Need help with resolving the following exercvise from Recursive Macroeconomic Theory by Ljungqvist and Sargent.

Exercise 1'15 'I'rade?? A consumer orders consumption streams according to 1-1 {1} 3023\"\" . BEEN} :20 1-? where fr 3:- 1 and E0 is the mathematical expectation conditional on time II} information. The consumer can borrow or lend a oneperiod riskfree security that bears a xed rate of return of R = 3'1 . The consumer's budget constraint at time i is {2} Ct + R-lbt+l = a 'I' 5i where s. is the level of the asset that the consumer brings into period t. The household is subject to a \"natural\" borrowing limit. The household's initial asset level is be 2 and his endowment sequence pt follows the process {3} so: = if: EXP(EEt+1 'l' P} where 5:44 is an i.i.d. Gaussian process with mean zero and 1variance II p. = .rfog, and HE :5 i]. The consumer chooses a process {ch bt+1}':0 to maximize {1} subject to (2)., (3], and the natural borrowing limit. a. Give a closedform expression for the consumer's optimal consumption and asset accumulation plan. Hint 1: If logs: is N(p..cr2). then E1\" = expiip. + 132,32}. Hint 2: You could start by trying to verify the following guess: the optimal policy has {n+1 =11] for all t 3 D. h. Discuss the solution that you obtained in part a in terms of Friedman's permanent income hypothesis. c. Does the household engage in precautionary savings