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Lecture 3: Ch.4 Financial Markets
4.1 The Demand for Money
• Suppose there are only two assets, money and bonds:
Money (= currency + checkable deposits) pays no interest;
Bonds pay a positive interest i.
• The demand for money refers to how much wealth people want to hold in a liquid form.
• Trade-off exists between liquidity and positive rate of return.
4.1.1 Money Demand (Md
) Function
• Factors affecting the money demand:
) $ level of transactions ; )d d
i Y M ii i M↑ ⇒ ↑ ⇒ ↑ ↑ ⇒ ↓
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• In a functional form,
d
M $ ( )Y L i= ,
where $Y = nominal income, and ( )L i = function of the interest rate i,
డ()
డ
< 0.
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4.2 The Determination of the Interest Rate without Checkable Deposits
4.2.1 Money Demand, Money Supply, and the Equilibrium Interest Rate
• For simplicity, assume the Fed fixes money supply (Ms
) at M and the only money in the
economy is currency.
• For financial market equilibrium, Ms
= Md
.
M = $YL(i) ⋯ ⋯ ⋯ ⋯ LM relation
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4.2.2 Monetary Policy and Open Market Operations
• How does the central bank control Ms
? Through open market operations (OMOs)!
i) The central bank buys bonds to increase Ms
⇒ expansionary OMOs
ii) The central bank sells bonds to decrease Ms
⇒ contractionary OMOs
• More about bonds: interest rate (yield) and bond prices
Suppose you buy a bond that will pay you $100 one year from now. Then what should be
the bond price $PB today?
• The rate of return (or interest) on holding a $100 bond for a year is ݅ =
$ଵି$ಳ
$ಳ
.
Solving for the bond price, we have
$100
$
1
BP
i
=
+ .
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• For example, if the interest rate is 10%, the bond price is roughly $91. Or, if you know that
the bond price is $91, the interest rate is roughly 10%. The bond price and the interest rate
tell us the same story.
• Notice that there is an inverse relation between i and $PB; The higher the price of bond,
the lower the interest rate. Thus, expansionary (contractionary) OMOs lead to an increase
(decrease) in the price of bonds and a decrease (increase) in the interest rate.
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4.3 The Determination of Interest Rate in the presence of Checkable Deposits
4.3.1 What Banks Do as Financial Intermediaries
• The Balance Sheet of Banks and the Central Bank
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• Banks do their business mainly by lending to people and companies, so loans make up a
large part of their assets.
• The banks keep reserves to meet depositors’ withdrawal and also to meet the central bank’s
required reserve ratio: the central bank requires banks to keep the ratio of bank reserves to
checkable deposits to be about 10% in the U.S.
• The liabilities of the central bank are the money it has printed, central bank money. Part of
the money printed is in the hands of the public and part of the money is held as reserves by
banks.
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4.3.2 The Supply and the Demand for Central Bank Money
• This is the easiest way to think about how the interest rate in the economy is determined.
• Demand for central bank money
= Demand for currency by people + Demand for reserves by banks
• The supply of central bank money is under the direct control of the central bank.
• The equilibrium interest rate is such that the demand and the supply for central bank money
are equal.
1) The Demand for Money
• Remember that the demand for money is Md
= $YL(i), but we did not distinguish the
demand for currency and checkable deposits before.
• Let’s assume that people hold a fixed fraction “c” of their money in currency and define
the demand for currency as CUd
= cMd
and
the demand for checkable deposits as Dd
= (1−c)Md
.
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2) The Demand for Reserves
• Define the reserve ratio as ߠ. Then we can write reserves (R) as a portion of deposits (D):
R = ߠD.
• Now bring in the demand for checkable deposits by people, we have the demand for
reserves by banks: Rd
= ߠDd
= ߠ(1−c)Md
.
3) The Demand for Central Bank Money (Hd
)
• The demand for central bank money is the sum of the demand for currency and the demand
for reserves: Hd
= CUd
+ Rd
• Using the definitions above, we can write:
Hd
= cMd
+ ߠ(1−c)Md
= [c + ߠ(1−c)]Md
= [c + ߠ(1−c)]$YL(i)
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4) The Determination of the Interest Rate
• The supply of central bank money is whatever the central bank has printed, and let’s call it
H. Then, the equilibrium in the market for central bank money requires:
H = [c + ߠ(1−c)]$YL(i)
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4.4 Money Demand, Money Supply, and the Equilibrium Interest Rate
• Now we derive an eq’m condition in terms of the overall supply and demand for money.
• We start with the equilibrium condition of central bank money and divide both sides by
[c + ߠ(1−c)] to get
[ ]
s d1
H $ ( ) M M
(1 )
Y L i
c cθ
= ⇔ =
+ −
• The condition above states that the overall supply of money (currency + checkable deposits)
and the overall demand for money must be equal in equilibrium.
• Notice that 0 < c + ߠ(1−c) < 1 and
ଵ
ሾାఏ(ଵି)ሿ
> 1.
So, the term
ଵ
ሾାఏ(ଵି)ሿ
is called the money multiplier.
• Remember that the central bank money (H) is also called high-powered money or the
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monetary base. According to Blanchard, “The term high powered reflects the fact that
increases in H lead to more than one-for-one increases in the overall money supply and are
therefore high powered. In the same way, the term monetary base reflects the fact that the
overall money supply depends ultimately on a “base” – the amount of central bank money in
the economy.”
• How does the money multiplier work?
Suppose people do not hold currency and only hold checkable deposits, or c = 0. The money
multiplier is then
ଵ
ఏ
. To further simplify, let’s assume ߠ = 0.1 and the money multiplier is
then 10. Now the Fed conducts an open market purchase of $100 (i.e. the Fed buys $100
worth of bonds from someone, say Ms.X). To buy the bonds, the Fed has to create $100
central bank money, or H increases by $100. Once Ms.X deposits $100 in her account at
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Bank A, the bank keeps $10 as reserves and makes a loan of $90 (why?). Let’s say Mr.Y
takes the $90 loan from Bank A. Again, once Mr.Y deposits $90 in his account at Bank B,
the bank keeps $9 and makes a loan of $81. As long as there are a number of banks in the
economy, this process keeps going on and on. Consequently, the final increase in money
supply (equivalently, the sum of increase in checkable deposits) is 10 × $100 = $1,000.
• Now you should know why we call
ଵ
ఏ
the multiplier.
• In words, when the Fed increases the central bank money (or monetary base, or high-
Powered money) by some amount, the final increase in money supply is that amount times
the money multiplier.
• Ask yourself: will the money multiplier be smaller or larger if
a) people do hold currency, and
b) the reserve ratio is higher?
