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) +u(Cf)(1) whereCandCfare current and future consumption andis the discount rate. They face a standard

budget constraint in the first period:

C+Af= A+Y(2) whereYis current income,Ais wealth andAfis the amount of resources that households wish to save for the next period. Assume that the government imposes a taxton savings so that the second

period budget constraint is:

Cf= (1-t)(1+r)Af+ Yf(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-taxtaffects 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. Using1+r=(1+i)/(1+e), find the relationship between the inflation rateeand savings taxtin 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]