The problem SET IS ABSOLUTELY CLEAR. IF YOU CANNOT DO THE QUESTION, LET ME KNOW

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The Problem Set Is Absolutely Clear If You Cannot Do The Question Let Me Know 1 (138.69 KiB) Viewed 71 times

1. (CRRA utility, CRRA properties, taxation effects) A representative household (HH) lives for 2 periods. Its assets discounted for the first period are 1. The market real interest rate is r and the household discounts the future at p. The one- period (instantaneous) HH utility function is U(c) = (note that this function belongs to the Constant Relative Risk Aversion [CRRA] class). c1-6 1-6 a. Find (either using the Lagrange method or with substitution) the optimal distribution of consumption over time. Under what condition is the consumption profile rising/falling? b. What happens to the distribution of consumption when r = p? c. (*) Assume that yı = 1, i.e. HH gets all its income in period 1, and from now on HH only consumes. Calculate the amount of savings in the period 1 and examine under what conditions it increases (decreases) relative to r. Discuss the result in the context of smoothing consumption over time and the relative importance of the income and substitution effects. d. Assume N = 1000, r = 0.1, p = 0.05,0 = 2. What is the distribution of consumption over time? Does consumption in both periods adds up to 1000? e. How will the consumption distribution change over time if 0 = 1/2? Compare the results with d). f. What happens to the distribution of consumption after introducing into this economy lump-sum taxes HH on income and balancing its budget in each period (when T2 = G1 = 200 and T2 = G2 = 100)? What happens to the HH utility (discuss the directions)? g. How does 2 change and what happens to the distribution of consumption across time when the government decides to increase its expenses (both the government and HH borrow at r) in period 1 and reduce expenditure in period 2 by y, so that this operation does not change the present discounted value of the government budget (i.e. increasing G7 by x while decreasing G2, so that y = x). 1+r