(a) Write down the balance sheet constraint faced by the bank when allocating assets at period 0. (b) At period 1, given C and the realization of withdrawals shock w, what is the reserve shortfall faced by the bank? (c) Write down the expected profits of period 2 as a function of the choice variable C. (Hint: the expected profits equal interests earned from loans less expected cost of financing the reserve shortfall.) (d) Assuming r > ry, solve for the optimal choice of C that maximizes the expected profits of period 2 from the first order condition with respect to C. (Hint: use the Leibniz rule of integral to simplify the derivation of the first order condition, which states that for F(x) defined as