I need help with the following exercise

Consider the Diamond-Dybvig model we learned in class. There are three periods, T = 0, 1, 2. Financiers each start with $1 of wealth. Utility is given by U = CI with probability A c + c2 with probability 1 - A There is a project that can be invested in for $1, and that there exist at least as many possible projects as financiers. At 7 = 1, if the project is liquidated, it pays a 1. Assume that A = 0.5. R = 1.2, and o = 0.2. 1. If there are no banks, should the financier invest directly in the project? What is the expected return? 2. Now suppose there are banks. In the good equilibrium, what is their expected utility? 3. What is the expected utility in the run equilibrium? 4. Suppose the government wants to implement deposit insurance, but they have a lim- ited amount of money with which to insure the bank. If we assume there are one million financiers with $1 each, and if the government has $200,000, is that enough to prevent the run equilibrium? Assume that in the run equilibrium, the bank still prioritizes everyone that shows up in the first period, including with the $200,000 from the government. 5. Suppose instead that the government has $900,000. Is that enough