Question 1: Savings Tax (35 points) We consider the effect of a tax on savings on the intertemporal consumption decision of households. Households maximize their lifetime utility: u(C) + Bu(C) (1) where C and C are current and future consumption and B is the discount rate. They face a standard budget constraint in the first period: C+A = A+Y (2) where Y is current income, A is wealth and A is the amount of resources that households wish to save for the next period. Assume that the government imposes a tax t on savings so that the second period budget constraint is: Of = (1-t) (1 +r)A/ + y (3) (a) [10 pts] Substitute the intertemporal budget constraint into the utility function and derive the first order condition of the utility maximization problem. (b) [5 pts] How does your expression differ from the Euler equation discussed in the lecture notes? How should we interpret the new equation? (c) [10 pts] Describe intuitively how an increase in the savings-tax t affects consumption and savings decision of households using the concepts of income and substitution effects. [No derivation required]. (d) [10 pts] Households are not subject to the savings tax anymore. Using Itr=(1 +i)/(1 + re), find the relationship between the inflation rate of and savings tax t in part (c) of Question 1 such that inflation and the saving tax have the same impact on consumption. (Hint: in the previous problem, r was fixed. We now assume that i is fixed]