1. Certainty Equivalence and Precautionary Savings Consider a consumer facing the following finite horizon problem: maxE0t=1T(1+)t11U(Ct) where U(Ct)=Ct21Ct2 subject to Ct+At=Yt+(1+rt)At1+A0=0 Note that Ct,Yt and At are consumption, income and an asset at time t, and rt is the return for the asset at time t and is the subjective discount rate. (a) Derive the stochastic Euler equation. From now on, suppose that rt=t. (b) How can you represent the solution for Ct in terms of present and future incomes. (c) What is the impact of future uncertainty on the choice of Ct ? (d) Replace the utility function with U(Ct)=1Ct1 where is the risk-aversion parameter. What happens to your answer in (c)? 1. Certainty Equivalence and Precautionary Savings Consider a consumer facing the following finite horizon problem: maxE0t=1T(1+)t11U(Ct) where U(Ct)=Ct21Ct2 subject to Ct+At=Yt+(1+rt)At1+A0=0 Note that Ct,Yt and At are consumption, income and an asset at time t, and rt is the return for the asset at time t and is the subjective discount rate. (a) Derive the stochastic Euler equation. From now on, suppose that rt=t. (b) How can you represent the solution for Ct in terms of present and future incomes. (c) What is the impact of future uncertainty on the choice of Ct ? (d) Replace the utility function with U(Ct)=1Ct1 where is the risk-aversion parameter. What happens to your answer in (c)