2) (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: $100 Equity: $20 Suppose that deposits cost the bank rd = 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