Consider the consumption savings problem SP 1 with a general utility function u, some income w, and some borrowing limit D.

1. Under what assumptions on the utility function, income, and the borrowing limit does the Bellman Equation have a unique solution in the space of bounded and continuous functions? (Provide direct proof via the contraction mapping theorem).
2. Under what assumptions is the optimal policy correspondence a policy function? Give a three-sentence educated guess.