2/6 Question 1 Consider the following utility maximization problem: 00 max E0 2 [Br (In ct | \"y In kt\") {ct,kt+120}:;o to st. kt+1 + qt 2 Aka/(:3 where or 6 (0,1), ,8 E (0,1), 7 > 0, ct 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), and At is the productivity of capital stock in period t. Assume that In At+1 = p In At + t+1 for all t, where p E (0,1! and et+1 is an independent white 3/6 You can guess and verify that the value function in the Bellman equation for this problem takes the following form: V(At, kt) Z Fl GlnAtIHln kt where F, G, and H are constants. Suppose that or = 0.6, ,8 = 0.9, 'y = 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.) oqo 3/6