Just Qustions 3-5 only!!! 0. What is the optimal level of consumption in each period? Answer this...

Just Qustions 3-5 only！！！

0. What is the optimal level of consumption in each period? Answer this q" src="https://files.transtutors.com/cdn/qimg/f1ddb77cb72c4b7dbdbb108162a9582e.jpg" aria-describedby="eqf">

Question 3. (4 points each) Consider sophisticated Robinson's two-period consumption decision problem. The notations of variables are the same as the slides for Chapter 4. His life time utility is given by U(C1,C2) = InC1 + InC2 Here we are assuming discount rate B=1. Budget constraints are given by C1 + B = Y- Ti C2 = Y2 – T2 + B in period 1 and 2 respectively. So, we are assuming interest rate is zero (r = 0). T1, and T2 are lump-sum taxes in period 1 and period 2 respectively. (1) Derive the intertemporal budget constraint for Robinson (Hint: Combine two budget constraints to eliminate B.). Provide the interpretation of the intertemporal budget constraint. (2) Solve the utility maximization problem and derive the optimal level of consumption in each period, G and C2 (i.e. Express C and C2 in terms of Y , Y2,71, and T2.). (3) Now suppose Robinson cannot borrow. Namely, B > 0. What is the optimal level of consumption in each period? Answer this question in each of the following two cases. (i) Y, – T1 > Y2-T2 (i.e. his disposable income is larger in period 1) (ii) Y - T < Y2 – T2 (i.e. his disposable income is smaller in period 1) Provide intuition for your answer. (Hint: With the optimal level of consumption you find in question (2), what is the implied borrowing B? Does it satisfy the borrowing constraint B > 0? If not, what is the best for Robinson to do? Is it optimal to set B = 0, namely consuming everything you have in period 1?) (4) Robinson still cannot borrow. Suppose the government plans to cut the lump-sum tax in period 1 by increasing the lump-sum tax in period 2, keeping the present value of lump-sum tax constant (i.e. T1 goes down while T2 goes up by the same amount so there is no change in T1 + T2.). What is the effect of this policy on the optimal level of consumption? Again, answer this question in each of the following two cases. (i) YZ - T, 2 Y2-T2 (ii) Y1 – T2 Consumption and Saving • Ricardian equivalence proposition • If future income loss exactly offsets current income gain, no change in consumption/saving G2- T 12 -=Ti + 1+r G1 + 1 + r . 1 + r + r Gz = 1+8 (vi+ 1 er -1,-177) Sz = Yų – C1 – G1 • Tax change affects only the timing of taxes