Consider the following planning economy problem: - 0 max Ct,K+41 1 - g 1 = 0 such that atthe = yt; yt = =thi ; and kt+1 = It + (1 - 6) kt. In addition, In = = plnot-1+ 8t. Above: c is aggregate consumption; & is the aggregate capital stock; E, is the ex- pectation operator conditional on the information available up and through period t inclusive; @ 0 is the depreciation rate of capital (o is the Greek letter "delta"); = is productivity; a 6 (0, 1) is a parame- ter (a is the Greek letter "alpha"); p E (0, 1)| is the productivity process persistence parameter (p is the Greek letter "rho"); and & is disturbance term associated with the exogenous productivity process ({ is the Greek letter "xi" ). As usual, all non-price variables are normalized by the aggregate population, which consists of a unit mass. (a) State the Lagrangian associated with this problem using a single constraint. (b) State the first order conditions associated with this problem. Please show /explain your work thoroughly. (c) Derive the steady state values of c, I, k, and 2. Please show/explain your work thoroughly