Questions 24 are a modication to the cakeeating problem so that there is a return to storage. Let p > 0 be the return to storing cake from one period to the next. Assume that the law of motion for cake is, Wt+1 = PW): Ct Assume that W1 is known, but that the return on the cake takes place before the consumption decision so that if an agent consumed all of the cake in the rst period, (:1 = le. Agents are assumed to evaluate ow utility according to \"(Ctl = 111(Ct) 3. t = 1, 2, Answer the following: (a) Write the sequence problem. (b) Write the Lagrangean function for this problem. ((3) Write the Bellman equation for this problem. ((1) Find the rst-order conditions by taking the derivative of the Bellman with respect to the control (Note: one control variable can be eliminated by substitution) (e) Find the envelope condition (there should be one for each state variable). (f) Find the Euler-equation and provide an intuitive comparison with the Euler from the rst problem. (g) Solve for the policy function and value function by positing that, V(W) = A + B ln(W) (h) What is the connection between the result in the innite horizon case and the T = 3 case? 4. There are two distinct economic interpretations of p depending on whether p 1. What are these interpretations