1 Question #1 (30 Marks) Consider the following innite horizon problem. Time is discrete, 1: : D,1,.... The period social welfare function WEE, m, pt} is dened on period consumption, ct, period labour effort, a;, and the period pollution level, pt. Period utility is discounted period byperiod by the discount factor ,3 so that the present value of period t social welfare is t'chhnhpt}. Let the social welfare function have the properties, ch'} ::+ Cl, Wm\" a: I}, W{-} f. '3, WW\" 1: I}, Wpf'l <: i wmi d where a rst subscript denotes the that partial derivative of function with respect to subscripted variable and double second variable. period consumption is equal output good. good depends on level production effort>