Chapter 25 The Banking System and the Money Supply
Chapter 25 - MONEY, BANKS, AND THE FEDERAL RESERVE
PROBLEM SET
2.The money supply can increase by a maximum of (1/0.15) x $50 million = $333.33 million. If the required reserve ratio is 0.18, the money supply can increase by a maximum of (1/0.18) x $50 = $277.78 million.
4.If the Central Bank buys 50 million zeeks worth of government bonds, this will increase the country’s money supply by 50 million*(1/0.05) = 500 million*20=1 billion zeeks. Remember that if banks want to hold reserves the effect on the money supply is just like with a required reserve.
6. There are two ways to answer this question. One is to assume that the cash that Mid-Size receives from insurance goes straight to property and building. Then the value of Property and Buildings will be $40 million - (0.2*$40 million destroyed) + (0.5*0.2*$40 million regained through insurance) = $40 - $8 + 4$ = $36 million. Total assets will be lower by $4 million, i.e. $1,000 - $4 million = $996 million. Total liabilities stay the same, but Shareholder’s Equity goes down to $121 million. Shareholder’s Equity = Total Assets – Total Liabilities = 996 – 875 = 121 million.
Another option is to assume that the money received from insurance is kept as cash in their vault. The final effect on assets, liabilities and equity is the same.
8. To find the answer, substitute the desired change in the money supply ($500 billion) and the money multiplier (10 = 1/0.10) into the equation for the change in the money supply, and solve for the change in reserves:
$500 billion = 10 x Reserves
Reserves = $500 billion/10 = $50 billion
The Fed will need to increase initial deposits by $50 billion. It can do this by buying government bonds worth $50 billion from the public.
If the required reserve ratio is 0.15 (so that the money multiplier = 1/0.15 = 6.67), the Fed will need to increase initial deposits by $500 billion/(6.67) = $74.96 billion. It can do this by buying government bonds worth $74.96 billion from the public.
10. a. The first five items listed in the problem statement are assets. Therefore, Assets = Property and buildings + Government bonds + Loans + Cash in vault + Accounts with the Fed = $20 + 200 + 300 + 5 + 95 = $620 million. The demand deposits are the only liability ($550 million). Bank’s capital = Assets – Liabilities = $620 – 550 = $70 million.
b. The bank will be solvent as long as the bank’s capital does not become negative. Consequently, it could “write off” as much as $70 million in bad loans (thereby reducing its assets to $550) without becoming insolvent.
MORE CHALLENGING QUESTIONS
12. a. Mid-Size Bank is permitted a maximum simple leverage ratio of 5. To find this, suppose that Mid-Size has exactly 20% (and no more) of its assets as bank capital. Then, Maximum Simple Leverage ratio = Total Assets/(0.2*Total Assets) = 1/0.2 = 5.
b. Mid-Size’s actual simple leverage ratio is Total Assets/Shareholder’s Equity = 1000/125 = 8.
c. To bring down the simple leverage ratio to 5, Mid-Size would have to sell $375 million in assets. To find this number we solve for X in the following equation (1000-X)/125 = 5. Rearranging we get 1000-X = 625, and X = 375. Notice that the shareholder’s equity stays at 125 because both total assets and total liabilities went down by the same amounts. In particular, Shareholder’s Equity = Total Assets – Total Liabilities = (1000-X) – (875-X) = 125.