Money and prices

1. Suppose that this year’s money supply is $500 billion, nominal GDP is $10 trillion, and real GDP is $5 trillion.

a. What is the price level? What is the velocity of money?

Nominal GDP = P x Y = $10,000 and Y = real GDP = $5,000,

So P = (P x Y₎/Y = $10,000/$5,000 = 2. 

Because M x V = P x Y, then V = (P x Y₎/M = $10,000/$500 = 20.

b. Suppose that velocity is constant and the economy’s output of goods and services rises by 5 percent each year. What will happen to nominal GDP and the price level next year if the Fed keeps the money supply constant?

If M and V are unchanged and Y rises by 5%, then because M x V = P x Y, P must fall by 5%. As a result, nominal GDP is unchanged.

c. What money supply should the Fed set next year if it wants to keep the price level stable?

To keep the price level stable, the Fed must increase the money supply by 5%, matching the increase in real GDP. Then, because velocity is unchanged, the price level will be stable. 

d. What money supply should the Fed set next year if it wants inflation of 10 percent?

If the Fed wants inflation to be 10%, it will need to increase the money supply 15%. Thus M x V will rise 15%, causing P x Y to rise 15%, with a 10% increase in prices and a 5% rise in real GDP.

2. Suppose that changes in bank regulations expand the availability of credit cards, so that people need to hold less cash.

a. How does this event affect the demand for money?

If people need to hold less cash, the demand for money shifts to the left, because there will be less money demanded at any price level.

b. If the Fed does not respond to this event, what will happen to the price level?

If the Fed does not respond to this event, the shift to the left of the demand for money combined with no change in the supply of money leads to a decline in the value of money (1/P), which means the price level rises, as shown in Figure 1. 

c. If the Fed wants to keep the price level stable, what should it do?

If the Fed wants to keep the price level stable, it should reduce the money supply from S1 to S2 in Figure 2. This would cause the supply of money to shift to the left by the same amount that the demand for money shifted, resulting in no change in the value of money and the price level.

3. It is often suggested that the Federal Reserve try to achieve zero inflation. If we assume that velocity is constant, does this zero-inflation goal require that the rate of money growth equal zero? If yes, explain why. If no, explain what the rate of money growth should equal.

With constant velocity, reducing the inflation rate to zero would require the money growth rate to equal the growth rate of output, according to the quantity theory of money (M x V = P x Y ).

4. The economist John Maynard Keynes wrote: “Lenin is said to have declared that the best way to destroy the capitalist system was to debauch the currency. By a continuing process of inflation, governments can confiscate, secretly and unobserved, an important part of the wealth of their citizens.” Justify Lenin’s assertion.

Lenin was certainly right. There is no subtler, no surer means of overturning the existing basis of society than to debauch the currency. The process engages all the hidden forces of economic law on the side of destruction, and it does it in a manner which not one man in a million is able to diagnose.”We’ve diagnosed and we’re taking action. The best way we know of to protect and increase your wealth in inflationary times is the proper use of leverage to buy income properties.

5. Suppose that a country’s inflation rate increases sharply. What happens to the inflation tax on the holders of money? Why is wealth that is held in savings accounts not subject to a change in the inflation tax? Can you think of any way in which holders of savings accounts are hurt by the increase in the inflation rate?

If inflation rate increases, the inflation tax on the holders money increases. Wealth in savings accounts are generally not subject to a change in the inflation tax because savings account rates move up and down with inflation rates. if the federal government decides to not increase the interest rates because of fear of recession, then a saving account holder will be hurt because the savings account rate will be lower than the inflation rate.

6. Hyperinflations are extremely rare in countries whose central banks are independent of the rest of the government. Why might this be so?

Hyperinflations usually arise when governments try to finance much of their expenditures by printing money. This is unlikely to occur if the central bank (which is responsible for controlling the level of the money supply) is independent of the government.

7. Let’s consider the effects of inflation in an economy composed only of two people: Bob, a bean farmer, and Rita, a rice farmer. Bob and Rita both always consume equal amounts of rice and beans. In 2000, the price of beans was $1, and the price of rice was $3.

a. Suppose that in 2001 the price of beans was $2 and the price of rice was $6. What was inflation? Was Bob better off, worse off, or unaffected by the changes in prices? What about Rita?

When the price of both goods doubles in a year, inflation is 100%. Let’s set the market basket equal to one unit of each good. The cost of the market basket is initially $4 and becomes $8 in the second year. Thus, the rate of inflation is ($8 − $4)/$4 × 100% = 100%. Because the prices of all goods rise by 100%, the farmers get a 100% increase in their incomes to go along with the 100% increase in prices, so neither is affected by the change in prices. 

b. Now suppose that in 2001 the price of beans was $2 and the price of rice was $4. What was inflation? Was Bob better off, worse off, or unaffected by the changes in prices? What about Rita?

If the price of beans rises to $2 and the price of rice rises to $4, then the cost of the market basket in the second year is $6. This means that the inflation rate is ($6 − $4) / $4 × 100% = 50%. Bob is better off because his dollar revenues doubled (increased 100%) while inflation was only 50%. Rita is worse off because inflation was 50% percent, so the prices of the goods she buys rose faster than the price of the goods (rice) she sells, which rose only 33%. 

c. Finally, suppose that in 2001 the price of beans was $2 and the price of rice was $1.50. What was inflation? Was Bob better off, worse off, or unaffected by the changes in prices? What about Rita?

If the price of beans rises to $2 and the price of rice falls to $1.50, then the cost of the market basket in the second year is $3.50. This means that the inflation rate is ($3.5 − $4) / $4 × 100% = -12.5%. Bob is better off because his dollar revenues doubled (increased 100%) while prices overall fell 12.5%. Rita is worse off because inflation was -12.5%, so the prices of the goods she buys didn't fall as fast as the price of the goods (rice) she sells, which fell 50%. 

d. What matters more to Bob and Rita—the overall inflation rate or the relative price of rice and beans?

The relative price of rice and beans matters more to Bob and Rita than the overall inflation rate. If the price of the good that a person produces rises more than inflation, he or she will be better off. If the price of the good a person produces rises less than inflation, he or she will be worse off.

8. If the tax rate is 40 percent, compute the before-tax real interest rate and the after-tax real interest rate in each of the following cases:

a. The nominal interest rate is 10 percent and the inflation rate is 5 percent.

Real interest rate before tax = 10 -5 =5

Nominal interest rate after tax = 10 × (1- 0.40) = 6

Real interest rate after tax = 6 -5 =1

b. The nominal interest rate is 6 percent and the inflation rate is 2 percent.

Real interest rate before tax = 6 - 2 = 4

Nominal interest rate after tax = 6 × (1-0.40) = 3.6

Real interest rate after tax = 3.6 - 2 = 1.6

c. The nominal interest rate is 4 percent and the inflation rate is 1 percent.

Real interest rate before tax = 4 -1 =3

Nominal interest rate after tax = 4 × (1-0.40) = 2.4

Real interest rate after tax = 2.4 -1 = 1.4

9. What are your shoe leather costs of going to the bank? How might you measure these costs in dollars? How do you think the shoe leather costs of your college president differ from your own?

The shoe leather costs of going to the bank include the value of your time, gas for your car that is used as you drive to the bank, and the inconvenience of not having more money on hand. These costs could be measured by valuing your time at your wage rate and valuing the gas for your car at its cost. Valuing the inconvenience of being short of cash is harder to measure, but might depend on the value of the shopping opportunities you give up by not having enough money to buy things you want. Your college president differs from you mainly in having a higher wage, thus having a higher cost of time.

10. Recall that money serves three functions in the economy. What are those functions? How does inflation affect the ability of money to serve each of these functions?

The functions of money are to serve as a medium of exchange, a unit of account, and a store of value.

Inflation mainly affects the ability of money to serve as a store of value, because inflation erodes money's purchasing power, making it less attractive as a store of value.

Money also is not as useful as a unit of account when there is inflation, because stores have to change prices more often and because people are confused and inconvenienced by the changes in the value of money.

In some countries with hyperinflation, stores post prices in terms of a more stable currency, such as the U.S. dollar, even when the local currency is still used as the medium of exchange. Sometimes countries even stop using their local currency altogether and use a foreign currency as the medium of exchange as well.

11. Suppose that people expect inflation to equal 3 percent, but in fact prices rise by 5 percent. Describe how this unexpectedly high inflation rate would help or hurt the following:

A. the government

Unexpectedly high inflation helps the government by providing higher tax revenue and reducing the real value of outstanding government debt.

B. a homeowner with a fixed-rate mortgage

Unexpectedly high inflation helps a homeowner with a fixed-rate mortgage because he pays a fixed nominal interest rate that was based on expected inflation, and thus pays a lower real interest rate than was expected.

C. a union worker in the second year of a labor contract

Unexpectedly high inflation hurts a union worker in the second year of a labor contract because the contract probably based the worker's nominal wage on the expected inflation rate. As a result, the worker receives a lower-than-expected real wage.  

D. a college that has invested some of its endowment in government bonds

Unexpectedly high inflation hurts a college that has invested some of its endowment in government bonds because the higher inflation rate means the college is receiving a lower real interest rate than it had planned. (This assumes that the college did not purchase indexed Treasury bonds.)

12. Explain one harm associated with unexpected inflation that is not associated with expected inflation. Then explain one harm associated with both expected and unexpected inflation.

The redistribution from creditors to debtors is something that happens when inflation is unexpected, not when it is expected.

The problems that occur with both expected and unexpected inflation include shoe leather costs associated with reduced money holdings, menu costs associated with more frequent adjustment of prices, increased variability of relative prices, unintended changes in tax liabilities due to no indexation of the tax code, and the confusion and inconvenience resulting from a changing unit of account.

 13. Explain whether the following statements are true, false, or uncertain.

a. “Inflation hurts borrowers and helps lenders, because borrowers must pay a higher rate of interest.”

False. Higher expected inflation means borrowers pay a higher nominal rate of interest, but it is the same real rate of interest, so borrowers are not worse off and lenders are not better off. Higher unexpected inflation, on the other hand, makes borrowers better off and lenders worse off. 

b. “If prices change in a way that leaves the overall price level unchanged, then no one is made better or worse off.”

False. Changes in relative prices can make some people better off and others worse off, even though the overall price level does not change. See problem 7 for an illustration of this. 

c. “Inflation does not reduce the purchasing power of most workers.”

 True because most workers' incomes keep up with inflation reasonably well.