Answer Happy

1 An intertemporal household problem In order to prepare for this question, revisit Question 4.5 from the Calculus exercises dis- tributed at the beginning of the course. The problem is also covered in Section 16.2 of the textbook which we will study soon. Consider a household problem that lives in two periods. In period 1, the household starts with wealth W, and it chooses how to divide it between consumption C and saving S. The saving earn an interest rate R. so that at the beginning of period 2, the agents owns (1 +R) S. He then consumes his saving completely in period 2. Denote Cy his consumption in period 2. Notice that this problem implies two budget constraints C+S = W C2 S (1+R) The first constraint states that wealth is split between consumption in period 1 and saving. The second constraint states that consumption in period 2 is given by savings, including the interest earned.

Question 1.3 Argue that when consumption C2 is kept fixed (for reasons outside of this model), then consumption C1 in period 1 is a decreasing function of the interest rate. a Observe that in Question 1.3, we proceeded differently than in Question 4.5 of the Calculus exercises. There, we found a full solution for C and C2 and actually inferred that C = 11 W, which is independent of the interest rate. The reason was that when interest rate changed, consumption C did not stay the same and actually increased. Why we assume here that C2 is assumed to be kept fixed will be explained in class. What you should take away is that the consumption Euler equation in this case implies (asuming that C, is fixed) that household demand for consumption is a decreasing function of the real interest rate.