(25 points) In this exercise we will study liquidity management and bank runs. Suppose that there is a bank which begins with the following balance sheet positions: Loans: $100 Cash Reserves: $20 Deposits: 5100 Equity: $20 Suppose that deposits cost the bank rCl = 0.05 in interest each period, and loans (if they are held on the balance sheet) earn r' = 0.10. Cash reserves do not earn any interest rates. The bank is not required to hold any cash but may choose to do so to meet withdrawal demands. If the bank is forced to sell loans, it must do so at a 50 percent discount. a. (5 points) Draw the balance sheet T for this bank and calculate the liquidity ratio, the leverage ratio and the equity multiplier. b. (5 points) Assume that during the first period there are no changes to the balance sheet of this bank. What are the return on assets and the return on equity? Show that the return on equity equals one plus the leverage ratio times the return on assets. c. (5 points) Assuming that the bank cannot borrow funds from a central bank (or another bank), what is the maximum withdrawal of deposits the bank can handle before it becomes insolvent? d. (10 points) Suppose now the bank starts with the following positions: Loans: $80 Cash Reserves: $40 Deposits: 5100 Equity: $20 Redo parts a, b and C. Is the bank's return on equity larger or smaller with this balance sheet compared to the original one? Is the bank more or less likely to be unable to handle a large withdrawal shock with this balance sheet or the original one