Questions 2-4 are a modification 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, W++1 = pWt 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 first period, C1 = PW1. Agents are assumed to evaluate flow utility according to = . u(c) = ln(c) = 2. t = 1, 2, ..., T: The T-period problem is to, T max {Ct, Wt+1} t=1 Bt-lu(a) Subject to: Wt+1 = PW+ Ct t Wt+1 > 0 Find the Euler-equation. What is the difference between the Euler in this problem and from the standard cake-eating problem without storage return? Provide an economic interpretation. Questions 2-4 are a modification 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, W++1 = pWt 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 first period, C1 = PW1. Agents are assumed to evaluate flow utility according to = . u(c) = ln(c) = 2. t = 1, 2, ..., T: The T-period problem is to, T max {Ct, Wt+1} t=1 Bt-lu(a) Subject to: Wt+1 = PW+ Ct t Wt+1 > 0 Find the Euler-equation. What is the difference between the Euler in this problem and from the standard cake-eating problem without storage return? Provide an economic interpretation