2. Consider the following planning economy problem: 9'3 lo' c max EgZt l: or C: .kr+1 i=1] such that C: + I: = yr; .0. '9': = viii-t a and kt+l 2 It +(1 TS} kt- In addition, 111;: = pin 311 + 5:. Above: c is aggregate consumption; lit"- is the aggregate capital stock; E: is the ex pectation operator conditional on the information available up and through period t inclusive; .3 E ([1; 1) is the subjective parametric discount factor (3 is the Greek letter \"beta\"); 3; is aggregate output; I is aggregate investment; 5 :> i] is the depreciation rate of capital {ti is the Greek letter \"delta\"); 3 is productivity; or E [i]; 1} is a parame ter {or is the Greek letter \"alplra\"); p E {0,1} is the productivity process persistence pan'anieter {p is the Greek letter \"rho\"]; and 53 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 g' explain your work thoroughly. (c) Derive the steady state values of c; I , It; and .2. Please showfexplain your work thoroughly