1. Consider a household with preferences given by (1) where p > 0 is the rate of time preference. The household has no initial wealth; i.e. a_1(1+r) = 0. Suppose further that the interest rate stays constant at rt = p for all t and that y =y for all t. t In Ct, (a) Set up the infinite horizon budget constraint. (b) Derive consumption co in the first period as a function of life-time income. (c) What is the sequence of consumption levels over time? (d) Suppose there is an anticipated permanent income shock such that y = y + for all t > 1. What happens to consumption and assets over time? (e) Suppose there is an anticipated temporary income shock in t = 1 such that y = y + and y = y for all t# 1. What happens to consumption and assets over time? (f) Suppose there is an unanticipated permanent income shock in period t = 1 such that y = y + e for all t > 1. What happens to the consumption and assets over time? (g) Suppose there is an unanticipated temporary income shock in t + 1 such that y = y + and y = y for all t 1. What happens to the consumption and assets over time?