Consider the following utility maximization problem: Eo pt (In ct + y ln kt+1) max {Ct, kt+1>0}=0 t=0 s.t. kt+1+Ct = -α Lα : AZ-^ where a € (0, 1), ß € (0, 1), y > 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 ln At + €t+1 for all t, where p € (0, 1) and €t+1 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: V(At, kt) = F + G In At + H Inkt where F, G, and H are constants. Suppose that α = 0.6, p=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 de-trend the model, because there is no trend in At.)
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