15宏观经济学英文版(多恩布什)课后习题答案全解

CHAPTER 15

THE DEMAND FOR MONEY

Solutions to the Problems in the Textbook:

Conceptual Problems:

1. Money is any asset that is widely used as a medium of exchange. People want to hold money since it

simplifies their current or future transactions. Since the nominal value of money is always known with certainty, it is a very safe and liquid asset, unless there is a very high rate of inflation. Therefore holding money protects asset holders against potential capital losses on riskier assets.

2. In a society in which there was no money, all trade would be completely based on barter. But barter is

fairly inefficient, since suppliers of goods and services can't always find people who are both in need of the goods and services being offered and willing to trade something of value to the suppliers.

Therefore, sooner or later, some form of money has to be invented to facilitate trade. A good example of a money substitute is U.S. cigarettes, which were used as medium of exchange during the hyperinflation in Germany in 1922/23, in P.O.W. camps after World War II, and in some Eastern European countries during the transition from command economies to more market-based economies when people lost confidence in their own currencies.

It is easier to imagine a society in which there is no currency but everyone has a credit or debit card. The cashless purchase of goods via credit or debit cards (or via e-commerce) is not only convenient for customers but can also provide valuable information to sellers about the buying habits of consumers (which is one reason grocery stores now willingly accept credit or debit cards). In a cashless society all transactions would require electronic fund transfers through bank computers. At the end of the month, all accounts would have to be settled with the company that issued the credit or debit card, again through electronic fund transfers. This requires investment in computer technology, not only for banks but also for merchants. Such a system may seem highly efficient, but it may not work well for very small purchases, such as a magazine at a newspaper stand, a can of soda from a vending machine, or a local phone call. However, financial institutions have already developed pre-paid cash cards or phone cards that allow the purchase of smaller items or phone calls, with the amount of the purchase automatically deducted from the card.

It should be noted, however, that a cashless society still requires money, that is, funds that can be stored in accounts, whether these are traditional bank accounts used to settle outstanding bills or accounts that exist simply for e-commerce. However, if pre-paid cash cards, debit and credit cards, or e-commerce funds are used increasingly, monetary aggregates may have to be redefined.

3. One could certainly make an argument for including credit card limits as part of money stock, since

people substitute credit cards for cash as a means of payment. They may also use unused credit lines for precautionary purposes. But if we include this form of credit in the money stock, it becomes difficult to justify excluding others. Therefore it may be better not to include credit card limits in the definition of money.

4. In deciding how many traveler's checks to take on a vacation, an individual has to weigh the cost of

obtaining the checks against the probability of cash being stolen and the possibility that personal checks or credit cards might not be honored. The lower the cost of traveler's checks and the higher the probability that cash may be stolen, the larger the sum that is likely to be carried in traveler's checks.

On the other hand, holding cash or traveler's checks involves an opportunity cost, since no interest can be earned on cash or traveler's checks. Therefore, if credit cards are accepted at the vacation spot, vacationers may rely primarily on credit cards as a means of payments, since they can earn interest on

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their money holdings until they have to pay their credit card bill. Many travelers now actually prefer to rely on ATM cards to obtain cash in foreign countries. This not only allows them to carry less cash or traveler's checks, but also eliminates the fee for exchanging currency. Some ATM cards also serve as debit cards and can be used for the purchase of goods or services. Possible drawbacks of relying on ATM cards include the possibility of a strike among bank employees in the foreign country or the absence of ATM machines in remote areas.

5. The opportunity cost measures the benefit or revenue foregone from using a resource in one way

rather than another. Individuals who hold money give up the return they could have earned had the money been invested in a bond (or any other interest-earning asset not included in the definition of money). To guarantee lenders a positive rate of return, bonds pay nominal interest rates that include an inflation premium to cover the expected loss in purchasing power over the period that the bond is held. Therefore it is the nominal and not the real interest rate that is the opportunity cost of holding money. However, when the rate of inflation is very high, nominal interest rates do not adequately reflect the rate of inflation. In this case, the inflation rate (if it is higher than the interest rate) should be used as the appropriate opportunity cost.

6. The more inflation increases, the more individuals fear a loss of purchasing power from their money

holdings. People are therefore not as likely to hold much money in periods of high inflation. An increase in inflation will increase the nominal interest rate, which is the opportunity cost of holding money. This will reduce the demand for money. From the equilibrium condition in the money sector (m d = L(i,Y) = M/P = m s), we can see that if prices (P) increase more than nominal money supply (M), then real money balances (M/P) will decrease and the demand for real money balances (m d) will also decrease to get the money sector back into equilibrium. In periods of high inflation, nominal money supply tends to increase rapidly, so nominal money holdings become larger.

7. During periods of deflation, the cost of holding cash decreases and people tend to carry more cash.

Therefore muggers can expect a much higher return from their activity.

Technical Problems:

1.a. Cash machines that allow withdrawals from saving accounts reduce the need to hold precautionary

funds in cash or checking accounts. Therefore the demand for M1 would decrease, but the demand for M2 would not be affected since M1 is included in M2.

1.b. If more tellers worked at your bank, then your waiting time would be reduced, so you might be

willing to go to the bank more often to make withdrawals. The demand for M1 would decrease, but the demand for M2 would not be affected since M1 is included in M2.

1.c. An increase in inflationary expectations would reduce the demand for money, since people would be

afraid of losing purchasing power. In times of low inflation, people may switch from low interest accounts to higher interest accounts. The demand for M1 decreases, while the demand for M2 is not affected. However, if inflation is very high, people may hold less money in any form and spend more on durable goods. In this case the demand for both M1 and M2 might decrease.

1.d. Increased use of credit cards would reduce the need to hold money for transactions, even though

people would still need to settle their monthly credit card charges in a convenient way. They would most likely shift funds from demand deposits into time deposits, that is, away from M1 and into M2.

The demand for M1 would decrease, but the demand for M2 would not be affected.

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1.e. If the fear of a collapse of the government led to the fear that money would lose its value, people

would try to spend as much money as possible to buy durable or tradable goods before the government collapses. Thus the demand for both M1 and M2 would decrease.

1.f. With an increase in the interest rate on time deposits, people would shift more funds from demand

deposits into time deposits. The demand for M1 would decrease while the demand for M2 would remain unaffected. However, if interest rates on M2 components increased much more than the yield on other assets, the demand for other assets could also decrease. In such a case, the demand for M2 would increase.

1.g. With the rise in e-commerce, more cashless transactions take place. Therefore people would most

likely shift funds from demand deposits into high-interest earning accounts until their accounts had to be settled. Most e-commerce transactions involve the use of credit cards, so the answer here is the same as in 1.d. Funds are shifted away from M1 and into M2, and the demand for M1 decreases, but the demand for M2 is not affected. However, some banks have already established e-cash accounts exclusively for e-commerce; increased use of e-cash requires a re-definition of monetary aggregates.

2.a. As the economy goes into a recession, income and interest rates are both likely to decline. Since

velocity decreases as income and interest rates decrease, we should expect the velocity to decline in a recession. Also, since velocity is defined as nominal GDP over nominal money supply, it is easy to see that velocity should decrease, since nominal income declines while nominal money supply is not affected.

2.b. The Fed can influence velocity by injecting or withdrawing money through its open market

operations. If money supply increases more than nominal GDP, velocity decreases.

3. This problem is just a reversal of the inventory approach used by Baumol and Tobin, since now only

one withdrawal has to be made at the end of the month, while many deposits can be made during the month. The firm would have to calculate the benefits from interest earned and compare them to the cost of making the deposits. It would therefore calculate its cash holdings in the same way as in the inventory approach.

4.a. The person tries to minimize the cost of managing the portfolio. This cost is: C = nt c + (iY/2n)

n = 1 ==> C = 1*1 + (0.005)(1,600)/(2*1) = 1 + 4 = 5

n = 2 ==> C = 2*1 + (0.005)(1,600)/(2*2) = 2 + 2 = 4

n = 3 ==> C = 3*1 + (0.005)(1,600)/(2*3) = 3 + 4/3 = 4.34

n = 4 ==> C = 4*1 + (0.005)(1,600)/(2*4) = 4 + 1 = 5

Therefore 2 transactions are optimal.

4.b. With two transactions, the optimal cash holding is: m d = Y/(2n) = 1,600/(2*2) = $400.

4.c. n = 1 ==> C = 1*1 + (0.005)(1,800)/(2*1) = 1 + 4.5 =

5.5

n = 2 ==> C = 2*1 + (0.005)(1,800)/(2*2) = 2 + 2.25 = 4.25

n = 3 ==> C = 3*1 + (0.005)(1,800)/(2*3) = 3 + 1.5 = 4.5

n = 4 ==> C = 4*1 + (0.005)(1,800)/(2*4) = 4 + 1.125 = 5.125

Therefore it is still optimal to make two transactions, but the optimal cash holding is now m d = 1,800/(2*2) = $450.

This is a 12.5% increase, since (450 - 400)/400 = .125.

Additional Problems:

1. Do people use credit cards more often when interest rates are high or low?

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Many credit card companies charge a high but fixed interest rate on all balances that are not immediately paid off. Therefore, in periods of high interest rates, the interest charge becomes relatively smaller and thus we should expect the use of credit cards to go up. Also, since it may take up to a month from the time of purchase to get the credit card bill and people generally have an additional month to pay the balance, card holders get, in effect, an interest-free loan for up to two months. In times of high interest rates people have a greater incentive to keep their funds in an interest-earning account for these two months. Therefore they have a greater incentive to use their credit cards in times of high interest rates.

2. “The opportunity cost of holding a bond is the return from holding money." Comment.

The opportunity cost is the benefit foregone when using a resource one way instead of another. People who hold bonds receive a rate of return but they are giving up the utility that holding money provides to them through its role as a medium of exchange. Since different individuals value such utility differently, the opportunity cost of holding a bond varies from one individual to another. Money is also held to protect against capital losses that may occur from a decrease in bond values arising from an increase in interest rates. The avoidance of such a capital loss can be seen as part of the return of holding money.

3. "The real interest rate is the opportunity cost of holding money." Comment on this statement. The opportunity cost measures the benefit or the revenue foregone when using a resource in one way rather than another. If individuals hold money, they give up the return they would have earned had they used the money to purchase a bond. Bonds pay nominal interest rates to guarantee the lender a real return plus a premium to cover the expected loss in the purchasing power of the principal over the period of the "loan." Therefore it is the nominal and not the real interest rate that is the opportunity cost of holding money. If the rate of inflation is higher than the prevailing nominal interest rate, then the rate of inflation should be used as the opportunity cost.

4. "Money market deposit accounts are offered by banks, are FDIC insured, and have check-

writing privileges. Therefore they should be included in M1 rather than M2." Comment on this statement.

Even though money market deposit accounts (MMDAs) limit the number of checks that can be written per month, they do provide a very cheap and convenient way of making immediate payments. Therefore it can be argued that they should be included as part of M1. However, once the check limit is reached, such accounts are much less liquid than normal checking accounts. Therefore it makes sense to include MMDAs as part of M2 rather than M1.

5. How did the introduction of so-called NOW-accounts affect the money demand of M1 and M2?

How did it affect the income velocity of M1 and M2?

With the introduction of NOW-accounts, many people transferred funds from their saving accounts to these interest-earning checking accounts. This meant that more money balances were held in M1 assets and the income velocity for M1 decreased. Since M1 is part of M2, such transfers did not affect money balances held in M2 or the income velocity of M2.

6. Derive the square-root formula of the Baumol-Tobin transactions demand model. Then explain

how this formula can be used to explain that high-income individuals on average hold a smaller proportion of their income in money assets than low-income people.

The square-root formula can easily be derived by minimizing the total cost of holding money with respect to the number of transactions n. This total cost is the sum of the transaction cost (nt c) and the interest cost im d, with m d being the average cash balance, that is,

m d = Y/(2n).

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Therefore from C = nt c + (iY)/(2n) ==>

?C/?n = t c - (iY)/(2n2) = 0 ==> t c = (iY)/(2n2) ==> (t c Y)/(2i) = [Y/(2n)]2 = m d2

==> m d = [(t c Y)/(2i)]1/2.

According to this formula, money holdings increase proportionally less than income. This implies that individuals in higher income brackets can hold proportionally less money than people in lower income brackets. Most likely this is due to the fact that high-income individuals tend to have better access to financial markets than low-income individuals, which means that they have a lower probability of becoming illiquid.

7. Use the Baumol-Tobin transactions demand approach to calculate the interest elasticity of

money demand for transaction.

From the Baumol-Tobin approach we can derive the square-root formula, that is,

m d* = [(t c Y)/(2i)]1/2.

This equation shows that money demand (m d) is positively related to income (Y) but inversely related to the interest rate (i). From this square-root formula, the interest elasticity of money demand can be derived as follows:

?m d/?i = - [(1/2)[(t c Y)/(2i)]-1/2(t c Y/2i2) = - (1/2)(1/i)m d

==> [(?m d/m d)]/[(?i/i)] = (?m d/?i)(i/m d) = - 1/2

8. "According to the classical quantity theory of money, any decrease in nominal money supply

will lead to a decrease in the unemployment rate." Comment on this statement.

The classical quantity theory of money suggests that velocity is constant and that output stays at its full-employment level. Any change in nominal money supply will therefore lead to a proportional change in the price level. According to the classical quantity theory, a decrease in nominal money supply will lead to a decrease in the price level and not the unemployment rate.

9. Which is greater: the transaction velocity of money or the income velocity of money?

The income velocity of money only includes transactions involving final goods and services, whereas the transaction velocity of money includes all transactions, including intermediate goods and wealth transfers. Therefore the transaction velocity of money is greater than the income velocity of money.

10. "Financial innovation raises the velocity of money." Comment on this statement.

The money demand function can be expressed as a function of interest rates, income, and financial innovation (e), where a positive value of e reduces the demand for money, that is,

m d = L(i, Y, e).

Velocity is defined as V = (PY)/M = Y/(M/P).

If we assume that the money sector is in equilibrium, then money demand can be substituted for money supply, and we get

m d = L(i,Y,e)= M/P = m s ==> V = Y/L(i, Y, e) ==> V = f(Y,i,e),

that is, velocity is a function of income, the interest rate and financial innovation. Therefore, if there are financial innovations (and the value of e goes up), the demand for money declines. This raises the number of times a dollar bill circulates in the economy during a given period of time. In other words, it increases the income velocity of money.

11. "An increase in the income tax rate will increase the income velocity of money." Comment on

this statement. In your answer consider only the short-run effects of such a policy change. Restrictive fiscal policy, such as an income tax increase, will affect GDP negatively and lead to lower interest rates, at least in the short run. Since the income velocity of money is positively affected by an

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increase in income and the interest rate, velocity should decrease. Another way of getting to the same result is to look at velocity as the ratio of nominal GDP to nominal money supply, that is, V = (PY)/M.

Since restrictive fiscal policy leads to a (short-run) decrease in nominal GDP (PY), while nominal money supply (M) remains unaffected (the Fed was not involved in this fiscal policy measure), velocity (V) should decrease.

12. "Fiscal expansion will increase the income velocity of money." Comment on this statement. Expansionary fiscal policy increases income and the interest rate. Since the income velocity of money is positively affected by increases in income and the interest rate, the income velocity should go up. Similarly, from the equation MV = PY, it follows that V = (PY)/M. Since expansionary fiscal policy raises nominal GDP (PY) but does not affect nominal money supply (M), we should expect velocity (V) to go up.

13. Assume you know that the supply of money (M) has increased by 6%, real output (Y) has

increased by 2.5% and the income velocity (V) of money has dropped by 3%. What is the rate of inflation?

From the quantity theory of money equation (MV = PY) ==> %?M + %?V = %?P + %?Y ==>

%?P = %?M - %?Y + %?V ==> %?P = 6% - 2.5% + (-3%) = + 0.5%.

Therefore the rate of inflation (%?P) should be 0.5%.

Note:The equation that shows the percentage changes in money supply, output, velocity, and prices generally only applies for very small changes in these variables. Therefore, the result for this problem is just an approximation of the actual change we should expect in the price level.

14. Assume that M2 has increased by 8%, inflation has increased by 4%, and real output has

grown at a rate of 1.5% over the same time period. What does this imply for V2, the income velocity of M2?

From the equation MV = PY, we get %?M + %?V = %?P + %?Y. It follows that

8% + %?V = 4% + 1.5% ==> %?V = - 2.5%,

that is, V2 must have decreased by 2.5%. (The note for question 14 applies here as well.)

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