Cake eating problem Cecilia got a chocolate cake. The cake is of size 1. She has to decide how much to eat from it every day, having pereferences over each days consumption given by u(c) and a discount factor B. The cake rottens over time so each period a fraction o of whatever is left has to be discarded and cannot be eaten. 1. Write the Bellman equation of this problem. 2. Describe the transformation T for which the solution of the value function is a fixed point. 3. Proof that T is a contraction mapping. State all the relevant assumptions you need for this result. 4. For u(c) = In(c) find the optimal consumption function. . Hint: Do two value function iterations using the initial guess Vo(k) = In(k) and find the pattern that the sequence of policy functions follow. Then take the limit