I hope that you can use the computer to type out the calculation steps of each question (handwritten answers may not be easy to read). Thank you

4. Bank Run Model: Consider the model about bank runs we covered in class and use the same set of parameters: the project pays 1 unit if aborted at T = 1 and pays 2 units if completed at T = 2, and that there are 100 people and 25 of them are the urgent type, and so on. The only difference now is that the utility function is U = 1 - instead. a) Calculate the expected utility at T = 0 when there is no bank and people have to invest in the project themselves. b) Use the optimality condition U'(r.) = 2U'(r2) and the constraint 75r2 = 2(100 25r1) to solve for the best deal r and r2. Notice that U' is the marginal utility (which in this case is zez), and U'(ra) means you use r to replace c in the marginal utility. c) Calculate the expected utility at T = 0 when there is a bank, based on the answer for b). d) Using the shape of the utility function, explain intuitively why the optimal r1 and r2 here are different from the version we have covered in class? Without doing the calculation, describe what will happen to the optimal r and r2 when the utility function is changed to U = 1 - to 4. Bank Run Model: Consider the model about bank runs we covered in class and use the same set of parameters: the project pays 1 unit if aborted at T = 1 and pays 2 units if completed at T = 2, and that there are 100 people and 25 of them are the urgent type, and so on. The only difference now is that the utility function is U = 1 - instead. a) Calculate the expected utility at T = 0 when there is no bank and people have to invest in the project themselves. b) Use the optimality condition U'(r.) = 2U'(r2) and the constraint 75r2 = 2(100 25r1) to solve for the best deal r and r2. Notice that U' is the marginal utility (which in this case is zez), and U'(ra) means you use r to replace c in the marginal utility. c) Calculate the expected utility at T = 0 when there is a bank, based on the answer for b). d) Using the shape of the utility function, explain intuitively why the optimal r1 and r2 here are different from the version we have covered in class? Without doing the calculation, describe what will happen to the optimal r and r2 when the utility function is changed to U = 1 - to