2. Request xation: at} points Consider a two period model: t = , 1. The parent lives in t = and has endowment W 2- and needs to decide how much to bequeath the kid. Denote bequest as E: 1'3 D. The kid lives in period t = 1. There are no labor decisions taken in any period. The parent loves the kid and puts an altruistic weight of qr on the kid. The parent has utility In (65) +14%): where d = l is the discount factor both the parent and the kid use. Suppose the interest rateisr = t1 Resident Selina Meyer is deciding whether to tax bequest with a bequest tax of T. Let E E [I], 1] denote weight Selina puts on the parent and 1 H the kid, i.e., Selina's objective is to maximize washes]shame)- a. Setup the parent's optimization problem. (4 points} b. Solve for the equilibrium bequest as a metion of the bequest tax. {3 points} c. Setup the social planner's optimization problem. Hint: the sum of consump- tions cannot be greater than W. {4 points] d. Solve the social planner's problem and nd the allocations in terms of H. {3 pews: e. Find the optimal bequest tax for a = 1,17. {s points} f. Is it ever optimal for Selina to introduce a positive tax on bequests in this econ- omy? Explain in one sentence. {8 points}