal condition of A3 = 0 and an initial condition of Ao = 0. (b) In the two-period model, we typically assume a terminal condition of A2 = 0. Explain why for the three-period model the terminal condition is instead A3 = 0. (c) Interpret the LBC. Does the interpretation differ from the two-period model?
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