Please answer all parts.

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: Cf = (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]