Please help with e) and f):

2. Bequest Taxation: 40 points Consider a two period model: t = 0, 1. The parent lives in t = 0 and has endowment W > 0 and needs to decide how much to bequeath the kid. Denote bequest as b 2 0. 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 'r on the kid. The parent has utility In (cg) +rrln (cf) , where 5 = 1 is the discount factor both the parent and the kid use. Suppose the interest rate is r = 0. President Selina Meyer is deciding whether to tax bequest with a bequest tax of 1'. Let 6 E [0, 1] denote weight Selina puts on the parent and 1 6 the kid, i.e., Selina's objective is to maximize 9 [111093) +7ln(c{()] +(1 9)]n (). Setup the parent's optimization problem. (4 points) b. Solve for the equilibrium bequest as a function of the bequest tax. (8 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 9. (8 points) e. Find the optimal bequest tax for 9 = 1, %. (8 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) 5\