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Answers Final Exam, ECN 200E, Spring 2005
1. a. The dynamic programming problem associated with the question is: V (zt1 , bt1 , ft1 , ft2 ; xt ) = max {U (ct ) + EV (zt , bt , ft , ft1 ; xt+1 )} (ct ,zt ,bt ,ft ) +t zt1 (qt + xt ) + bt1 + ft2 ct pt bt t1 ft1 (1)
The arguments of the value function denote the state variables. Note that prices have been suppressed (for simplicity) since, in equilibrium, these are a function of the aggregate state variable, xt . Also note that, since the endowment is distributed as i.i.d., there is no time subscript on the expectations operator. The rst order conditions associated with bonds and equity have been derived numerous times, so I will not do that here. Focusing on the forward contract, we have the derivative: V (zt , bt , ft , ft1 ; xt+1 ) =0 (2) E ft This derivative is the change in utility due to forward conracts purchased in the previous period. Applying the envelope theorem to eq.(1) yields: V (zt , bt , ft , ft...
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