Questions 2-4 are a modication to the cake-eating 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 u(ct) = ln(ct) 2. t = 1, 2, ..., T: The T-period problem is to, T {.a:.}:e;'w Subject to: Wt+1 = PW: " Ct Wt+1 Z 0 (a) What is the value function and consumption for the T = 1 problem? (b) What is the value function and optimal consumption sequence for the T = 2 problem? (c) What is the value function and optimal consumption sequence for the T = 3 problem? ((1) Write the Lagrangean function for the T-period problem. (e) Find the rst order conditions. (f) Find the envelope condition. (g) Find the Euler-equation. (h) What is the difference between the Euler in this problem and from the standard cakeeating problem without storage return? Provide an economic interpretation