1. Money, Interest Rates, and Economic Activity
Chapter 28
Money, Interest Rates, and Economic Activity
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2. 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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3. 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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4. 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.
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5. Present Value and the Interest Rate
- 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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6. 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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7. 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) = $ or $95.24(1.05) = $100
If the interest rate is 2% per year, the PV of the asset is
PV = $100/(1.02) = $ or $98.04(1.02) = $100
If the interest rate is 10% per year, the PV of the asset is
PV = $100/(1.10) = $ or $90.91(1.10) = $100
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8. 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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9. 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) = $ or $95.24(1.05) = $100
If the payment is in two year’s time
PV = $100/(1.05)2 = $ or $90.70(1.05)(1.05) = $100
If the payment is in ten year’s time
PV = $100/(1.05)10 = $ or $61.39(1.05)10 = $100
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10. 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 If the Red Sox deposit $15,521,758 in the bank today, then they can pay for Jeter contract
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11. 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 /
= $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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12. 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 = $ $ $1100
(1.07)2 (1.07)3
PV = $100/ $100/ $1100/1.2250
PV = $ $ $ = $1,078.76
Again $1, 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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13. Conclusion: if the market rate of interest goes up (down)
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, PV = $ $ $1100
(1.10)2 (1.10)3
PV = $ $ $ = $
If the interest rate is 7% then, PV = $ $ $1100
(1.07)2 (1.07)3
PV = $ $ $ = $1,078.76
If the interest rate is 12% then, PV = $ $ $1100
(1.12)2 (1.12)3
PV = $ $ $ = $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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14. A Sequence of Future Payments - the general formula
PV = R R2 + … + RT
(1+i) (1+i) (1+i)T
This simple present value formula tells how to price
any promise of future payments.
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15. 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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16. 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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17. 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/ $1,100/(1.10)2 = $1,000
This investment makes sense if the current market interest rate is 10%.
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18. 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/ $1,100/(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, for your bond. Buyers should be willing to pay $1, for your bond.
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19. 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/ $1,100/(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 $ for your bond
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20. 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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21. 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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22. The bond market?
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).
Price of bonds BS
pB2 •
B’D
pB0 • BD
Investors want to invest more in bonds so they drive up their prices – drive down the interest rate that borrowers must pay. B0 B1
Quantity of Bonds
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23. The bond market?
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).
Price of bonds BS
B’S •
pB0 •
pB2 BD
Borrowers want to borrow more by issuing bonds so they drive down their prices – drive up the interest rate inducing more investment in bonds. B0 B1
Quantity of Bonds
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24. 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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25. 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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26. *
Recall
Interest are not
always as low
as they are
currently
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27. The Determinants of Money Demand
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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28. Changes in Y or P cause the MD curve to shift.
This money demand (MD) curve is sometimes called the liquidity preference function. i i1 •
Changes in Y or P cause the MD curve to shift.
Changes in the interest rate cause movements along the MD curve. i0 •
MD(Y,P) M1 M0
Quantity of Money
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29. 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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30. excess demand for money
MONETARY EQUILIBRIUM AND
NATIONAL INCOME
Monetary Equilibrium
Interest Rate
Monetary equilibrium occurs when the quantity of money demanded equals the quantity of money supplied:
 equilibrium interest rate MS
excess supply of money i2 •
excess demand for money i0 • i1 • MD M2 M0 M1
Quantity of Money
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31. excess demand for money
Monetary Equilibrium – what’s happening?
Whatever the MS someone is holding it
If MS > MD (excess supply of money) at the current i
The public will want to decrease their money holdings. How?
By using the excess money to buy bonds (which earn interest).
But as the demand for bonds goes up, bond prices rise – but that means interest rates are falling.
Interest Rate MS
excess supply of money i2 •
excess demand for money i0 • i1 • MD M2 M0 M1
Quantity of Money
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32. Monetary Equilibrium – what’s happening in the bond market?
If MS > MD (excess supply of money) at the current i
Price of bonds BS
The public will want to decrease their money holdings.
By buying bonds.
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.
pB2 •
B’D
pB0 •
pB1 • BD B2 B0 B1
Quantity of Bonds
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33. excess demand for money
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).
Interest Rate MS
excess supply of money
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. i2 •
excess demand for money i0 • i1 • MD M2 M0 M1
Quantity of Money
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34. • • 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).
Stock prices
Equities S
In general this situation means that the public will want to look for a place to ‘invest’ the excess money that they hold.
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
TSXB2 •
Equities D’
TSXB0 •
Equities D E0 E1
Quantity of Equities
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35. • • What’s happening in the financial (asset) markets in general?
If MS > MD (excess supply of money) at the current i
Price of houses
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.
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. HS
hB2 •
H’D
hB0 • HD H2 H0 H1
Quantity of Housing
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36. Copyright © 2011 Pearson Canada Inc.36
Back to the textbook story
Demand shocks cause P and Y to change in the same direction.
Possible causes:
- ΔG > 0
- ΔI > 0 (fall in i?)
- ΔX > 0 (fall in i – rise in exchange rate?)
- ΔC > 0 (fall in i ?)
Price Level
AD1 AS
AD0 P1 • E1 E0 P0 • Y0 Y1
Real GDP
Interest rate is normally an important determinant of AD
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Copyright © 2011 Pearson Canada Inc.

37. The Monetary Transmission Mechanism
- connects changes in MD and/or MS with aggregate demand
Three stages:
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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38. decrease in money demand Increase in money supply
Interest Rate
Interest Rate
MS0
MS1 MS
decrease in money demand
Increase in money supply i0 • i0 • i1 • MD i2 •
MD0
MD1 M0 M1 M0
Quantity of Money
Quantity of Money
Stage 1. Shifts in the MS or MD curves cause the equilibrium interest rate to change.
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39. Interest Rate
Interest Rate
MS0
MS1 i0 i0 • • i1 • i1 • MD ID M0 M1 I0 I1
Quantity of Money
Desired Investment Expenditure
Stage 2. Changes in the equilibrium interest rate lead to changes in desired investment (and consumption).
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40. AE
AE1 E1 •
AE0 •
I, C E0
Stage 3. Changes in desired investment and consumption lead to a shift in the AE function, and thus a shift in the AD curve. Y Y0 Y1 P P0 • •
AD1
AD0 Y0 Y1 Y
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41. An increase in the supply of money 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
A rightward shift in the AD curve
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42. 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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43. An increase in the supply of money 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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44. 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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45. 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.
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46. 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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47. - MS increases causing i to fall from i0 to i1
Price Level
MS0
MS1
Interest Rate
AS0 E0 i0 • • P1
AD1 P0 • E1 E0 •
i1’
AD0
MD0 Y* Y1
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
- and Y to increase from Y* to Y1
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48. • • • • • • • But in the long-run AS1 MS0 MS1 AS0 E0 P2 E2 i0 E2 P1 E1
Price Level
AS1
MS0
MS1
Interest Rate
AS0 E0 P2 E2 • i0 • • E2 • P1 E1 i1 •
AD1 P0 • E1
MD2 E0 •
i1’
AD0
MD1
MD0 Y* Y1
Quantity of Money
Real GDP
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
(P increases further) and MD shifts further out
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49. Finally after the long-run adjustment is finished
Price Level
AS1
MS0
MS1
Interest Rate
AS0 E0 P2 E2 • i0 • • E2 • P1 E1 i1 •
AD1 P0 • E1
MD2 E0 •
i1’
AD0
MD1
MD0 Y* Y1
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’)
- only P has changed (increased – inflation) – more M, higher P
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50. 11/23/10

51. What if we begin in a recession? • • • • In the short-run
Price Level
AS1
MS0
MS1
Interest Rate
AS0 E0 i0 • • P1
AD1 • E1 P0 E0 •
i1’
AD0
MD0 Y0 Y*
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
- and Y to increase from Y0 to Y*
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52. • • • • • But in the long-run MS0 MS1 AS0 E0 i0 P1 E1 i1 AD1 P0 E1 E0
Price Level
MS0
MS1
Interest Rate
AS0 E0 i0 • • P1 E1 i1 •
AD1 P0 • E1 E0 •
i1’
AD0
MD1
MD0 Y0 Y*
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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53. Finally after the long-run adjustment is finished - i is lower
Price Level
MS0
MS1
Interest Rate
AS0 i0 • • P1 E1 i1 • E1
AD1 P0 • E0 •
i1’
AD0
MD1
MD0 Y0 Y*
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)
- P has changed (increased – inflation) – more M, higher P
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54. 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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55. 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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56. 11/23/10

57. 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:
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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58. Increase in money supply
What is actually suppose to happen?
Central bank creates more reserves
Commercial banks do more lending – create more money then interest rates fall because the demand for bonds increases.
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?
1. They are afraid to invest in bonds (uncertain)
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.
Interest Rate
MS0
MS1 i0 • MD M0 M1
Quantity of Money
Stage 1. Shifts in the MS curves cause the equilibrium interest rate to change.
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59. • • • • Interest Rate Interest Rate MS0 MS1 i0 i0 i1 i1 MD ID M0 M1 I0
Desired Investment Expenditure
Quantity of Money
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
Stage 2. Changes in the equilibrium interest rate lead to increased desired investment (and consumption).
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60. AE • • This doesn’t happen Y P • • Y 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. E1 •
AE0 •
I, C E0
This doesn’t happen
We never get here!
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. Y Y0 Y1 P P0 • •
AD1
AD0 Y0 Y1 Y
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61. They are uncertain and pessimistic about the future.
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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62. 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.
11/23/10

63. 11/23/10