Macroeconomics
Chamberlin and Yueh
Chapter 5
Lecture slides
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The Money Market
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What is Money?
Monetary Aggregates
The Bond Market
Determining the Interest Rate
Demand for Money
Money Supply
Equilibrium in the Money Market
The Term Structure of Interest Rates: Yield Curves
Monetary Policy: Money Supply or Interest Rate?
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Learning Objectives
• Understanding the role of money in the economy
• Analysing the various mechanisms of money
transmission
• Comprehension of the determinants of the interest
rate
• Understanding the term structure of interest rates or
yield curves
• Assessing the impact of different forms of
monetary policy
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Money and Money Markets
• Money plays an important role in the economy. It is used
to settle the transactions which make up the circular flow of
income. Also, the price of holding money is the interest
rate, which has a role to play in determining consumption
and investment.
• Therefore, monetary policy – the act of controlling the
supply or price of money – may exert a powerful influence
over the economy.
• Like all prices, the interest rate is determined by demand
and supply in the money market.
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What is Money?
• Money is defined as anything which performs the following
four functions:
–
–
–
–
Medium of Exchange
A Unit of Account
A Store of Value
Standard for Deferred Payments
• The most common type of money, which is currency in the
form of notes and coins, is known as fiat money.
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Monetary Aggregates
• The monetary aggregate is the total quantity of money in an
economy. It is much harder to measure than one would have
first thought.
• A standard definition of the money supply is the total
amount of currency and demand deposits. These are
aggregates which can be used as a medium of exchange.
However, this is regarded as being a narrow definition of
the money supply.
• Once it is accepted that current accounts constitute part of
the money supply, it becomes questionable as to where to
draw the line. A broad definition of the monetary aggregate
would not just consist of currency and current accounts, but
also stocks of near money.
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Ratio of notes and coins to GDP
(M0/GDP), UK
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The Bond Market
• The opportunity cost of holding money is the rate of interest
that could have otherwise been achieved by investing in
bonds. It is for this reason that the interest rate is referred
to as the price of money.
• We start with a simple type of bond known as a Treasury
Bill (often referred to as a T-bill). The Treasury bill is a
means by which the government can borrow to fund its
deficits or to exert some influence in the money markets.
They are essentially short term (usually 90 days in the UK)
IOU’s, which promise to pay a fixed amount on maturity.
For example, the UK government could sell a bill offering
to pay £100 in 90 days’ time.
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The Bond Market
• The price at which this bill sells for is likely to be less than
£100, and this is what makes the bill attractive to investors.
Suppose the bill is sold for £98. This will offer the investor
a return of £2 in 90 days. The rate of return will simply be
given by: r  100  98  2.04%
98
• This is equivalent to an annual interest rate of
approximately 8%, because 90 days represents about a
quarter of a year. This rate of return can simply be
understood as the interest on the bill.
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The Bond Market
• In general terms, the rate of interest on a bond that
is purchased at price and pays on maturity is:

PP 
r
B
PB
• As T-bills are directly marketable assets, their price
and thus the rate of interest will change with
fluctuations in demand and supply in the bond
market. As bonds are a direct substitute for money,
the interaction between the bond and money
markets will be influential in determining the
interest rate.
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Determining the Interest Rate
• If the interest rate is the price of money, then
like all prices, it will be determined by the
forces of demand and supply.
• Once we know what factors are responsible
for influencing the demand and supply of
money, we will better understand how
interest rates are set in the money market.
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The Demand for Money
• A simple money demand function could be
written as follows: M d  LY , r, c
  
• The demand for money will depend on three
things: income (Y), interest rates (r), and the
cost of liquidating financial assets (c).
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The Demand for Money
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Changes in income or in the costs of
liquidating assets
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Baumol-Tobin Model
• This is a simple model of the demand for money which
incorporates many of the issues discussed above.
• It is essentially a model of cash management, asking how
many times a person should go to the bank during a certain
period of time, and therefore what their optimal holdings of
money will be.
• The choice is between making lots of trips to the bank and
holding relatively small amounts of money, or making few
trips to the bank but holding much larger cash balances. In
making this choice, a trade-off is faced. There is a cost of
making a trip to the bank; we call this a shoe-leather cost
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Baumol-Tobin Model
• This shoe-leather cost is essentially the same as the
liquidation cost mentioned above. Minimising these costs
would require us to make relatively few trips to the bank
and thus hold larger cash balances.
• However, the downside to this is that in holding more
money, we are giving up the interest that we would
otherwise have earned by leaving the money in the bank.
• The trade-off between the costs and benefits of holding
money is a choice between minimising liquidation costs or
minimising forgone interest payments.
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Baumol-Tobin Model
• Assume that in a given time period income Y is earned. If
this income is withdrawn straight away in one trip to the
bank and spent gradually over this period, then money
holdings would be as follows.
• The first trip to the bank is made straight away and all the
income Y is withdrawn. This means that average money
holdings will simply be Y/2.
• If two trips are made, half the income Y/2 is withdrawn
straight away, with the other half being withdrawn half way
through the period. The average money holdings in this
case are Y/4.
• If three trips were made to the bank, each of the three times
the bank is visited a total of Y/3 is withdrawn, meaning that
average money holdings are Y/6.
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Baumol-Tobin Model
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Baumol-Tobin Model
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Baumol-Tobin Model
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Baumol-Tobin Model
• Hopefully a pattern is beginning to emerge. So, in general
terms, if N trips are made to the bank then:
• Amount taken out each time = Y/N.
• Average money holdings = Y/2N.
• Time between trips to the bank = 1/N.
• The household must now decide the optimal number of trips
they should make to the bank and therefore the amount of
money to hold during this period.
• If every trip costs c, the total shoe-leather costs of making N
trips would equal Nc.
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Baumol-Tobin Model
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Baumol-Tobin Model
• Therefore, total costs (TC) associated with N trips
to the bank will be given by the sum of the shoeleather and foregone interest
costs:
Y
TC  r  Nc
N
• Effective cash management would aim to choose N
so as to minimise these total costs. These costs are
minimised, and therefore the optimal number of
trips, is where the shoe-leather and foregone
interest costs are equal.
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Baumol-Tobin Model
• From the parameters of the model (those who like calculus
can check for themselves by minimising TC with respect to
N), the optimal number of trips to the bank will be:
N 
rY
2c
• From this, we can simply devise the optimal average money
holdings as:
M 
Y
Yc

2N 
2r
• Optimal cash holding will increase with income and shoeleather (liquidation) costs and fall with increases in interest
rates. This corresponds to the properties of the money
demand function we set out earlier.
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Money Supply
• The supply of money consists of everything which
is available as a medium of exchange, which is the
total quantity of currency and demand deposits
(current accounts).
• In accepting this (to make the forthcoming analysis
much easier), we are disregarding the possible
existence of near money.
• Money Supply = Currency + Demand Deposits
• M=C+D
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Money Supply
• Although the central bank is the monopoly supplier of notes
and coins, the actual supply of money is largely determined
by the banking system.
• M0 is the aggregate amount of cash in circulation, which is
controlled by the central bank. M1 is the money aggregate
which includes M0, and also current accounts in the
banking sector.
• However, M1 is much larger than M0. In fact, throughout
recent history, the magnitude has been in the order of
around thirteen-fold.
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M1/M0 for the UK
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Money Creation
• To see how the banking sector can create
demand deposits, let us look at a bank’s
balance sheet.
Bank 1
Assets
Currency: £1000
Liabilities
Deposits: £1000
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Money Creation
• Banks run profitable businesses loaning out their
excess reserves and charging interest. If only 10%
of their currency needs to be held in reserve, this
means that 90% is available for loans. Therefore,
Bank 1 would be able to create loans to the value
of £900.
Bank 1
Assets
Currency: £100
Loans: £900
Liabilities
Deposits: £1000
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Money Creation
• Once Bank 1 has lent the money, the borrower will
deposit the £900 of currency in their own bank,
Bank 2. Exactly the same situation now occurs.
Bank 2 knows that they must only keep 10% of
their total currency in reserve, so loans to the value
of £810 (90% of £900) can be created.
Bank 2
Assets
Liabilities
Currency: £90
Deposits: £900
Loans: £810
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Money Creation
• The total change in deposits is represented by the total
change in the assets of the entire banking sector:
• Bank 1’s assets increase by £1000, Bank 2’s by £900 (0.9 x
£1000), Bank 3’s by £810 (0.9 x £900) and so on.
• The series representing the change in the banking sector’s
assets is:
M 1  £1000  0.9£1000  0.92 £1000  0.93 £1000  ..............
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Money Creation
• Summing this process to infinity, we achieve:
£1000 
1
£1000

 £10000
1  0.9
0.1
• Therefore, the original £1000 in cash (M0) increases the
money supply ( M1) by £10000, a factor of 10. This
implies that:
M 1
 10
M 0
• The creation of demand deposits is a feature of the
fractional reserve banking system, where the banking sector
knows that only a limited proportion of total reserves are
required to meet daily demands for cash. The total amount
of currency is known as the monetary base or the stock of
high powered money.
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The Money Multiplier
• The stock of high powered money is given by C and the reserve asset
ratio is given by rr:
M  C  1  rr C  1  rr  C  1  rr  C  ...............
2
3
• Using the sum to infinity, we achieve:
1
M 
C
1  1  rr 
• where
1
M  C
M  mC
rr
• The money multiplier is 1 over the reserve ratio.
m
1
rr
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Extensions to the multiplier theory
• There are two further considerations which may affect the
size of the money multiplier: Leakages and Banking
behaviour.
• Leakages: Not all currency necessarily finds its way into, or
stays in, the banking system. The banking sector can only
create deposits on its reserves. If households decide to hold
some of their deposits in currency, this reduces the reserves
of the banking sector and the ability to create money. The
currency deposit ratio (cr = C/D) represents the proportion
of deposits households hold as cash. If this exceeds zero,
then there is a leakage from the banking system, which will
reduce the size of the money multiplier.
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Leakages
• The money supply again consists of total currency
and demand deposits: M=C+D. The stock of high
powered money, H, or in other words, the monetary
base, is H=C+R. This consist of currency held by
households (C) and the reserves of the banking sector
(R).
M CD

H CR
• The money multiplier is simply the ratio of the total
money supply to the money base.
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Leakages
• Rewriting, where rr = (R/D), reserve deposit ratio.
• And,
M
cr  1

H cr  rr
, where M=m’H.
• As long as cr<0, it will be true that m’<m.
• Therefore, changes in the currency-deposit ratio of
m 
cr  1
cr  rr
households would change the value of the money
multiplier.
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Banking behaviour
• There are many reasons why the bank may hold higher
reserves than the minimum permitted reserve-deposit ratio.
• First, banks may not wish to advance loans if it considers
lending to be too risky. In a recession when bankruptcies
tend to rise, the risk of default on any loan also tends to rise
which may discourage bank lending.
• Second, a bank may decide to keep some reserves for future
business. For example, if future interest rates were
predicted to rise, the bank may withhold current lending
with the aim of lending in the future at the higher rate.
• These two factors both suggest that calculating the actual
money multiplier may be more complicated than finding the
inverse of the minimum permitted reserve-deposit ratio of
the banking sector.
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Changing the Money Supply
• The stock of money is independent of the interest rate, so
the money supply function will be vertical. Changes in the
money supply will lead to shifts in the function, an increase
to the right and a decrease to the left.
• There are effectively two ways in which the government
can control the money supply. It can either act to control
the stock of high powered money, or the size of the money
multiplier.
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Money supply function
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Open Market Operations
• By buying and selling bonds to the general public, the
government can attempt to control the size of the monetary
base, and therefore the money supply.
• When the government sells bonds, the private sector
purchases them with cash, drawn from the reserves of the
banking sector. The money supply would then be expected
to fall by an amount equal to the product of these reserves
and the money multiplier.
• If the government wished to increase the money supply,
then it would simply purchase bonds from the private
sector. Cash would then be deposited in the banks and lead
to a multiplied increase in the money supply.
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Reserve Asset Requirements
• Simply by controlling the size of the reserve asset
requirement (rr), the government can control the size of the
entire money stock.
• A higher reserve asset ratio will reduce the size of the
multiplier, and therefore the extent to which the money
supply can be expanded from the stock of high powered
money.
• A lower reserve-asset ratio will of course have the opposite
effect, and generate an increase in the money supply.
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Problems in controlling the money supply
• Estimating the size of the multiplier
• Near money
• Financial deregulation and off-shore
banking
• Example, financial deregulation in the UK
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M4/GDP, UK
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Equilibrium in the Money Market
• Equilibrium in the money market is simply
determined by the intersection of money demand
and money supply.
• Because bonds are the substitute to holding money,
a description of how the interest rate is determined
lies in how the money and bond markets interact
with each other.
• Anything that acts to shift the demand or supply of
money would be expected to change the
equilibrium interest rate.
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Money Market Equilibrium
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Changes in Money Demand/Supply
• Changes in income or the costs of
liquidating financial assets will lead to shifts
in the demand for money.
• An increase in the demand for money would
be expected to put upward pressure on the
interest rate.
• Changes in the money supply will lead to
simple shifts in the money supply schedule.
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Increase in income on money
demand
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Increase in money supply
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The Term Structure of Interest
Rates: Yield Curves
• The maturity of a bond is the length of time over which the
bond makes payments.
• The yield on a bond describes the per period return until its
maturity and can be thought of as the average return each
period. The yields on bonds with maturities of a year or
less are known as short run interest rates, whilst the yields
on bonds of longer maturities are described as long run
interest rates.
• There is no reason why the short run and long run interest
rates need to be the same. This is because the demand and
supply of money and therefore the equilibrium interest rate
can change over time.
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Yield Curves
• The term structure of interest rates describes the yields on
bonds of different maturities.
• The yield curve is a graphical representation of this concept,
which plots yields against maturity.
• If the yield curve is upward sloping, then it suggests that
future interest rates are expected to be above current rates.
• If the yield curve is downward sloping, then it suggests that
short term rates exceed long term rates.
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Yield Curves
• The yield at each maturity is calculated by
finding the geometric average of all the per
period interest rates.
• One period yield:  1  r1 
• Two period yield:  1  r 1  r 
• Therefore, if the interest rate is 2% this
period, and 5% in period two, then the two
period yield is 3.5%:
1

1  0.021  0.05 
2
1.02 1.05  1.035
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Yield Curves
• In general, N-period yield
 n 1  r1 1  r2 ............1  rn 
• This can be approximated by taking the
arithmetic mean of all the interest rates.
• N-period yield 1  r1   1  r2   ...........  1  rn 

n
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Yield Curves
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Yield Curves
• It is a useful description of the expectations that financial
markets have concerning the future state of the economy.
• Normally, an upward sloping yield curve implies that
growth and/or inflation will increase in the future, so long
term interest rates exceed those in the short term.
• Alternatively, a downward sloping yield curve is an
indicator that growth and/or inflation will be lower in the
future, implying a downward trend in interest rates over
time.
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Monetary Policy: Money Supply or
Interest Rate?
• The government, through its central bank, is the
monopoly supplier of currency.
• It is a standard result that monopolies cannot
control both the price and quantity of their output.
They can either set the price, and let output be
determined by demand, or alternatively, they can
set the supply, and let the price be determined by
demand and supply.
• Exactly the same result must apply to the operation
of monetary policy. The government cannot target
both the money supply and the interest rate.
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Monetary Policy: Money Supply or
Interest Rate?
• The general mechanism which central banks use to set the
interest rate is known as discounting.
• If the bank wishes to change the interest rate, it could sell
excess bonds to the private sector, which will purchase
these using reserves from their bank accounts.
• This will make the banking sector short of cash, which
would be forced to borrow reserves from the central bank in
order to maintain sufficient reserves to meet daily demand
for cash.
• The rate of interest at which the central bank makes these
loans is called the discount rate. By changing the discount
rate, the government can effectively change the rate of
interest set by the entire banking sector.
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Summary
• We have analysed what constitutes money and its role in the
economy.
• We have analysed the various mechanisms of money
transmission.
• The determinants of the interest rate, including money
demand, supply and equilibrium in the money market, were
examined.
• In this chapter, we also analysed the term structure of
interest rates or yield curves.
• Finally, we concluded with an assessment of different forms
of monetary policy.
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