I. $(30$ Points Total$)[$MONEY SUPPLY AND MONETARY POLICY$]$ Given below are the cumulative monetary statistics for United States. The monetary policy of the US is determined by the Federal Reserve $($FED$).$ American banks collectively hold $400$ dollars of treasury bonds and $2000$ million dollars of loans, whereas their customers hold $3000$ million dollars of deposits. The required reserve ratio is equal to $5\%$ and the excess reserve ratio is equal to $15\%.$ There is no currency. Use this information to solve the questions given below. Show your work and draw the appropriate balance sheets when required.

$(5$ Points$)$ In addition to the items listed above, the only other item American Banks hold on their balance sheets is reserves. Show the collective balance sheet of the American banking system. Calculate the amount of both the required and excess reserves.

$(5$ Points$)$ Suppose that the Federal Reserve conducted an open market sale of $$200$ million. Also suppose that the required and excess reserve ratios stay the same. What is the new money supply? Draw the new balance sheet.

$(10$ Points$)$ Suppose that instead of an open market operation, the money supply changes in response to a discount loan of $$50$ million. Also suppose that the excess reserve ratio falls to $5\%-$ the same as the required reserve ratio. By how much does the money supply change? Draw the new balance sheet.

$(10$ Points$)$ Suppose that the commercial banking system decides to pay back the discount loans described above. However, they are planning to do so without reducing their reserves and deposits. Explain how this can be done? Show it on a new balance sheet.