Economics Consider the following utility maximization problem: max E; t In ct+7ln kt+1 {chosen}; Ell; ( ) s.t. kf+1 + c. = Ail\"k? where a: E (0.1)I [3' E (0.1), qr 2: O. or denotes consumption in period t. kt+1 is the amount of capital stock held at the end of period t (and thus at the beginning of period t + 1)1 and Air is the productivity of capital stock in period t. Assume that in At+1 = P I" Ar + Eff-+1 for all t, where p E (D, 1) and 6:44 is an independent white noise. You can guess and verify that the value function in the Bellman equation for this problem takes the following form: \"TAB kt) = F + GlnAt + Hln kt where F , G. and H are constants. Suppose that it = 0.5. = 0.9. "r = 0.2. and p = 0.5. Given these parameter values. derive the values of F . G, and H with 2 decimal places (i.e.. if the value of F is 1.6875. only' answer 1.68). (Note: you do not need to detrend the model, because there is no trend in At.) answer the question in steps