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A consumer’s income in the current period is y1= 170 and income in the future period is y2 = 150. He pays lump-sum taxes t1 = 20 in the current period and t2 = 7 in the future period. The real interest rate is 10% every period.Suppose that current and future consumption are perfect complements for the consumer and he wants to have equal consumption in the current and future periods. Determine the consumer’s optimal consumption bundle (C1, C2). Is he a saver or a borrower?

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Chika Ilonah
Chika IlonahLv10
28 Sep 2019

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Related questions

A consumer's income in the current period is y1= 170 and income in the future period is y2 = 150. He pays lump-sum taxes t1 = 20 in the current period and t2 = 7 in the future period. The real interest rate is 10% every period. Suppose that current and future consumption are perfect complements for the consumer and he wants to have equal consumption in the current and future periods. Determine the consumer's optimal consumption bundle (C1, C2). 

1. State the Lifetime Government Budget Constraint

2. Write the Consumers Lifetime BC in real terms with a lump sum tax “t”

3. Combine BC’s from 1.) and 2.) to form the economy wide BC using the common taxes.

4. Suppose Government holds spending fixed but decides to decrease t1. a. Explain what happens to t2 b. Show what happens to the overall changes in taxes by expressing the change in t2 as a function of the change in t2 c. Consumer has full knowledge of the economy. What does the consumer do with the period 1 tax break? Explain why? d. What is the overall effect on national savings and why?

5. Write the Consumer’s LBC with a consumption tax “tau” in each period. 6. Solve to express the LBC with c2 as a function of c1 in order to graph it. 7. Suppose first period taxes decrease a. What happens to the slope of the BC? b. What occurs with optimal c1 and c2 and why? c. What occurs with national savings? i. Is there a shift and if so, which direction? ii. Graphically show the change in the funds market iii. What happens to the optimal investment choice of firm and why

(Exercise 3.3, Capital controls, optional) Consider a two-period model of a small open economy with a single good each period and no investment. Let preferences of the representative household be described by the utility function U(C1, C2) = √(C_1 ) + √(C_2 ) The parameter  is known as the subjective discount factor. It measures the consumer’s degree of impatience in the sense that the smaller is , the higher is the weight the consumer assigns to present consumption relative to future consumption. Assume that  = 1/1.1. The representative household has initial net foreign wealth of (1 + r0) B_0^* = 1, with r0 = 0.1, and is endowed with Q1 = 5 units of goods in period 1 and Q2 = 10 units in period 2. The world interest rate paid on assets held from period 1 to period 2, r* = 10% (i.e., r* = 0.1) and there is free international capital mobility. Calculate the equilibrium levels of consumption in period 1, C1, consumption in period 2, C2, the trade balance in period 1, TB1, and the current account balance in period 1, CA1. Suppose now that the government imposes capital controls that require that the country’s net foreign asset position at the end of period 1 be nonnegative (B_1^* ≥ 0). Compute the equilibrium value of the domestic interest rate, r1, consumption in periods 1 and 2, and the trade and current account balances in period 1. Evaluate the effect of capital controls on welfare. Specifically, find the level of utility under capital controls and compare it to the level of utility obtained under free capital mobility. For this question and the next, suppose that the country experiences a temporary increase in the endowment of period 1 to Q1 = 9, with period 2 endowment unchanged. Calculate the effect of this output shock on C1, C2, TB1, CA1, and r1 in the case that capital is freely mobile across countries. Finally, suppose that the capital controls described in part (b) are in place. Will they still be binding (i.e., affect household behavior)?

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