2. Consider a Lucas-tree type economy in which the level of the endowment is indepen- dently...

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2. Consider a Lucas-tree type economy in which the level of the endowment is indepen- dently and identically distributed with support xt ≤ (x',x”). Agents trade one- and two-period bonds that have prices plt and p2t, respectively, and return 1 unit of con- sumption at maturity. In addition, agents can purchase a one-period futures contract for the price flt. A futures contract purchased at time t states that the owner agrees to give up f1 units of consumption in period t+1 for the return of 1 unit of consumption in period t + 2. Note that in this economy, equity is not traded; agents receive the endowment, xt, at the beginning of each period. Given this setup, do the following: (a) Assuming standard preferences (i.e. infinitely lived, risk-averse agents), set up the household's maximization problem as a dynamic programming problem. (Sugges- tion: The setup is easier if it is assumed that households sell all two period bonds after holding them for one period.) 2. Consider a Lucas-tree type economy in which the level of the endowment is indepen- dently and identically distributed with support xt ≤ (x',x”). Agents trade one- and two-period bonds that have prices plt and p2t, respectively, and return 1 unit of con- sumption at maturity. In addition, agents can purchase a one-period futures contract for the price flt. A futures contract purchased at time t states that the owner agrees to give up f1 units of consumption in period t+1 for the return of 1 unit of consumption in period t + 2. Note that in this economy, equity is not traded; agents receive the endowment, xt, at the beginning of each period. Given this setup, do the following: (a) Assuming standard preferences (i.e. infinitely lived, risk-averse agents), set up the household's maximization problem as a dynamic programming problem. (Sugges- tion: The setup is easier if it is assumed that households sell all two period bonds after holding them for one period.)