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Question 5 Consider the following sequence problem max B'u(CE) (4) subject to ditita = (1 + ri )as + w, 1=0,1.... (5) a. Assume that , = r(x,), w = w(x,), and that x,+1 = (1 - p)x + px,. What is the Bellman equation corresponding to the above sequence problem? b. Now assume for simplicity that , = r, (a constant), but that wr+ 1 = aw, + Bw-2. What is the relevant (the smallest sufficient) state vector? c. What is your answer to (b) if with = Eidy' w-? d. How does your answer to (c) change if N = Do? Note that in all problems associated with Question 5, there is an implicit assumption that there are sufficient givens in (4)-(5) in order to accurately predict future prices. E.g. in (i) it is implicitly assumed that xo is given, and so on. Question 6 Consider the following simple RBC model with capital adjustment costs in which output is a function of beginning of period capital and an i.i.d. stochastic technology shock: M = =k; ; a