Brief answers to problems and questions for review
1.
Money has to perform three separate but important functions. First, it must act as a
medium of exchange. This is money’s most important function and without money
every price of every good would be a relative price. Money’s second purpose is to
function as a unit of account. This function is analogous to using standardized
measures of length and weight. The efficiency of economic transactions is greatly
enhanced if there is only one measure of money that is universally used as a unit of
account. When this is the case, all economic transactions are easier to compare.
Money’s final function is the store of value function. As the streams of income and
consumption do not perfectly match, most of us store money in a convenient place
such as a checking account. Since the money that is stored is not perishable we can
use money earned today to consume goods and services at some point in the future.
Money provides a convenient way to smooth out any inconsistencies between money
earned and money spent. Money can also help to solve the problem of storing value
earned early in life for use later in life, such as saving for retirement.
2.
The monetary base (B) is composed of the sum of cash in the hands of the public (C)
and the total quantity of bank reserves (R) on deposit at the central bank. A country’s
money supply is equal to the monetary base multiplied by the banking money
multiplier. The banking money multiplier is equal to 1 divided by the reserve
requirement. If the monetary base is $100 billion and the reserve requirement for
banks is 20 percent, the money supply would be $500 billion.
3.
The three tools the central bank can use to control the monetary base are the discount
rate, the reserve requirement, and open market operations. The discount rate is the
interest rate the central bank charges commercial banks for borrowing reserves. When
a commercial bank borrows reserves from the central bank, the monetary base rises by
an equal amount. Given the money multiplier, as total reserves of the banking system
increase, the money supply increases by a multiple of that amount. When a central
bank lowers the discount rate, commercial banks tend to borrow more from the central
bank and bank reserves rise and the money supply rises. When the central bank
changes the reserve requirement, two effects occur. First, changes in the reserve
requirement change the amount of funds a bank must keep on deposit at the central
bank. If the reserve requirement were lowered, banks would only need to hold a
smaller fraction of their deposits as reserves and could make more loans, expanding
the money supply. Second, changes in the reserve requirement change the size of the
money multiplier. For instance, if the reserve requirement were lowered from 10
percent to 8 percent, the value of the money multiplier would rise from 10 to 12.5. In
this case, each dollar in the monetary base is multiplied by a larger amount. As a
result, a relatively small change in the reserve requirement brings about relatively
large changes in the money multiplier. When the central bank conducts open market
operations, it buys and/or sells bonds. When the central bank buys or sells a bond,
either the banking system’s reserves change or the amount of currency in circulation
changes. In either of these two cases, this transaction changes the monetary base. As a
result, the money supply within the country will change by a multiple of that amount.
4.
To see why this must be so, the monetary base (B) consists of total depository
reserves (R) plus cash in the hands of the public (C). In addition, a country’s money
© 2015 W. Charles Sawyer and Richard L. Sprinkle
supply (M) consists of total deposits (D) plus cash in the hands of the public (C). If
we assume no currency drains then C in both the monetary base and the money supply
is zero. In equilibrium all depository institution reserves are required reserves (RR) =
[r]D, where r denotes the required reserve ratio imposed by the central bank. The
monetary base equals B = [r]D and total deposits of all financial institutions are D = B
(1/r). To put this in terms of the money supply, rather than deposits, MS = D = B (1/r)
and the money supply is equal to the monetary base multiplied by the money
multiplier.
5.
Narrowly defined, the money supply includes cash in the hands of the public and
demand deposits. Broadly defined, money includes narrow money plus near monies
such as savings accounts, time deposits, and short-term government securities.
6.
The supply of money is equal to the monetary base (B) multiplied by 1/r where r is the
reserve requirement. If r goes up then the money supply will fall. A decrease in r
would cause the money supply to rise.
7.
The discount rate is the interest rate that the central bank charges private banks for
borrowing. If the discount rate falls, banks will tend to borrow more from the central
bank and the reserves of the banking system will rise. A rise in reserves will increase
the monetary base and the money supply. An increase in the discount rate would tend
to lead to less borrowing from the central bank. In turn, this would reduce the reserves
of the banking system, the monetary base, and the money supply.
8.
The US reserve requirement is approximately 10 percent and Germany’s is
approximately 2 percent. If the US suddenly adopted the reserve requirement that
Germany uses, the US money supply would dramatically increase. First, changes in
the reserve requirement change the amount of funds a bank must keep on deposit at
the central bank. When the reserve requirement is lowered, banks would only need to
hold a smaller fraction of their deposits as reserves and could make more loans,
expanding the money supply. Second, as the reserve requirement is lowered the size
of the money multiplier changes. For instance, if the reserve requirement were
lowered from 10 percent to 2 percent, the value of the money multiplier would rise
from 10 to 50. In this case, each dollar in the monetary base is multiplied by a larger
amount.
9.
If the central bank buys a bond the reserves of the banking system will rise. A bond is
not part of the monetary base but the payment for the bond is. This would cause the
monetary base and the money supply to rise. An open market sale would have the
reverse effect. The central bank would be taking in reserves from the sale of the bond
and the reserves of the banking system would fall. This would reduce the monetary
base and the money supply.
10.
There are potentially three tools of monetary policy. These are changes in the reserve
requirement, changes in the discount rate, and open market operations. In a country
that does not have an active secondary market for government bonds, open market
operations cannot be performed. In such cases, the central bank must try to control the
money supply using changes in the reserve requirement and/or changes in the
discount rate.
© 2015 W. Charles Sawyer and Richard L. Sprinkle
11.
This demand for money is related to three factors. First, it is inversely related to the
interest rate. As interest rates rise, the demand for money declines and vice versa. This
relationship indicates that fluctuations in the interest rate will cause the demand for
money to fluctuate. Second, the demand for money is directly related to the price
level. As the price level rises, the average value of any economic transaction
(purchase or sale) rises. As the average price level increases, individuals and firms
increase their holdings of money in order to maintain their real level of spending.
Finally, the demand for money is directly related to the real level of economic activity
or real income. As the economy’s real income rises, consumers buy more goods and
services. In order to purchase these additional goods and services, consumers must
increase their holdings of money. In summary, the aggregate demand for money in an
economy is inversely related to the interest rate and positively related to the price
level and the level of real income and these relationships can be expressed in the
following manner: MD = f (-i, + P, + Y) where i is the interest rate; P is the price
level; and Y is real GDP.
12.
If the Federal Reserve decreases the money supply, this will cause interest rates in the
US to rise, assuming the demand for money is constant. The rise in US interest rates
causes a capital inflow to the US from foreign countries. This capital inflow causes an
increase in the supply of foreign exchange. The increase in supply causes a decrease
in the exchange rate and the dollar appreciates against foreign currencies.
13.
a. As the domestic price level increases, the demand for money increases and
interest rates rise.
b. As domestic real incomes rises, the demand for money increases and interest
rates rise.
c. As the domestic price level declines, the demand for money declines and
interest rates fall.
d. As domestic real incomes fall, the demand for money declines and interest
rates fall.
14.
Suppose that the Mexican central bank increases the money supply. This increase in
the money supply will cause interest rates in Mexico to fall, assuming the demand for
money is constant. The fall in Mexican interest rates causes a capital outflow from
Mexico to the US. This capital outflow causes an increase in the supply of foreign
exchange. The increase in the supply of foreign exchange causes a decrease in the
exchange rate and the dollar appreciates against the Mexican peso.
15.
If the demand for money in the US declines, this will cause interest rates in the US to
fall, assuming the supply of money is constant. The fall in US interest rates causes a
capital outflow from the US to foreign countries. This capital outflow causes an
increase in the demand for foreign currencies. The increase in the demand for foreign
exchange causes an increase in the exchange rate and the dollar depreciates against
foreign currencies.
16.
The relationship between interest rates in two countries and the spot and forward
exchange rates can be shown as follows: let
A
=
the amount of dollars to be invested for three months
© 2015 W. Charles Sawyer and Richard L. Sprinkle
rUS
rUK
S
F
=
=
=
=
the three-month interest rate in New York
the three-month interest rate in London
the spot-exchange rate, dollars per pound
the three month forward exchange rate, dollars per pound
Consider a US investor who has A dollars available for a three-month investment. The
investor would invest in New York when:
A(1 + rUS)
>
A(1/S)(1 + rUK)F
The investor would invest in London when:
A(1 + rUS)
<
A(1/S)(1 + rUK)F
Interest parity prevails when the profitability in London is equal to the profitability in
New York. This is when:
A(1 + rUS)
=
A(1/S)(1 + rUK)F
Now, define the forward difference (d) as follows:
d
=
=
(F – S)/S
(F/S) – 1
The pound is at a forward premium when d > 0, and the pound is at a forward
discount when d < 0. Using the interest parity condition, and the definition of the
forward difference, one obtains the following:
A(1 + rUS)
(1 + rUS)
(1 + rUS)
rUS
rUS
rUS
=
=
=
=
=
=
A(1/S)(1 + rUK)F
(1/S)(1 + rUK)F
(F/S)(1 + rUK)
(F/S)(1 + rUK) – 1
(d + 1)(1 + rUK) – 1
d + rUK + d(rUK)
The term d(rUK) is assumed to be zero because it is the product of two small fractions.
As a result,
rUS
=
d + rUK
This shows that the currency of the low interest rate country is at a forward premium.
17.
In order to make a decision one would need to know what the current exchange rate is
and the future exchange rate over the relevant time period. It is the joint knowledge of
the differences in the interest rate and potential changes in the exchange rate that is
necessary to make an investment decision.
18.
A basic principle embodied within the balance of payments statement is that over time
a country’s inflows and outflows of money are balanced. The interaction of the
current account and the capital account jointly determined this balance. If the current
© 2015 W. Charles Sawyer and Richard L. Sprinkle
account is negative, then the balance of capital flows has to be positive. If the current
account was positive, then the balance of capital flows must be negative. We can
further analyze this relationship between trade flows, capital flows, and the
equilibrium exchange rate using the demand and supply of foreign exchange. Without
capital flows, price levels and income would primarily determine the exchange rate.
Exchange rates and trade flows would respond to changes in incomes and price levels
and a country’s current account would continually balance. However, with capital
flows, as the money supply and interest rates change, capital flows are affected. As
capital flows change, the exchange rate changes. The current account is affected and
the inflow of capital causes a current account deficit.
19.
When there are no capital flows between countries, the demand and supply of foreign
exchange will balance the current account (Panel A). When capital flows are
introduced into the foreign exchange market (Panel B), the total inflows and outflows
of foreign exchange balance. However, the new equilibrium balances both the current
account and capital flows. In this case, an inflow of capital creates a current account
deficit.
© 2015 W. Charles Sawyer and Richard L. Sprinkle
Exchange Rate
Dollar-Pound
Supply of Pounds
$/£
Panel A
Foreign Exchange
Market Without
Capital Flows
E
Demand for
Pounds
Pounds
Exchange Rate
Dollar-Pound
Supply of Pounds (S)
S1
$/£
$/£1
E Capital
Inflow
G
Panel B
Foreign Exchange
Market With
Capital Flows
F
Demand for Pounds
Pounds
© 2015 W. Charles Sawyer and Richard L. Sprinkle
20.
a.
$/FX
S
S1
R0
R1
X
M
D
FX
Examine the figure where we have graphed the demand and supply of foreign
exchange and the equilibrium exchange rate without capital flows. The current
account is balanced at the equilibrium exchange rate (R0) – meaning exports equal
imports. Now, let’s introduce capital flows between countries. Assume that there is a
capital inflow into the US. In this case, investors will sell foreign currency and buy
dollars in order to move capital into the US. This capital movement would cause the
supply of foreign currency to shift to the right from S to S1 and the dollar appreciates.
The new equilibrium exchange rate occurs at the intersection of D and S1, where total
inflows and outflows of foreign exchange balance – R1. Even though total inflows and
outflows of foreign currency balance, the current account is in deficit. Total exports of
goods and services are shown where the new equilibrium exchange rate crosses the
original supply curve. At the new exchange rate, imports of goods and services are
greater than exports of goods and services, indicating a current account deficit.
b.
$/FX
R1
S
M
X
R0
D1
D
FX
Examine the figure where we have graphed the demand and supply of foreign
exchange and the equilibrium exchange rate without capital flows. The current
account is balanced at the equilibrium exchange rate (R0) – meaning exports equal
imports. Now, let’s introduce capital flows between countries. Assume that there is a
capital outflow from the US; in this case, investors will sell dollars and buy foreign
currency in order to move capital out of the US. This capital movement causes the
demand for foreign currency to shift to the right from D to D1 and the dollar
depreciates. The new equilibrium exchange rate occurs at the intersection of D1 and S,
© 2015 W. Charles Sawyer and Richard L. Sprinkle
where total inflows and outflows of foreign exchange balance – R1. Even though total
inflows and outflows of foreign currency balance, the current account is in deficit.
Total imports of goods and services are shown where the new equilibrium exchange
rate crosses the original demand curve. At the new exchange rate, imports of goods
and services are less than exports of goods and services, indicating a current account
surplus.
© 2015 W. Charles Sawyer and Richard L. Sprinkle