Modern Principles:
Macroeconomics
Tyler Cowen
and Alex Tabarrok
Chapter 8:
Saving, Investment, and
the Financial System
Copyright © 2010 Worth Publishers • Modern Principles: Macroeconomics • Cowen/Tabarrok
Introduction
• In this chapter we learn how the
loanable funds market:
 brings savers and borrowers together
to make both better off.
 gathers savings and allocates it to
the most profitable investments.
 promotes economic growth.
Slide 2 of 64
Introduction
• Some Important Definitions
 Saving: income that is not spent on
consumption goods.
 Investment: purchase of new capital
goods.
• Caution: Investment is not defined by
economists the same way a stockbroker
defines investment.
Slide 3 of 64
The Supply of Savings
•
What Determines the Supply of
Savings?
1. Smoothing consumption
2. Impatience
3. Market and psychological factors
4. Interest rates
• Let’s look at these in turn.
Slide 4 of 64
The Supply of Savings
1. Individuals Want to Smooth
Consumption
 Save during working years to provide for
retirement.
• Important application
 Lower life expectancies in developing
countries contribute to lower saving
rates. Why?
 Manage fluctuations in income.
 Save during good times in order to ride
out the bad times.
Slide 5 of 64
The Supply of Savings
2. Individuals Are Impatient
 Time preference: the desire to have goods
and services sooner rather than later.
• Anything with immediate costs and
future benefits must overcome time
preference.
• College education
• Crime is a reflection of impatience.
 The greater the preference for things now
the smaller will be saving.
Slide 6 of 64
The Supply of Savings
2. Individuals Are Impatient (cont.)
 An interesting study:
•
Four-year old children were asked
whether they wanted one cookie now or
two cookies in 20 minutes.
• Many years later the same children were
evaluated again.
 Result: the children who waited were less
impulsive and had higher grades than the
children who had not waited.
Slide 7 of 64
The Supply of Savings
3. Marketing and Psychological Factors
 The way choices are presented makes a
difference.
• Real Example 1: Retirement savings plans
 Result: Participation in the savings plan was
25% higher for companies with automatic
enrollment.
•
Real Example 2: Default savings rate
 Result: When the company switched from
Default 1 (3%) to Default 2 (6%), the
number of workers choosing 3% fell from
25% to almost zero.
Slide 8 of 64
The Supply of Savings
4. The Interest Rate
 Interest is the reward for savings.
• It is the “market price” of savings.
 Other things being equal, the quantity
supplied of savings increases as the
interest rate increases.
The relation between the interest rate and the
supply of savings is shown in the next diagram.
Slide 9 of 64
The Supply of Savings
4. The Interest Rate (cont.)
Interest
rate
Supply
of savings
10%
The higher the interest
rate, the greater the
amount of savings.
5%
$200
$280
Savings
(billions of dollars)
Slide 10 of 64
The Demand to Borrow
•
•
What determines the demand for
savings?
1. Smoothing consumption
2. Financing large investments
3. The interest rate
Let’s look at these in turn.
Slide 11 of 64
The Demand to Borrow
1. Smoothing Consumption
 Lifecycle Theory of Saving
•
•
Nobel laureate Franco Modigliani
By borrowing, saving, and dissaving at
different times in life, workers can
smooth their consumption path,
improving their overall satisfaction.
The next figure illustrates the lifecycle theory
of saving.
Slide 12 of 64
The Demand to Borrow
By borrowing, saving, and dissaving,
Income
Consumption workers can smooth their consumption.
Saving
Consumption
Path
Income
Borrowing
Dissaving
Time
College,
buying first
home
Prime working
years
Retirement
Slide 13 of 64
The Demand to Borrow
Income
Consumption
Path A: consumption = income,
Path B: By saving during working
years, consumption can be smoothed.
Saving
Path B
Dissaving
Path A
Working Years
Retirement
Time
Slide 14 of 64
The Demand to Borrow
2. Borrowing Is Necessary to Finance Large
Investments
 Some investments require large amounts of
money to get started.
 Without the ability to borrow many profitable
investments will not happen.
 Example:
• Fred Smith and FedEx
• Why couldn’t Fred Smith have “started
small”?
Slide 15 of 64
The Demand to Borrow
3. The Interest Rate
• Determines the cost of the loan.
• An investment will be profitable only if its rate
of return is greater than the interest rate.
• The higher the interest rate the smaller the
quantity demanded of savings will be:
 because there are fewer investments with a
rate of return higher than the interest rate.
The relation between borrowing and the interest
rate is shown in the next figure.
Slide 16 of 64
The Demand to Borrow
Interest
rate
The higher the interest
rate, the lower the
demand to borrow.
10%
5%
Demand
to borrow
$190
$300
Savings
(billions of dollars)
Slide 17 of 64
Equilibrium in the Market for Loanable Funds
•
•
The Market for Loanable Funds
Determines:
 the equilibrium interest rate.
 the equilibrium quantity of
savings/borrowing.
We are ready to put everything
together in one model.
Slide 18 of 64
Equilibrium in the Market for Loanable Funds
Interest
rate
Supply
of savings
Surplus → ↓ i
10%
Equilibrium
interest 8%
rate
5%
Shortage → ↑ i
Demand
to borrow
$190$200
$250
$280$300
Equilibrium quantity
of savings/borrowing
Savings/borrowing
(in billions of dollars)
Slide 19 of 64
Equilibrium in the Market for Loanable Funds
• Shifts in Supply and Demand
 Factors that shift the supply and demand
curves change the equilibrium interest rate and
the equilibrium quantity of savings/borrowing.
• Let’s use the model to analyze some
examples.
 The stock market crashes reducing household
wealth → people become more thrifty in order
to restore their wealth.
 The economy goes into a recession and
investors become more pessimistic.
Slide 20 of 64
Equilibrium in the Market for Loanable Funds
• People Become More Thrifty
Interest
rate
Result:
1.Lower equilibrium interest rate
2.Greater savings/borrowing
Supply
of savings
New
supply of
savings
8%
5%
Demand
to borrow
$250
$300
Savings/borrowing
(in billions of dollars)
Slide 21 of 64
21
Equilibrium in the Market for Loanable Funds
• Investors Become More Pessimistic
Interest
rate
Supply
of savings
Result:
1.Lower equilibrium interest rate
2.Lower savings/borrowing
8%
5%
New demand
to borrow
$200 $250
Demand
to borrow
Savings/borrowing
(in billions of dollars)
Slide 22 of 64
22
CHECK YOURSELF
How will greater patience shift the
supply of savings and change the
interest rate and quantity of savings?
How will an increase in investment
demand change the equilibrium
interest rate and quantity of savings?
Slide 23 of 64
Role of Intermediation: Banks, Bonds, Stock Markets
•
Financial Intermediaries - reduce the
costs of moving savings from savers to
borrowers and investors.
 Help coordinate financial markets.
 Help move savings to more highly valued uses.
•
We examine three financial intermediaries:
Banks
Bond market
Stock market
Slide 24 of 64
Role of Intermediation: Banks, Bonds, Stock Markets
•
•
Banks
 Gather savings.
 Reduce risk by evaluating ability to pay off
loans.
 Spread risk
• When a borrower defaults on a loan, the
bank spreads the loss among many
lenders.
 Coordinate lenders and borrowers.
 Minimize information costs.
Conclusion: Banks help gather savings
and allocate it to the most productive uses.
Slide 25 of 64
Role of Intermediation: Banks, Bonds, Stock Markets
•
The Bond Market
 Definition: A bond is a sophisticated IOU that
documents who owns how much and when
payment must be paid.
 Issuing bonds allows borrowing directly from
the public.
• Lender: one who buys a bond
• Borrower: one who issues a bond
 Corporations and governments at all levels
borrow money by issuing bonds.
Slide 26 of 64
Role of Intermediation: Banks, Bonds, Stock Markets
•
The Bond Market (cont.)
 All bonds involve a risk.
• Major issues are graded by rating companies.
 Standard and Poor’s
 Moody’s
• Grades range from
 lowest risk (AAA)
 bonds in current default (D)
• The higher the risk the greater the interest
rate required to get lenders to buy the bonds.
Slide 27 of 64
Role of Intermediation: Banks, Bonds, Stock Markets
• The Bond Market: Examples
 Berkshire Hathaway (Warren Buffett)
• Bond rating: AAA
• Interest rate: 4.48%
 Ford Motor Company
Note: lower bond
ratings increase the
cost of borrowing
• Bond rating: B
• Interest rate: 5.76%
 Home mortgage rates are lower than vacation
loans because mortgage loans are backed by
collateral.
 Conclusion: the higher the risk the higher will
be the rate of return.
Slide 28 of 64
Role of Intermediation: Banks, Bonds, Stock Markets
•
The Bond Market (cont.)
 Governments issue bonds to borrow money.
 Government borrowing can crowd out private
spending.
 Crowding-out: the decrease in private
consumption and investment that occurs when
government borrows more.
 Here’s how crowding-out works:
↑borrowing→ ↑interest rate →
↑Saving
↓consumption
↓Investment
Let’s use our model to illustrate crowding out.
Slide 29 of 64
Role of Intermediation: Banks, Bonds, Stock Markets
• The Bond Market: Crowding Out (cont.)
Interest
rate
9%
7%
Govt. borrows
$100 billion
b
c
a
Supply
of savings
↑govt. borrowing: a→b
Result: a→c
1. ↑interest rate
2. ↓private spending
= $50 billion
Private
demand
$150 $200 $250
Private demand
+$100 billion
govt. demand
Savings/borrowing
(in billions of dollars)
Slide 30 of 64
Role of Intermediation: Banks, Bonds, Stock Markets
•
The Bond Market (cont.)
 Different kinds of U.S. bonds
•
•
•
T-bonds: 30 year maturity, pay interest every 6
months.
T-notes: 2 to 10 year maturity, pay interest
every 6 months.
T-bills: mature in 2 days to 26 weeks, pay
interest only at maturity.
 Bonds that pay interest at maturity are called
zero-coupon bonds.
 Short-term U.S. government bonds tend to be
the safest assets.
Slide 31 of 64
Role of Intermediation: Banks, Bonds, Stock Markets
•
The Bond Market (cont.)
 Bond Prices and Interest Rates
•
•
A bond can be sold any time before maturity.
Sellers of bonds compete to attract lenders.
 Face Value (FV): how much the bond is
worth at maturity.
 Rate of Return (RoR): the implied interest
rate (%) the bond earns.
 Market price of the bond.
RoR f or a zero - coupon bond 
FV - Price
100
Price
Slide 32 of 64
Role of Intermediation: Banks, Bonds, Stock Markets
• The Bond Market (cont.)
 Bond Prices and Interest Rates
 Example: Suppose a low risk bond will pay
$1,000 one year from now. If you pay $950
for the bond now, the RoR on the bond will
be:
$1,000  $950
100  5.26%
$950
Slide 33 of 64
Role of Intermediation: Banks, Bonds, Stock Markets
• Conclusions:
 Unless the market rate of interest is
less than 5.26%, no one will buy the
bond.
 The less paid for the bond, the greater
will be the RoR.
 The higher the market rate of interest,
the less anyone will pay for the bond.
Slide 34 of 64
Role of Intermediation: Banks, Bonds, Stock Markets
•
The Stock Market
 A stock is a certificate of ownership in a
corporation.
 Stocks are traded in organized markets called
stock exchanges.
•
•
New York Stock Exchange (NYSE) is the largest.
Tokyo Stock Exchange (TSE) is the second largest.
 Sales of new shares:
•
•
Called an IPO (initial public offering).
Typically used to buy new capital goods.
 Stock markets encourage investment and
growth.
Slide 35 of 64
CHECK YOURSELF
What is the primary role of financial
intermediaries?
If your $1,000 corporate bond pays you $60
in interest every year and the interest rate
falls to 4 percent, what happens to the price
of the bond? What happens if the interest
rate rises to 8 percent?
Why does an IPO increase net investment
in the economy but your purchase of 200
shares of IBM stock does not increase
investment?
Slide 36 of 64
What Happens When Intermediation Fails?
• The bridge between saving and investment
breaks down.
• Economic growth suffers.
• Four causes of failure:
1. Insecure property rights
2. Controls on interest rates and inflation
3. Politicized lending and government owned
banks
4. Bank failures and panics
•
Let’s look at these in turn.
Slide 37 of 64
What Happens When Intermediation Fails?
1. Insecure Property Rights

Some governments fail to protect property
rights.
•
•

Saved funds are not immune to confiscation,
freezes, and other restrictions.
Result: people are reluctant to put their savings in
domestic institutions.
Example: Argentina and Brazil
•
•
•
Both have a history of freezing bank accounts.
Argentines and Brazilians save less.
Result: less investment and lower economic
growth.
Slide 38 of 64
What Happens When Intermediation Fails?
2. Controls on Interest Rates and Inflation

Usury Laws: create legal ceilings on interest
rates.
•
•
Result: less saving and investment.
Most American states have usury laws but:
 they often have loopholes (e.g., don’t apply
to credit cards).
 set at levels too high to affect most loan
markets.
We can use the loanable funds market model to
illustrate the effect of a usury law.
Slide 39 of 64
What Happens When Intermediation Fails?
2. Controls on Interest Rates and Inflation (cont.)
Interest
rate
Supply
of savings
10% Market
Results:
1.Shortage of savings
2.Less savings/investment
3.Slower economic growth
Equilibrium
8%
Controlled
Interest rate
Shortage
Demand
$190
$250 $300
Savings/borrowing
(in billions of dollars)
Effect of Usury Laws
Slide 40 of 64
What Happens When Intermediation Fails?
2.
Controls on Interest Rates and Inflation (cont.)
 Inflation
•

When combined with controls on interest rates,
inflation destroys the incentive to save.
Nominal and real interest rates:
•
•
•
Nominal interest rate: the named rate; the
rate on paper.
Real interest rate: the rate of return after
adjusting for inflation.
Therefore:
Real rate  Nominal rate - Inflationrate
Slide 41 of 64
What Happens When Intermediation Fails?
2. Controls on Interest Rates and Inflation (cont.)
 Inflation (cont.)


Example: Suppose interest rates are controlled at
a nominal rate of 10% and the rate of inflation is
30%. Then:
Real rate  10% - 30%  - 20%
Result:
• Savers are losing 20% a year.
• Saving is discouraged.
• Less investment and slower economic growth
The following table shows the effect of
negative interest rates on growth of per
capita GDP.
Slide 42 of 64
What Happens When Intermediation Fails?
• Negative Interest Rates and Economic Growth
Country
Argentina
Bolivia
Chile
Ghana
Peru
Poland
Sierra Leone
Turkey
Venezuela
Zaire
Zambia
Years
1975-1976
1982-1984
1972-1974
1976-1983
1976-1984
1981-1982
1984-1987
1979-1980
1987-1989
1976-1979
1985-1988
Real Interest
Rate (%)
-69
-75
-61
-35
-19
-33
-44
-35
-24
-34
-24
Per capita
growth (%)
-2.2
-5.2
-3.6
-2.9
-1.4
-8.6
-1.9
-3.1
-2.7
-6.0
-1.9
Source: Easterly (2002, p. 228)
Slide 43 of 64
What Happens When Intermediation Fails?
3. Politicized Lending and Government
Owned Banks

Example: Japan 1990 to 2005.
•
•
•
•
Many banks were bankrupt or propped up by
the government.
They were not loaning funds for efficient uses.
Other banks were pressured to lend money to
well-connected political allies.
Result: economic growth was zero during this
period.
Slide 44 of 64
What Happens When Intermediation Fails?
3. Politicized Lending and Government
Owned Banks (cont.)
 Government ownership of banks
•
•
Useful to authoritative regimes that use the
banks to direct capital to political
supporters.
The larger the fraction of governmentowned banks a country had in 1970:


the slower the growth in per capita GDP.
the slower the productivity growth.
Slide 45 of 64
What Happens When Intermediation Fails?
4. Bank Failures and Panics


Systemic problems usually lead to large-scale
economic crises.
During the Depression, between 1929-1933:
•
•
11,000 banks (almost half of U.S. banks)
failed.
Ripple effects:
 Businesses could not get working
capital.
 Many people lost their life savings,
resulting in lower spending.
 Result: many businesses failed.
Slide 46 of 64
What Happens When Intermediation Fails?
4. Bank Failures and Panics (cont.)
 Financial Crisis 2007-2008
•
•
•
•
Many mortgage loans were bundled and
sold as if they had very low risk.
Some were sold on false terms.
Credit rating agencies failed at their job.
People expected housing prices to
continue to rise.
Slide 47 of 64
What Happens When Intermediation Fails?
4. Bank Failures and Panics (cont.)
 Financial Crisis 2007-2008 (cont.)
•
•
•
Housing prices fell.
Many people defaulted on their mortgages.
Result:
 Huge amounts of bad loans on the
books of financial institutions.
 Banks could not get funds to loan.
 The bridge between savers and
borrowers collapsed.
Slide 48 of 64
CHECK YOURSELF
 How do usury laws (controls on interest rates)
cause savings to decline?
 Besides decreasing the number of banks, how do
bank failures hinder financial intermediation?
 How does awarding bank loans by political
criteria or by cronyism (to your pals) affect the
efficiency of the economy?
Slide 49 of 49
Takeaway
•
•
Financial institutions bridge the gap
between savers and borrowers.
They:
 collect savings.
 evaluate investments and reduce
risk.
Banks, bond markets, and stock
markets serve as financial
intermediaries.
Slide 50 of 64
Takeaway
•
When final intermediation breaks
down, economic growth suffers.
 This can be caused by:
•
•
•
•
insecure property rights.
inflation and interest rate ceilings.
politicized lending.
bank failures.
Slide 51 of 64
Modern Principles:
Macroeconomics
Tyler Cowen
and Alex Tabarrok
Chapter 8 Appendix:
Bond Pricing
and Arbitrage
Copyright © 2010 Worth Publishers • Modern Principles: Macroeconomics • Cowen/Tabarrok
Bond Pricing and Arbitrage
• Present Value, Future Value, and Interest
 Suppose you invest $100 in a savings
account at a 10% interest.
•
•
•
•
Present value (PV): the amount you invest.
Future value (FV): the amount you will withdraw
in one year.
r is the interest rate you earn on the savings
account.
The relationship between PV, FV, and r is given
by:
PV  (1 r)  FV
$100  (1 0.10)  $110
Slide 53 of 64
Bond Pricing and Arbitrage
• Present Value, Future Value, and Interest
(cont.)


Now, suppose the interest rate is 10% and in
one year you would like to have $100. How
much do you have to put in the bank today?
Since PV × (1.10) = $100, dividing both sides
by 1.10 gives our answer.
$100
PV 
 $90.90
1.10
Slide 54 of 64
Bond Pricing and Arbitrage
• Present Value, Future Value, and Interest
(cont.)
 More generally, there are three ways to solve
for PV, FV, and r.
PV  (1 r)  FV
(1)
FV
PV 
(1 r)
(2)
FV
(1  r) 
PV
(3)
Slide 55 of 64
Bond Pricing and Arbitrage
• Bond Pricing
 A bond is simply a promise to pay a certain
amount at a future date. It will sell today for a
price = PV.
 A bond that has an initial interest rate of 10%
and a future value of $100 will sell for $90.90.
 What if the interest rate falls to 5%? It will sell
for:
$100
PV 
 $95.24.
(1.05)
 Important Conclusion: ↓ r → ↑ price of the
bond.
Slide 56 of 64
Bond Pricing and Arbitrage
• Arbitrage
 The buying and selling of equally risky assets
is called arbitrage.
 The rate of return on a bond can be
determined by:
FV
$100
(1 r) 

 1.10
PV $90.90
 Interpretation: In one year the bond will be
worth 1.10 times its selling price now. This
represents a 10% rate of return.
Slide 57 of 64
Bond Pricing and Arbitrage
• Arbitrage (cont.)
 Investors compare the rates of return on
alternative assets.
• Given a choice among equally risky
assets, they will choose the one with
the highest rate of return.
• Result: Buying and selling will
equalize the rate of return on equally
risky assets.
Slide 58 of 64
Bond Pricing and Arbitrage
• Arbitrage (cont.)
 Let’s see how this works. If…

buy asset1 Price1  RoR1
RoR1(asset1)  RoR2 (asset2) 

sell asset2 Price2  RoR2
buy asset2 Price 2  RoR

2
RoR (asset1)  RoR (asset2) 
1
2
sell asset1 Price 1  RoR

1

 Conclusion: arbitrage continues until
RoR1 = RoR2.
Slide 59 of 64
Bond Pricing and Arbitrage
• Prices of Bonds that Mature in More Than
a Year
 Bond that is worth $100 in two years will sell
for $82.64 now with r = 10% for each.
 Alternatively:
$82.64 (1 .10) (1 .10)  $100
 Or, generally:
PV  (1 r )  (1 r )  FV
1
2


 Solving for PV we get:
FV
$100
PV 

 $82.64
(1  r )(1  r ) (1  .10)(1 .10)
1
2
Slide 60 of 64
Bond Pricing and Arbitrage
• Prices of Bonds that Mature in More Than
a Year (cont.)
 What is the price of a bond with an initial
interest rate of 10% that pays $100 at
the end of year 1 and another $100 at
the end of year 2?
$100
$100
PV 

 $90.90  $82.64  $173.55
(1 .10) (1 .10)(1 .10)
Slide 61 of 64
Bond Pricing and Arbitrage
• Prices of Bonds that Mature in More Than
a Year (cont.)
 The price of a bond that makes
potentially different payments for n
years is given by...
pm t3
pm tn
pm t1
pm t2
PV 


 ...
2
3
(1 r) (1  r )
(1  r )
(1  r ) n
 This can be calculated easily using a
spreadsheet.
Slide 62 of 64
Bond Pricing and Arbitrage
• Bond Pricing with a Spreadsheet
Year Payment Present Value Interest Rate
1
$100
$95.24
0.05
2
$100
$90.70
3
$100
$86.38
4
$100
$82.27
5
$100
$78.35
6
$100
$74.62
7
$100
$71.07
8
$100
$67.68
9
$100
$64.46
10
$1,000
$613.91
Sum PV
or Price->
$1,324.70
Slide 63 of 64
Bond Pricing and Arbitrage
• Bond Pricing with a Spreadsheet
Year
1
2
3
4
5
6
7
8
9
10
Payment Present Value Interest Rate
$100
$90.91
0.1
$100
$82.64
$100
$75.13
$100
$68.30
$100
$62.09
$100
$56.45
$100
$51.32
$100
$46.65
$100
$42.41
$1,000
$385.54
Sum PV
or Price->
$961.45
Slide 64 of 64