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Chapter 28
Money, Interest Rates, and
Economic Activity
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In this chapter you will learn
1. why the price of a bond is inversely related to the market
interest rate.
2. how the demand for money is related to the interest rate,
the price level, and real GDP.
3. how monetary equilibrium determines the interest rate in
the short run.
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In this chapter you will learn
4. about the transmission mechanism of monetary policy.
5. the difference between the short-run and long-run effects of
monetary policy.
6. when monetary policy is most effective in influencing real
GDP in the short run.
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28.1 UNDERSTANDING BONDS
For simplicity, we assume that people have two types of
financial assets:
- money (earns no interest)
- bonds (earn interest)
For readers interested in learning more about the stock market,
the market in which equities are traded, look for “A Beginner’s
Guide to the Stock Market” in the Additional Topics section
of this book’s MyEconLab.
www.myeconlab.com
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Present Value and the Interest Rate
Present value:
- the value now of one or more payments or receipts
made in the future
Consider an asset that pays $X in one year’s time. If the
interest rate is i% per year, the PV of the asset is
PV = $X/(1+i)
Notice that, ceteris paribus, the PV is negatively related to the
interest rate.
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Present Value and the Interest Rate
Examples
Consider an asset that pays $100 in one year’s time. If the interest rate is
5% per year, the PV of the asset is
PV = $100/(1.05) = $95.24
If the interest rate is 2% per year, the PV of the asset is
PV = $100/(1.02) = $98.04
If the interest rate is 10% per year, the PV of the asset is
PV = $100/(1.10) = $90.91
The PV is negatively related to the interest rate.
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Present Value and the Interest Rate
The PV is the sum of money that you would need to invest
today at interest rate i in order to have $X in n years time
PV = $100/(1.05) = $95.24
or $95.24(1.05) = $100
If the interest rate is 2% per year, the PV of the asset is
PV = $100/(1.02) = $98.04
or $98.04(1.02) = $100
If the interest rate is 10% per year, the PV of the asset is
PV = $100/(1.10) = $90.91
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or $90.91(1.10) = $100
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Present Value and Time Period
Examples
Consider an asset that pays $100 in one year’s time. If the interest rate is
5% per year, the PV of the asset is
PV = $100/(1.05) = $95.24
If the payment is in two year’s time
PV = $100/(1.05)2 = $90.70
If the payment is in ten year’s time
PV = $100/(1.05)10 = $61.39
Notice that, ceteris paribus, the PV is negatively related to the
length of time to payment of the money.
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Present Value and the Time Period
The PV is the sum of money that you would need to invest
today at interest rate i in order to have $X in n years time
Consider an asset that pays $100 in one year’s time. If the interest rate is
5% per year, the PV of the asset is
PV = $100/(1.05) = $95.24
or $95.24(1.05) = $100
If the payment is in two year’s time
PV = $100/(1.05)2 = $90.70
or $90.70(1.05)(1.05) = $100
If the payment is in ten year’s time
PV = $100/(1.05)10 = $61.39
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or $61.39(1.05)10 = $100
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A Sequence of Future Payments
OPTIONAL
Consider this, Derek Jeter is 30 years of age. He quits the
Yankees to play for Boston. You read in the newspaper that
he got a three year contract ‘worth’ $73 million.
Well, actually you read on and find that the contract is
as follows: - $1 million per year for each of the next three years plus
a $70 million retirement payment at age 55.
If the current interest rate is 7% what is this contract worth today?
PV = $1,000,000/(1.07) + $1,000,000/(1.07)2 + $1,000,000/(1.07)3
+ $70,000,000/(1.07)25
= $934,579 + $873,439 + $816,298 + $12,897,442
= $15,521,758
contract
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If the Red Sox deposit $15,521,758 in the
bank today, then they can pay for Jeter
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A Sequence of Future Payments
OPTIONAL
You cannot play lotteries if you do not know about present values.
A million dollars a year for life! What’s that worth?
Consider a million dollars a year for 20 years! Is this a $20 million dollar
lottery prize?
Well, actually not - If the current interest rate is 8% what is a million
dollars a year for twenty years worth?
Consider the PV of the last $1 million (20 years from now)
PV = $1,000,000/(1.08)20 = $1,000,000 / 4.6609
= $214,548
If you work out all the terms the PV of $1 million a year for 20
years is actually $9,818,000 (invest it at 8% and you can withdraw
$1 million a year for 20 years).
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A Sequence of Future Payments – a bond example
Suppose a $1,000 bond pays $100 at the end of each of three
years, at which point it is redeemed (the $1,000 is returned to
the investor). What is the PV if the interest rate is 7 percent?
PV =
$100 + $100 + $1100
1.07 (1.07)2 (1.07)3
PV = $100/1.07 + $100/1.1449 + $1100/1.2250
PV = $93.46 + $87.34 + $897.96 = $1,078.76
Again $1,078.76 invested at 7% today would generate the above
stream of annual payments ($100, $100 and $1,100)
What would you pay for such a bond ( such a promise)? - $1,078.76
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Again consider a bond that pays $100 at the end of each of three years, at
which point it is redeemed and an additional $1,000 is returned to the
investor. What would you pay for such a bond? – it depends on the current
interest rate
If the interest rate is 10% then,
$100 + $100 + $1100
1.10 (1.10)2 (1.10)3
PV = $90.01 + $82.64 + $826.45 = $1000.00
If the interest rate is 7% then,
PV =
$100 + $100 + $1100
1.07 (1.07)2 (1.07)3
PV = $93.46 + $87.34 + $897.96 = $1,078.76
If the interest rate is 12% then,
PV =
PV =
$100 + $100 + $1100
1.12 (1.12)2 (1.12)3
PV = $89.29 + $79.72 + $782.96 = $951.97
Conclusion: if the market rate of interest goes up (down)
then the price of existing bonds (promises) goes down (up)
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A Sequence of Future Payments - the general formula
PV =
R1 + R2 + … + RT
(1+i) (1+i)2
(1+i)T
This simple present value formula tells how to price
any promise of future payments.
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Present Value and Market Price for an asset
Consider a competitive market for bonds.
- buyers should be prepared to pay no more than the
bond’s PV
- sellers should be prepared to accept no less than the
bond’s PV
 the equilibrium market price of a bond (or other
financial asset) should be the PV of the stream of income
generated by the bond.
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Bond Yields
Bonds are sold as a promise to pay a certain dollar amount
of interest each period plus a redemption amount at the end
of the term of the bond
For example: If you buy a two year bond which promises to
pay $100 at the end of each year and an additional $1,000
at the end of the second year. You pay $1,000 for this
bond. This bond would have a coupon rate of 10%
($100/$1,000 or 10%)
The bond yield is that discount rate (interest rate) which
equates the PV of the promised future payments to the price
of the bond
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Bond Yields
You paid $1,000 for a promise to pay $100 at the end of
year one and $1,100 at the end of second year two.
Term to maturity of the bond - 2 years
Issuing price of the bond (face value) - $1,000
Coupon payment - $100
Coupon rate on bond - 10%
(10% each year ($100/$1,000))
What is the yield (implied interest rate) on this bond?
$1,000 = $100/1.10 + $1,100/(1.10)2 = $1,000
This investment makes sense if the current market interest rate is 10%.
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Bond Yields
What if the market rate of interest falls to 5%?
New bond purchasers are paying $1,000 for a promise to pay $50 at the
end of year one and $1,050 at the end of second year.
What is the price of your old bond now that interest rates have gone
down? Recall, you get $100 the first year and $1,100 at the end of the
second year!
PV = $100/1.05 + $1,100/(1.05)2 = $1,092.97
To make the yield on your bond 5% it must sell for $1,092.97
You should not accept less than $1,092.97 for your bond. Buyers
should be willing to pay $1,092.97 for your bond.
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Bond Yields
What if the market rate of interest rises to 15%?
New bond purchasers are paying $1,000 for a promise to pay $150 at the
end of year one and $1,150 at the end of second year two.
What is the price of your old bond now that interest rates have gone up?
Recall, you get $100 the first year and $1,100 at the end of the second
year!
PV = $100/1.15 + $1,100/(1.15)2 = $918.71
To make the yield on your bond 15% it must sell for $918.71
No investor would pay more than $918.71 for your bond
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Interest Rates, Market Prices and Bond Yields
This discussion leads to two important propositions:
1. The PV of an existing bond is negatively related to the market
interest rate.
2. The market price for a bond should equal its PV.
Since a bond’s yield is inversely related to its price, we conclude that:
If the market rate of interest falls then the price of bonds will increase.
If the market rate of interest increases then the price of bonds will
decrease.
ALSO
If investors bid up (down) the price of existing bonds, then the interest
rate will fall (rise).
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Interest Rates, Market Prices and Bond Yields
Conclusion: The price of bonds is inversely related to the
market rate of interest
As a simplification we can say that the price of bonds = 1/i
Note it works both ways:
If the demand for bonds increases this drives up the price of
bonds and i falls (since Pb = 1/i).
But also
If interest rates fall, then the price of bonds will increase (since
Pb = 1/i).
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The bond market?
BS
•
pB2
pB0
B’D
•
BD
B1
B0
Quantity of Bonds
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If the demand for bonds
increases (shifts out),
then the equilibrium
price of bonds increases
– but an increase in the
price of bonds means
the interest rate must
have fallen (since Pb =
1/i).
Investors want to invest more in
bonds so they drive up their prices
– drive down the interest rate that
borrowers must pay.
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The bond market?
BS
•
pB0
•
pB2
BD
B1
B0
Quantity of Bonds
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B’S
If the supply of bonds
increases (shifts out),
then the equilibrium
price of bonds
decreases – but an
decrease in the price of
bonds means the
interest rate must have
risen (since Pb = 1/i).
Borrowers want to borrow more by
issuing bonds so they drive down
their prices – drive up the interest
rate inducing more investment in
bonds.
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Bond Riskiness - an aside
An increase in the riskiness of any bond leads to a decline in
its expected PV, and thus to a decline in the bond’s price
 high risk leads to high yield
APPLYING ECONOMIC CONCEPTS 28-1
Understanding Bond Prices and Bond
Yields
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28.2 THE DEMAND FOR MONEY
Reasons for Holding Money
The amount of money that everyone wishes to hold is the
demand for money.
The opportunity cost of holding money is the interest that
could have been earned if the money had been used to
purchase bonds or other interest earning investments.
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*
Recall
Interest are not
always as low
as they are
currently
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There are three reasons for holding money:
• the transactions motive
f (P, real GDP)
• the precautionary motive - liquidity f (P, real GDP, i)
• the speculative motive
f (i, expectations)
The Determinants of Money Demand
We focus on three variables:
- real GDP (+)
- the price level (+)
- the interest rate (-)
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This money demand (MD) curve is sometimes called
the liquidity preference function.
i
•
i1
i0
Changes in Y or P cause
the MD curve to shift.
•
MD(Y,P)
M1
M0
Quantity of Money
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Changes in the interest rate
cause movements along
the MD curve.
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Money Demand: Summing Up
- + +
MD = MD (i, Y, P)
Remember there are two assets — bonds and money.
The decision to hold money is the same as the decision not
to hold bonds or other interest/income earning investments.
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28.3 MONETARY EQUILIBRIUM AND
NATIONAL INCOME
Monetary Equilibrium
MS excess supply
of money
•
i2
•
i0
excess demand
for money
•
i1
MD
M1
M2 M0
Quantity of Money
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Monetary equilibrium
occurs when the
quantity of money
demanded equals the
quantity of money
supplied:
 equilibrium interest
rate
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Monetary Equilibrium – what’s happening?
Whatever the MS someone is holding it
If MS > MD (excess supply of money) at the current i
MS excess supply
The public will want to
decrease their money holdings.
How?
of money
•
i2
•
i0
excess demand
for money
•
i1
M1
M2 M0
Quantity of Money
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By using the excess money to
buy bonds (which earn
interest).
MD
But as the demand for bonds
goes up, bond prices rise – but
that means interest rates are
falling.
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Monetary Equilibrium – what’s happening in the
bond market?
If MS > MD (excess supply of money) at the current i
BS
The public will want to
decrease their money
holdings.
•
pB2
By buying bonds.
pB0
B’D
•
•
pB1
B1
B2 B0
Quantity of Bonds
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BD
The demand for bonds shifts
out and the equilibrium price
of bonds increases – but an
increase in the price of bonds
means the interest rate must
have fallen.
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Monetary Equilibrium – what’s happening?
If MS > MD (excess supply of money) at the current i, the public might
Buy bonds but they might also buy other assets (anything that
promises a return on their investment (money).
MS excess supply
of money
•
i2
•
i0
excess demand
for money
•
i1
M1
M2 M0
Quantity of Money
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MD
Alternatively – recall that banks
create money by making loans.
Think of the Ms as the amount
of money the banks can create
(and lend out) But they must
get us to borrow it. How?
By lowering interest rates.
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What’s happening in the financial (asset) markets in general?
If MS > MD (excess supply of money) at the current i, the public might
buy bonds but they might also buy other assets (anything that
promises a return on their investment (money).
Equities S
•
TSXB2
TSXB0
In general this situation means
that the public will want to look
for a place to ‘invest’ the excess
money that they hold.
Equities D’
•
Equities D
E0
We keep the story simple by
focusing on the bond market but the
excess money might end up flowing
into any asset – the stock market,
junk bonds, housing, foreign debt,
etc.
Sub-prime mortgages
E1
Quantity of Equities
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What’s happening in the financial (asset) markets in general?
If MS > MD (excess supply of money) at the current i
What determines where the ‘new
money’ shows up? Many things but
basically banks must find new
borrowers – so the demand for
loans often leads the way.
HS
•
hB2
hB0
H’D
•
HD
H2
H0
H1
Quantity of Housing
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If banks have too much money to
lend they may be tempted to lend
to higher risk borrowers (higher
defaults and financial instability
follow). Maybe they lend to
borrowers investing in housing sub-prime mortgages, maybe
‘dot com companies’, maybe
junk bonds.
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Back to the textbook story
Possible causes:
AD1
Price Level
Demand shocks cause P
and Y to change in the
same direction.
AS
AD0
- ΔG > 0
P1
- ΔI > 0 (fall in i?)
- ΔX > 0 (fall in i – rise in
exchange rate?)
P0
- ΔC > 0 (fall in i ?)
• E1
E0
•
Y0
Y1 Real GDP
Interest rate is normally an important determinant of AD
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The Monetary Transmission Mechanism
Monetary transmission mechanism:
- connects changes in MD and/or MS with aggregate
demand
Three stages:
1. ΔMD or ΔMS  Δ in equilibrium interest rate
2. Δi  Δ in desired investment (and consumption) expenditure
3. ΔID and ΔC and Δ NX  Δ in AD
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MS0
MS1
MS
decrease in
money demand
Increase in
money supply
•
i0
•
i1
MD
i0
•
i2
•
MD1
M0
M1
Quantity of Money
M0
Quantity of Money
Stage 1. Shifts in the MS or MD curves cause the
equilibrium interest rate to change.
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MD0
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MS0
MS1
i0
•
i0
•
•
i1
M0
MD
M1
Quantity of Money
•
i1
ID
I1
I0
Desired Investment Expenditure
Stage 2. Changes in the equilibrium interest rate lead to
changes in desired investment (and consumption).
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AE
E1
•
AE1
AE0
I, C
P
P0
•E
0
Y0
Y1
•
•
Y
Stage 3. Changes in
desired investment
and consumption
lead to a shift in the
AE function, and thus
a shift in the AD curve.
AD1
AD0
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Y0
Y1
Y
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An increase in the
supply of money
or
A decrease in the
demand for money
Excess supply of money
A fall in interest rates
An increase in desired
investment expenditure
An upward shift in the AE
curve
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A rightward shift in the AD
curve
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An Open-Economy Modification
In an open economy with mobile financial capital, there is
an extra channel to the transmission mechanism.
As interest rates change, financial capital flows between
countries, putting pressure on the exchange rate.
-Lower Cdn interest rates mean lower demand for Cdn
dollars (to invest in Cdn bonds) and the value of the Cdn
dollar decreases – the exchange rate increases
As the exchange rate changes (increases), net exports
change (increase), adding to the effect on aggregate
demand.
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An increase in the
supply of money
or
A decrease in the
demand for money
Excess supply of money
A fall in interest rates
An increase in desired
investment expenditure
Capital outflow and
currency depreciation
Increase in net exports
An upward shift in the AE curve
A rightward shift in the AD curve
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The Slope of the AD Curve
OPTIONAL
In Chapter 23, there were two reasons for the negative slope
of the AD curve:
- ΔP leads to Δwealth
- ΔP leads to ΔNX
We can now add a third reason — the effect of interest rates.
A rise in P leads to:
- an increase in money demand
- a higher interest rate
 reduces desired investment
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For more details about how changes in the price level influence
money demand, interest rates, and investment, and help explain
the negative slope of the AD curve, look for “Interest Rates and
the Slope of the AD curve” in the Additional Topics section of
this book’s MyEconLab.
www.myeconlab.com
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28.4 THE STRENGTH OF
MONETARY FORCES
Long-Run Neutrality of Money
A shift in the AD curve will lead to different effects in the
short run than in the long run.
In the long run, output eventually returns to Y*.
Money neutrality is the idea that changes in the money
supply do not have real effects on the economy.
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AS0
Interest Rate
Price Level
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MS0
i0
P1
P0
E0
MS1
•
•
•
E0
E1
AD1
AD0
•
i1’
Y* Y1
MD0
Quantity of Money
Real GDP
In the short-run
- MS increases causing i to fall from i0 to i1
- this causes AD to shift out from AD0 to AD1
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- and Y to increase from Y* to Y1
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AS1
AS0
E2 •
P2
•
E0
MS0
i0
•
P1
P0
Interest Rate
Price Level
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E1
AD1
AD0
E0
MS1
•
• E2
• E1
•
i1
i1’
Y* Y1
MD0
But in the long-run
- P increases (in short-run) causing MD to shift out
- and Y1 > Y* causes wages to increase shifting AS inwards
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MD1
Quantity of Money
Real GDP
(P increases further) and MD shifts further out
MD2
P2
P1
P0
AS1
AS0
E2 •
E0
MS0
i0
•
•
Interest Rate
Price Level
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E1
AD1
AD0
E0
•
i1
i1’
Y* Y1
MS1
• E2
• E1
•
MD0
MD2
MD1
Quantity of Money
Real GDP
Finally after the long-run adjustment is finished
- i has returned to its original level
- Y has returned to Y* (this is the ‘neutrality’)
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- only P has changed (increased – inflation) – more M, higher P
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What if we begin in a recession?
AS1
AS0
P0
•
E0
Y0
MS0
i0
•
P1
Interest Rate
Price Level
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E1
E0
MS1
•
AD1
AD0
•
i1’
Y*
MD0
Quantity of Money
Real GDP
In the short-run
- MS increases causing i to fall from i0 to i1
- this causes AD to shift out from AD0 to AD1
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- and Y to increase from Y0 to Y*
MFC2007MFC2007,MFC2007,MFC2007MFC2007MFC2007
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AS0
Interest Rate
Price Level
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MS0
i0
•
P1
P0
•
E0
E1
AD1
AD0
E0
MS1
•
i1
i1’
Y0 Y*
• E1
•
MD0
MD1
Quantity of Money
Real GDP
But in the long-run
- P increases (in short-run) causing MD to shift out a bit
- But Y0 goes to Y* (normal level of employment) therefore no
unusual increases in wages and no shift in AS
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P1
P0
AS0
•
•
E1
E0
Y0 Y*
AD1
AD0
Interest Rate
Price Level
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MS0
MS1
i0
•
i1
• E1
•
i1’
MD0
MD1
Quantity of Money
Real GDP
Finally after the long-run adjustment is finished
- i is lower
- Y has returned to Y* (we are out of the recession – money is
not neutral)
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- P has changed
(increased – inflation) – more M, higher P
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Short-Run Non-Neutrality of Money
Is there such a thing as monetary policy?
The short-run effect of a change in the money supply
depends on the extent of the shift of the AD curve.
Important debate in the 1950s and 1960s regarding the
effectiveness of monetary policy:
- centered around the slopes of the MD and ID curves
- Keynesians versus Monetarists
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Keynesians argued that monetary policy was not very
effective:
- MD curve was relatively flat
- ID curve was relatively steep
Monetarists argued that monetary policy was very effective:
- MD curve was relatively steep
- ID curve was relatively flat
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The Monetary Transmission Mechanism
Not today ! The following describes what is happening
in the US – the monetary transmission mechanism
appears to be broken – Liquidity Trap
Monetary transmission mechanism
Recall the three stages:
1. ΔMS  Δ in equilibrium interest rate
2. Δi  Δ in desired investment (and consumption) expenditure
3. ΔID and ΔC and Δ NX  Δ in AD
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MS0
Increase in
money supply
What is actually suppose to happen?
MS1
Central bank creates more reserves
Commercial banks do more lending –
create more money then interest
rates fall because the demand for
bonds increases.
•
i0
MD
M0
M1
1. They are afraid to invest in bonds
(uncertain)
Quantity of Money
Stage 1. Shifts in the MS
curves cause the equilibrium
interest rate to change.
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But what if the MD is highly inelastic
– the public (including corporations
are willing to hold as much money as
the banks create at the current
interest rate. Why?
2. They buy gold, or some other
asset that does not affect interest
rates.
3. Interest rates are higher in other
countries so they buy foreign bonds
– should cause exchange rate affect.
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MS0
MS1
i0
•
i0
•
i1
M0
MD
M1
Quantity of Money
Stage 2. Changes in the
equilibrium interest rate lead to
increased desired investment
(and consumption).
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•
•
i1
ID
I0I1
Desired Investment Expenditure
But uncertainty and poor
expectations, unused productive
capacity, diminished wealth
(housing bust) more than offset
the interest rate effects on I and
C – lower i has little or no effect
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AE
E1
•
AE1
Stage 3. Changes in desired
investment and consumption
lead to a shift in the AE
function, and thus a shift in
the AD curve.
AE0
I, C
P
P0
•E
0
This doesn’t happen We never get here!
Y0
Y1
•
•
Y
AD1
AD0
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Y0
Y1
Y
The central bank cannot lower
interest rates and even if they
do, lower i has little effect on
AE (AD)
In fact the apparent panic
among central bankers and
other policy makers makes
economic agents more
nervous, less certain, less
optimistic.
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Investors are not buying new plant and equipment
(housing) even though interest rates are very very low.
Why? Their current stock of capital is underutilized (excess
productive capacity combined with poor
expectations/uncertainty)
What about consumers? – they can borrow at very very
low interest rates? In the US they are trying to re-establish
their asset levels following the crash in the housing market.
They are uncertain and pessimistic about the future.
What about falling value of the dollar and the increase
in net exports? What if other countries lower their interest
rates?
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Where does that leave a country like the US?
Monetary policy is ineffective
- changes in the Ms (interest rates) have
little impact
What about fiscal policy?
- currently it is politically unacceptable
What will happen – maybe a long slow recovery as real wages fall
and AS shifts out (hopefully) Existing capital wears out along with cars
and refrigerators, TV’s, new ‘must have’ products appear, etc and AD
shifts out.
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