2. Consider the following planning economy problem: '00 10 C max E t t china1 t gig 1 0' such that a+h=w y: = 212k? ; and kt+l : It + (1 6) kt- In addition, lIth : ph'IZt_1 +:. Above: (3 is aggregate consumption; k: is the aggregate capital stock; E is the ex pectation operatOr conditional on the information available up and through period t inclusive; 13 6 (0,1) is the subjective parametric discount factor (5 is the Greek letter \"beta\"); y is aggregate output; I is aggregate investment; 6 > D is the depreciation rate of capital (6 is the Greek letter \"delta\"); 2 is productivity; at E (0, 1) is a parame ter (a is the Greek letter \"alpha\"); p 6 (0,1) is the productivity process persistence parameter (p is the Greek letter \"rho\"); and EZ is disturbance term associated with the exogenous productivity process (5 is the Greek letter \"xi\"). As usual, all nonprice 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 rst 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