## 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 5.8

1. • In the country of Wiknam, the velocity of money is constant. Real GDP grows by 3 percent per year, the money stock grows by 8 percent per year, and the nominal interest rate is 9 percent. What is

1. the growth rate of nominal GDP?

2. the inflation rate?

3. the real interest rate?

### Question 5.9

2. Suppose a country has a money demand function (M/P)d = kY, where k is a constant parameter. The money supply grows by 12 percent per year, and real income grows by 4 percent per year.

1. What is the average inflation rate?

2. How would inflation be different if real income growth were higher? Explain.

3. How do you interpret the parameter k? What is its relationship to the velocity of money?

4. Suppose, instead of a constant money demand function, the velocity of money in this economy was growing steadily because of financial innovation. How would that affect the inflation rate? Explain.

### Question 5.10

3. • An economy has the following money demand function: (M/P)d = .2Y/i½.

1. Derive an expression for the velocity of money. What does velocity depend on? Explain why this dependency may occur.

2. Calculate velocity if the nominal interest rate i is 4 percent.

3. If output Y is 1,000 units and the money supply M is \$1,200, what is the price level P?

4. Suppose the announcement of a new head of the central bank, with a reputation of being soft on inflation, increases expected inflation by 5 percentage points. According to the Fisher effect, what is the new nominal interest rate?

5. Calculate the new velocity of money.

6. If, in the aftermath of the announcement, both the economy’s output and the current money supply are unchanged, what happens to the price level? Explain why this occurs.

7. If the new central banker wants to keep the price level the same after the announcement, at what level should she set the money supply?

### Question 5.11

4. Suppose that the money demand function takes the form

(M/P)d = L(i, Y) = Y/(5i)

1. If output grows at rate g and the nominal interest rate is constant, at what rate will the demand for real balances grow?

2. What is the velocity of money in this economy?

3. If inflation and nominal interest rates are constant, at what rate, if any, will velocity grow?

4. How will a permanent (once-and-for-all) increase in the level of interest rates affect the level of velocity? How will it affect the subsequent growth rate of velocity?

5. If the central bank wants to achieve a long-run target inflation rate of π, at what rate should the money supply grow?

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### Question 5.12

5. A newspaper article once reported that the U.S. economy was experiencing a low rate of inflation. It said that “low inflation has a downside: 45 million recipients of Social Security and other benefits will see their checks go up by just 2.8 percent next year.”

1. Why would policymakers link increases in Social Security and other benefits to inflation?

2. Is the small increase in benefits a “downside” of low inflation, as the article suggests? Why or why not?

### Question 5.13

6. During World War II, both Germany and England had plans for a paper weapon: they each printed the other’s currency, with the intention of dropping large quantities by airplane. Why might this have been an effective weapon?

### Question 5.14

7. In each of the following scenarios, explain and categorize the cost of inflation.

1. Because inflation has risen, the J. Crew clothing company decides to issue a new catalog monthly rather than quarterly.

2. Grandpa buys an annuity for \$100,000 from an insurance company, which promises to pay him \$10,000 a year for the rest of his life. After buying it, he is surprised that high inflation triples the price level over the next few years.

3. Maria lives in an economy with hyperinflation. Each day after being paid, she runs to the store as quickly as possible so she can spend her money before it loses value.

4. Gita lives in an economy with an inflation rate of 10 percent. Over the past year, she earned a return of \$50,000 on her million-dollar portfolio of stocks and bonds. Because her tax rate is 20 percent, she paid \$10,000 to the government.

5. Your father tells you that when he was your age, he worked for only \$4 an hour. He suggests that you are lucky to have a job that pays \$9 an hour.

### Question 5.15

8. Some economic historians have noted that during the period of the gold standard, gold discoveries were most likely to occur after a long deflation. (The discoveries of 1896 are an example.) Why might this be true?

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