## PROBLEMS AND APPLICATIONS

For any problem marked with , there is a Work it Out online tutorial available for a similar problem. To access these interactive, step-by-step tutorials and other resources, visit LaunchPad for Macroeconomics, 9e at www.macmillanhighered.com/launchpad/mankiw9e

### Question 4.7

1. What are the three functions of money? Which of the functions do the following items satisfy? Which do they not satisfy?

1. A credit card

2. A painting by Rembrandt

3. A subway token

### Question 4.8

2. Explain how each of the following events affects the monetary base, the money multiplier, and the money supply.

1. The Federal Reserve buys bonds in an open-market operation.

2. The Fed increases the interest rate it pays banks for holding reserves.

3. The Fed reduces its lending to banks through its Term Auction Facility.

4. Rumors about a computer virus attack on ATM machines increase the amount of money people hold as currency rather than demand deposits.

5. The Fed flies a helicopter over 5th Avenue in New York City and drops newly printed \$100 bills.

### Question 4.9

3. An economy has a monetary base of 1,000 \$1 bills. Calculate the money supply in scenarios (a)–(d) and then answer part (e).

1. All money is held as currency.

2. All money is held as demand deposits. Banks hold 100 percent of deposits as reserves.

3. All money is held as demand deposits. Banks hold 20 percent of deposits as reserves.

4. People hold equal amounts of currency and demand deposits. Banks hold 20 percent of deposits as reserves.

5. The central bank decides to increase the money supply by 10 percent. In each of the above four scenarios, how much should it increase the monetary base?

### Question 4.10

4. • In the nation of Wiknam, people hold \$1,000 of currency and \$4,000 of demand deposits in the only bank, Wikbank. The reserve–deposit ratio is 0.25.

1. What are the money supply, the monetary base, and the money multiplier?

2. Assume that Wikbank is a simple bank: it takes in deposits, makes loans, and has no capital. Show Wikbank’s balance sheet. What value of loans does the bank have outstanding?

3. Wiknam’s central bank wants to increase the money supply by 10 percent. Should it buy or sell government bonds in open-market operations? Assuming no change in the money multiplier, calculate, in dollars, how much central bank needs to transact.

### Question 4.11

5. • In the economy of Panicia, the monetary base is \$1,000. People hold a third of their money in the form of currency (and thus two-thirds as bank deposits). Banks hold a third of their deposits in reserve.

1. What are the reserve–deposit ratio, the currency–deposit ratio, the money multiplier, and the money supply?

2. One day, fear about the banking system strikes the population, and people now want to hold half their money in the form of currency. If the central bank does nothing, what is the new money supply?

3. If, in the face of this panic, the central bank wants to conduct an open-market operation to keep the money supply at its original level, does it buy or sell government bonds? Calculate, in dollars, how much the central bank needs to transact.

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### Question 4.12

6. As a Case Study in the chapter discusses, the money supply fell from 1929 to 1933 because both the currency–deposit ratio and the reserve–deposit ratio increased. Use the model of the money supply and the data in Table 4-2 to answer the following hypothetical questions about this episode.

1. What would have happened to the money supply if the currency–deposit ratio had risen but the reserve–deposit ratio had remained the same?

2. What would have happened to the money supply if the reserve–deposit ratio had risen but the currency–deposit ratio had remained the same?

3. Which of the two changes was more responsible for the fall in the money supply?

### Question 4.13

7. To increase tax revenue, the U.S. government in 1932 imposed a 2-cent tax on checks written on bank account deposits. (In today’s dollars, this tax would amount to about 34 cents per check.)

1. How do you think the check tax affected the currency–deposit ratio? Explain.

2. Use the model of the money supply under fractional-reserve banking to discuss how this tax affected the money supply.

3. Many economists believe that a falling money supply was in part responsible for the severity of the Great Depression of the 1930s. From this perspective, was the check tax a good policy to implement in the middle of the Great Depression?

### Question 4.14

8. Give an example of a bank balance sheet with a leverage ratio of 20. If the value of the bank’s assets rises by 2 percent, what happens to the value of the owners’ equity in this bank? How large a decline in the value of bank assets would it take to reduce this bank’s capital to zero?

### Question 4.15

9. • Jimmy Paul Miller starts his own bank, called JPM. As owner, Jimmy puts in \$2,000 of his own money. JPM then borrows \$4,000 in a long-term loan from Jimmy’s uncle, accepts \$14,000 in demand deposits from his neighbors, buys \$7,000 of U.S. Treasury bonds, lends \$10,000 to local businesses to finance new investments, and keeps the remainder of the bank’s assets as reserves at the Fed.

1. Show JPM’s balance sheet. What is JPM’s leverage ratio?

2. An economic downturn causes 5 percent of the local businesses to declare bankruptcy and default on their loans. Show JPM’s new balance sheet. By what percentage does the value of JPM’s assets fall? By what percentage does JPM’s capital fall?

1 R. A. Radford, “The Economic Organisation of a P.O.W. Camp,” Economica (November 1945): 189–201. The use of cigarettes as money is not limited to this example. In the Soviet Union in the late 1980s, packs of Marlboros were preferred to the ruble in the large underground economy.

2 Norman Angell, The Story of Money (New York: Frederick A. Stokes Company, 1929), 88–89.

3 To read more about bitcoin, see David Yermack, “Is Bitcoin a Real Currency? An Economic Appraisal,” NBER Working Paper No. 19,747 (December 2013).

4 Mathematical note: The last step in the derivation of the total money supply uses the algebraic result for the sum of an infinite geometric series. According to this result, if x is a number between −1 and 1, then

1 + x + x2 + x3 + … = 1/(1 − x).

In this application, x = (1 − rr).

5 On the case for greater capital requirements, see Anat Admati and Martin Hellwig, The Bankers’ New Clothes: What’s Wrong with Banking and What to Do About It (Princeton NJ: Princeton University Press, 2013).

6 To read more about quantitative easing, see Arvind Krishnamurthy and Annette Vissing-Jorgensen, “The Ins and Outs of LSAPs,” Economic Policy Symposium – Jackson Hole, Federal Reserve Bank of Kansas, 2013.

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