3. Consider a simple model in which the expected gain for a bank's shareholders is E(V~)E=C+(1)DP. Where V is the future equity value of the bank (a random variable), E is the current equity value of the bank, C is a constant, (0,1) is the probability of success for projects, D is the deposit the bank collects, P is the deposit insurance premium that the bank pays. The object of the bank's shareholders is to maximize . Please answer the following questions. (25P) (a) Explain why would a fixed deposit insurance scheme (when P is a constant) induce the moral hazard issue both intuitively ( 8P) and mathematically (2P, hint: show