FIN 30220:
Macroeconomics
Capital Markets
The US Capital market by the
numbers*…
Commercial
Banks
$20T
Total Assets
$200T
Bond Market
$37T
Equities /
Mutual Funds
Other
$75T
Pension
Entitlements
$48T
$20T
*Source: Flow of Funds
The Capital Markets
connect the various
sectors of the economy
Government
• $5T Assets
• $22T Liabilities
Capital Markets
Households
• $68T Assets
• $14T Liabilities
Business
• $105T Assets
• $102T Liabilities
Rest of the World
• $23T Assets
• $10T Liabilities
*Source: Flow of Funds
Income
Minus Taxes
Minus Consumption of Non-Durables and Services
Households were net lenders in 2014*…
Gross Saving: $2,300B
+ Borrowing: $420B
Bank Loans: $122B
Mortgages: $50B
Consumer Credit: $248B
$2,720B
Real Assets Purchased: $1,811B
Financial Assets Acquired: $1,265B
•
•
•
•
•
•
•
•
•
•
Consumer Durables : $1,229B
Residential: $453B
Non-Residential: $137B
Other: -8B
Note: Sector Discrepancy = -$356B
Deposits: $481B
Bonds: -$477B
Equities: $29B
Mutual Funds: $520B
Pension Fund Entitlements: $548
Other: $164B
Total Financial Assets – Total Borrowing = Net Lending
*Source: Flow of Funds
$1,265B
-
$420B
=
$845B
Net Savers
Households
Net Borrowers
Approximately $1T Passed
through the capital market
in 2014
Government
Capital Markets
$845B
$794B
$166B
$213B
*Source: Flow of Funds
Note: Statistical Discrepancy = $4B
Rest of World
Businesses (Financial + Non-Financial)
Non-Financial Business were net borrowers…they used these funds primarily for
capital investment
Undistributed Profits
Gross Saving: $2,058B
+ Total Borrowing: $683B
Bank Loans: $379B
Bonds: $265B
Other:$39B
$2,702B
Capital Expenditures: $2,040B
Financial Assets Purchased: $375B
•
•
•
•
•
Residential: $99B
Non-Residential: $1,859B
Other: $82
Deposits: $120B
Equities: $255B
Note: Sector Discrepancy = $287B
Total Borrowing – Financial Assets = Net Borrowing
$683B
*Source: Flow of Funds
-
$375B
=
$308B
Non-Financial Business were net borrowers…they used these funds primarily for capital
investment
Capital Expenditures: $2,040B
•
•
•
Residential: $99B
Non-Residential: $1,859B
Other: $82
Recall our expression for the evolution of the nation’s capital stock….
K '  1    K  I
In 2014
• Capital Stock: $40T
• Depreciation: $1.5T (4%)
K  K  K  I
'
$40T
$1.5T
$2T
In 2015
• Capital Stock: $40.5T
Bond
Coupon
Price (Per $100)
3 Month Treasury
----
$99.985
6 Month Treasury
----
$99.895
12 Month Treasury
----
2 Year Treasury
Investment
Banks
Asset
Rate
$99.64
Interest Checking
.38%
.625%
$99.82
Savings
.46%
5 Year Treasury
1.62%
$100.23
10 Year Treasury
2.125%
$99.61
1 Year CD
1.06%
30 Year Treasury
3.00%
$103.44
2 Year CD
1.19%
5 Year CD
1.81%
Loan
Rate
30 Year Fixed Mortgage
4.10%
15 Year Fixed Mortgage
3.28%
60 Month Car Loan
4.37%
48 Month Used Car Loan
4.32%
Bond
Coupon
Price (per $100)
Chevron - 5 year
1.961%
$99.90
IBM – 5 year
1.625%
$97.80
Wal-Mart – 20 year
5.25%
$72.79
Stock
Dividend
Price
Chevron
$4.28
$85.19
IBM
$5.40
$156.32
Wal-Mart
$1.99
$72.79
vs.
Commercial
Banks
Investment banks and commercial banks
provide the same service. They connect
borrowers with lenders.
Commercial banks accept deposits
from households – they pay
interest on some of these deposits
Commercial banks use these
deposits to provide loans – they
charge interest on these loans
A bank makes money from the spread between
these interest rates
If we model the capital market using commercial banks, we get
this…
Real
Interest
rate
We should be able to find an
equilibrium interest rate where
supply of loanable funds equals
demand
The supply of loanable
funds comes from
household savings
r
S
r*
I  G  T 
S  I  G  T 
Loanable
Funds
In equilibrium, household savings equals private
plus public borrowing
The demand for loanable
funds comes from
borrowers (both private
and public)
Investment banks and commercial banks
provide the same service. They connect
borrowers with lenders.
Investment banks buy bonds from
borrowers (governments and
businesses) at a posted price
Investment banks then sell these
securities to savers (households)
at a posted price
Investment banks make money from the spread
between these prices
If we model the capital market using investment banks, we get
this…
Bond
Price
We should be able to find an
equilibrium bond price where
supply of bonds equals demand
PB
I  G  T 
The supply of bonds
comes from borrowers
(both public and private)
PB*
The demand for bonds
comes from savers
(households)
SBonds
S  I  G  T 
In equilibrium, household savings equals private
plus public borrowing
Commercial Banks accept deposits
from one group (savers) and lends
those funds out to others (borrowers)
Real
Interest
rate
r
Investment Banks buy
bonds from one group
(borrowers) and sell those
bonds to others (savers)
S
PB
r*
I  G  T 
PB*
I  G  T 
S  I  G  T 
Loanable
Funds
SBonds
S  I  G  T 
Suppose that the government runs a
large deficit. The increase in the public
demand for loanable funds should
increase the interest rate
Real
Interest
rate
r
The government borrows
money by selling bonds.
The increased supply of
bonds should lower bond
prices
S
PB
r*
I  G  T 
PB*
I  G  T 
S  I  G  T 
Loanable
Funds
SBonds
S  I  G  T 
Treasury Bills are short term ( 1 year or less) securities issued by the federal government. They
make no interest payments and therefore, sell at a discount from face value.
Bond
Coupon
Price (Per $100)
3 Month Treasury
----
$99.985
Now
Pay $99.985
90 Days
Receive $100
Bond Equivalent Yield
 FV  P  365 
BEY  

 *100
 P  n 
 $100  $99.985  365 


 *100  0.06%
$99.985

 90 
Discount Yield
 FV  P  360 
DY  

 *100
 FV  n 
 $100  $99.985  360 


 *100  0.06%
$100

 90 
There are currently
around $1.5T worth of
Treasury Bills
outstanding!!
Treasury Notes and Bonds are a bit more complicated because they make multiple payments
until maturity (semi-annual interest payments)
Bond
Coupon
Price (Per $100)
5 Year Treasury
1.62%
$100.23
There are currently
around $12T worth of
Treasury Notes and
Bonds outstanding!!
1.62% per year
Now
6 months
1 year
4 year, 6
months
Pay $100.23
Receive $.81
Receive $.81
Receive $.81
5 year
Receive $100.81
Yield To Maturity
Current Yield
1.62
1.62
101.62
$100.23 

...

1  i  1  i 2 1  i 5
C 
 $1.62 
CY    *100  
 *100  1.61%
P
 $100.23 
Solve for the interest
rate….
YTM  1.57%
We could do the same thing with corporate bonds…
Bond
Coupon
Price (per $100)
Wal-Mart – 20 year
5.25%
$128.95
5.25% Annual Coupon
6 months
Now
Pay $128.95
Receive $2.625
5.25
5.25
105.25

...

1  i  1  i 2 1  i 20
YTM  3.26%
Receive $2.625
Receive $2.625
Yield To Maturity
$128.95 
19 years,
6 months
1 year
5 year
Receive $102.625
Coupon Yield
C 
 $5.25 
CY    *100  
 *100  4.07%
P
$128.95
 


Stock
Dividend
Price
Chevron
$4.28
$85.19
Now
Pay $85.19
1 year
We could do the same thing with equities(at least those that pay
dividends)…
Forever
Receive $4.28
Dividend Yield
D
 $4.28 
DY    *100  
 *100  5.02%
P
 $85.19 
We can really think of a stock as an infinite
maturity bond with a potentially variable
coupon payment
What do all these yields have in common?
Yield To Maturity
$128.95 
Bond Equivalent Yield
 $100  $99.985  365 
BEY  

 *100  0.06%
$99.985
90



5.25
5.25
105.25

...

1  i  1  i 2 1  i 20
YTM  3.26%
Coupon Yield
C 
 $5.25 
CY    *100  
 *100  4.07%
P
 $128.95 
Dividend Yield
D
 $4.28 
DY    *100  
 *100  5.02%
P
 $85.19 
A higher (lower) price implies
a lower (higher) yield!
Nominal Return/Price - 1 Year Treasury Bill (1948-2014)
17
105
Average Yield = 4.36%
Average Price = $95.89
100
7
95
2
90
1948
1958
1968
1978
1988
1998
2008
-3
85
Correlation = -1.00
-8
80
Yield
Price
Price (per $100 of Face Value)
Annual Return
12
Suppose that you pay $95 today for
a bond that will pay out $100 in one
year. Your nominal return would be
1 year
Now
Pay $95
However, if inflation over the course of the year is 3%
Receive $100
Price Level
Now
1.00
1 Year
1.03
That $100 you receive in one year will have less
purchasing power (3% less). In fact, the inflation
adjusted value of that dollar in today’s terms
would be
 $100  $95 
i
 *100  5.3%
$95


Therefore, in real (inflation adjusted) terms, your return would be
 $97.09  $95 
r 
 *100  2.2%
$95


Date
 1 
$100 
  $97.09
 1.03 
Real
Return
Nominal
Return
r  i 
Inflation
US Real Returns (1948-2014)
17
Average Nominal = ~4.5%
Minus Average
Inflation = ~3.5%
12
Average Real = ~1%
7
2
1948
1958
1968
1978
1988
1998
2008
-3
Negative Real
Returns!!!
Negative Real
Returns!!!
-8
Negative Real
Returns!!!
Real
Nominal
Inflation
How can we have negative real returns?
You expect inflation to be 3% at the time you purchase the
bond. Therefore, your Ex Ante real return is 2.3%
Suppose that you pay $95 today for
a bond that will pay out $100 in one
year. Your nominal return would be
1 year
Now
Receive $100
Pay $95
 $100  $95 
i
 *100  5.3%
$95


Ex Ante
Real
Return
Nominal
Return
Expected
Inflation
r  i 
e
e
r e  5.3  3  2.3%
At the end of the year, you learn that you were wrong…inflation turned out to be 6%
r  5.3  6  0.7%
Underpredicting inflation can lead to negative ex post returns….
Ex Post
Real
Return
Nominal
Return
Actual
Inflation
r  i 
Inflation vs. Expectations (1978-2014)*
12
8
4
0
1978
1983
1988
1993
1998
Inflation
*University of Michigan Survey
Expectation
2003
2008
2013
Inflation Expectation Error (1978-2014)
Actual Inflation – Expected Inflation
5.0
3.0
1.0
1978
-1.0
-3.0
-5.0
*University of Michigan Survey
1983
1988
1993
1998
2003
2008
2013
US Ex Ante/Ex Post Real Returns (1978-2014)
7.0
3.0
1978
-1.0
1983
1988
1993
1998
-5.0
Ex Ante
*University of Michigan Survey
Ex Post
2003
2008
2013
We have Treasury Rates for a variety of maturities…the yield curve.
3.5
Treasury Bonds (>10 years)
2.94
3
Treasury Notes (1 – 10 yrs.)
2.64
2.5
Annual Return
2.28
2.02
2
1.65
1.5
Treasury Bills (<1 year)
1.1
1
0.73
0.5
0.38
0.19
0.05
0.08
0
1 Mo.
3 Mo.
6 Mo.
1 Yr.
2 Yr.
3 Yr.
5 Yr.
7 Yr.
10 Yr.
20 Yr.
30 Yr.
US Treasury Rates
6 Month
5 Year
10 Year
18
16
14
12
10
8
6
4
2
0
1958
1963
1968
1973
1978
Inverted Yield Curve
9
8
6.73
1993
1998
2003
2008
“Normal” Yield Curve
11.63 11.86 11.75
7
6.04
6
11
6.92
7
1988
Flat Yield Curve
13
7.96
1983
5.2
5
9
4
6
5
3.07
7
6 Mo.
5 yr.
10 Yr.
5
3
6 Mo.
5 yr.
10 Yr.
2
6 Mo.
5 yr.
10 Yr.
2013
Inverted/Flat Yield Curves tend to precede recessions…
18
16
14
12
10
8
6
4
2
0
1958
1963
1968
1973
1978
1983
6 Month
1988
5 Year
1993
10 Year
1998
2003
2008
2013
For simplicity, let’s assume a risk free world (i.e. one with zero uncertainty)
2.25% per year
Now
1 Year
2 Year
Assume the following yield curve
4
3.25
Cumulative return
from holding a 2 year
bond for two years
Cumulative return
from holding a 3 year
bond for three years
2.75
3
2.25
2
0
4 Year
What should this
interest rate be?
1.5 % per year
1
3 Year
1.0225
1.5
3
 1.015  1  i1,2 
1
1 yr.
2 yr.
3 Yr.
4 yr.
5 yr.
Annual rate of return on a one year
bond purchased two years from today
2
5 Year
Forward rates aren’t known with certainty because they haven’t happened yet,
but are suggested in the yield curve…
i4,1
i2,2
Now
1 Year
i1,1
4
3
i3
2
1
0
i1
1 yr.
i4
i1,2
5 Year
4 Year
i1,3
i1,4
i5
i2
2 yr.
3 Year
2 Year
The interest rates given by the yield curve are known as spot
interest rates…they are known with certainty based off of current
market prices
3 Yr.
4 yr.
5 yr.
Let’s assume a risk free world (i.e. one with zero uncertainty)
2.25% per year
Now
1 Year
3 Year
2 Year
5 Year
4 Year
3.78% per year
1.5 % per year
1.0225
3
 1.015  1  i1,2 
2
Assume the following yield curve:
3.25
2.75
3
2.25
2
1
0
1.0225
2
1.015
3
4
 1  i1,2   1.0378
1.5
i1,2  .0378
1
1 yr.
2 yr.
3 Yr.
4 yr.
5 yr.
Let’s try another one….
2.75% per year
Now
1 Year
2 Year
1.0275
Assume the following yield curve:
4
3.25
2.75
2.25
2
1
0
5 Year
4 Year
???
2.25 % per year
3
3 Year
1.5
4
 1.0225  1  i1,3 
3
1.0275
4
1.0225
3
 1  i1,3   1.042
1
i1,3  .042  4.2%
1 yr.
2 yr.
3 Yr.
4 yr.
5 yr.
Let’s try another one….
2.75% per year
Now
1 Year
2 Year
1.0275
Assume the following yield curve:
4
3.25
2.75
1
0
4
 1.015  1  i2,2 
2
1.0275
1.015
2.25
2
5 Year
4 Year
???
1.5 % per year
3
3 Year
1.5
4
2
 1  i2,2 
2
1
i2,2  .04  4%
1 yr.
2 yr.
3 Yr.
4 yr.
5 yr.
2
Every yield curve suggests a future path for interest rates
Now
1 Year
1.015
1.01
i1  1%
3 Year
2 Year
1.0225
2
1.015
1.0275
3
1.0225
3
2
 1.02
i1,2  3.78%
i1,1  2%
1.0325
4
1.0275
5
4
 1.0378
 1.042
6
5.3
4
5
Annual Return
2.75
3
2.25
2
1
0
1.5
1
3.78
4
 1.053
i1,4  5.3%
i1,3  4.2%
3.25
5 Year
4 Year
4.2
Predicted
1 Year
Treasury
Rate
3
2
2
1
1
Time
0
1 yr.
2 yr.
3 Yr.
4 yr.
5 yr.
1
2
3
4
5
Downward Sloping Yield Curves suggest falling interest rates
Now
1 Year
1.0726   1.0621
1.0832 
2
i1  8.32%
3 Year
2 Year
1.0702 
2
1.0726 
1.0695
3
1.0702 
3
i1,2  6.54%
i1,1  6.21%
1.0693
4
1.0695
5
4
 1.0654
5 Year
4 Year
 1.067
 1.0685
i1,4  6.85%
i1,3  6.7%
1 Year Treasury Rate
Yield Curve 1973
8.5
9
8.32
8
8.32
8
7.26
7.02
7
6.95
6.93
Annual Return
7.5
7
6.54
6.7
6.85
Predicted
6.21
6.5
Actual
6
5.5
6
Time
5
1 yr.
2 yr.
3 Yr.
4 yr.
5 yr.
1973
1974
1975
1976
1977
Upward Sloping Yield Curves suggest rising interest rates
Now
1 Year
1.0448
1.0356 
1.0503
2
1.0448
 1.054
i1,2  6.14%
i1,1  5.4%
1.059 
4
1.0554 
5
4
 1.0614
5 Year
4 Year
1.0554 
3
1.0503
3
2
i1  3.56%
3 Year
2 Year
 1.07
 1.073
i1,4  7.3%
i1,3  7.0%
1 Year Treasury Rate
Yield Curve 1993
8
7
7
7.3
Predicted
7
5.9
6
5.03
5
4
3
Annual Return
5.54
6.14
4.48
3.56
6
5.4
Actual
5
4
3.56
Time
3
1 yr.
2 yr.
3 Yr.
4 yr.
5 yr.
1993
1994
1995
1996
1997
MOODY'S INVESTORS SERVICE
Obligations rated Aaa are judged to be of the highest
quality, subject to the lowest level of credit risk.
Obligations rated Aa are judged to be of high quality and
are subject to very low credit risk.
MOODY'S INVESTORS SERVICE
6
5.13
5
4.19
Annual Return
4
3
2.36
2
1
0
10 Year Treasury Moody’s Aaa
Bond
Corporate Bond
Moody’s Baa
Corporate Bond
Obligations rated Baa are judged to
be medium-grade and subject to
moderate credit risk and as such
may possess certain speculative
characteristics. Ba Obligations
rated Ba are judged to be
speculative and are subject to
substantial credit risk.
The Risk Premium Tends to increase during recessions….
20
18
16
14
12
10
8
6
4
2
0
1958
1963
1968
1973
1978
1983
10 Year
1988
Aaa
1993
Baa
1998
2003
2008
2013
Recall, that we are interested in understanding the business cycle…
% Deviation
From Trend
Recovery
Recession
Peak
Peak
GDP
0
Trough
Time
The nominal interest rate is pro-cyclical….but we need to be careful here…
8
6
6
5
4
2
0
1/1/2007
-2
4
1/1/2009
1/1/2011
1/1/2013
3
-4
2
-6
Correlation = .20
-8
-10
1
Trough
-12
0
1 Year Treasury Rate
Industrial Production
1 Year Treasury Rate
Industrial Production (% Deviation from Trend)
Peak
What really matters is the real (inflation adjusted) return
Nominal interest rate
Pro-cyclical
CORR(i, GDP) = .20
r  i 
Real (inflation adjusted) interest rate
Countercyclical
CORR(r, GDP) = -.35
Inflation
Pro-cyclical
CORR(INF, GDP) = .18
Consumer Expenditures are highly pro-cyclical
4
Peak
3
GDP (Deviation from Trend)
2
1
0
2007-01-01
2009-01-01
2011-01-01
2013-01-01
-1
-2
-3
-4
Trough
Consumption
Correlation = .83
GDP
So is investment…note that business investment is much more volatile that GDP
15
% Deviation from Trend
10
5
Peak
0
2007-01-01
-5
2009-01-01
2011-01-01
2013-01-01
Trough
-10
-15
-20
Correlation = .78
-25
Gross Investment
GDP
Recall, our story about the macro economy as an apple orchard…
GDP  F  A, K , L 
GDP  C  I
OR
At some point in time,
you have a fixed number
of trees (Capital) and
workers
Those workers/capital combine with
productivity to produce apples
(output)
Investment today determines your capital stock next year
Those apples are allocated either
towards consumption or investment
(planting them to grow new trees)
Recall, our story about the macro economy as an apple orchard…
GDP  C  I  G
GDP  F  A, K , L 
OR
At some point in time,
you have a fixed number
of trees (Capital) and
workers
Those apples are allocated either
towards consumption, investment, or
government
Those workers/capital combine with
productivity to produce apples
(output)
w
p
S
r
S
L
r*
*
 w
 
 p
*
L
LD
L
For a given capital stock and
productivity level, labor markets
determine total employment
I  G  T 
S *  I *  G  T 
S, I
For a given output, capital markets
determine the consumption/investment
allocation
Recall the accounting
identities
Capital Markets
Total Savings
r
S
Equilibrium
real interest
rate
S  I   G  T   CA
Let’s assume this is
zero for now
Y  C  I  G  NX
r*
Total Borrowing
(Public and Private)
Let’s assume this is
zero for now
I  G  T 
S  I  G  T 
*
*
Equilibrium savings
(equals equilibrium
investment)
Total loanable
funds
To say that savings is equal to
borrowing is equivalent to saying
expenditures equal output!!
Capital Markets
Recall that Output = Income
Labor Income + Capital Income
r
S
=
r*
I  G  T 
S *  I *  G  T 
Equilibrium savings
equals equilibrium
borrowing
Loanable funds
r * * S * = Capital Income
Capital Markets
r
S  I  G  T 
OR
Y  C  I G
S
If the interest rate is too high, we have excessive savings (expenditures
are lower than output). This should push interest rates down to induce
more people to spend more (save less)
r*
If the interest rate is too low, we have excessive borrowing for investment
(expenditures are higher than output). This should push interest rates up
to induce more people to spend less (save more)
S  I  G  T 
OR
Y  C  I G
I
S, I
Capital Demand
Again, we assume that labor markets are
populated by perfectly competitive firms
r
These firms are making capital decisions to maximize profits.
Y  F  A, K , L 
I
I
Profit  pY Y  wL  pk  r    K
Total
Revenues
Labor
Costs
Capital
Costs
These firms use a production process that exhibits diminishing marginal productivity – that is as
capital rises, its contribution to production of output shrinks
Y
MPK 3
MPK 2
K
Y
Y
Y  F  A, K , L 
K
MPK1
Y
MPK 
Y
K
K
K1
K2
K3
K
These firms are making hiring decisions to maximize profits.
Profit  pY Y  wL  pk  r    K
Consider what happens to profits
if we change capital a little bit…
Adding capital will
generate more
production which will
increase revenues
pY MPK
Value marginal
product of capital
pY MPK  pK  r   
Businesses equate the nominal
value of a unit of capital with the
nominal user cost
OR
Adding capital will
generate additional
costs (user cost)
pK  r   
p
MPK  K  r   
pY
Businesses equate the real
value of an unit of capital with
the real user cost
Profits are maximized when benefits and costs of capital are equated at the margin!
MPK
Profit
PK
r   
PY
MPK
K*
K1
PK
 r     MPK
PY
PK
 r     MPK
PY
K2
PK
 r     MPK
PY
K
K
K1
Profits are
increasing
K2
K*
Profits are
Decreasing
Profits are
constant
(maximized)
So, these perfectly competitive businesses observe a real interest rate and make a profit
maximizing decision of how much capital to employ.
MPK
r
PK
 r1   
PY
r1
PK
 r2   
PY
r2
MPK
K1
K2
K
K1
K2
KD
K
As the interest rate falls, the real user cost of capital for businesses drops. This allows them to profitably
expand their capital stock– even in the light of diminishing marginal returns to capital.
Investment represents purchases of new capital required to hit your new target capital stock.
K D  1    K  I
I  K D  1    K
r
r
r1
r1
r2
r2
KD
K1
K2
K
I
I1  K1  1    K
I 2  K 2  1    K
I
Suppose the economy experiences an increase in productivity….
MPK
Y
Y  F  A, K , L 
K1
K2
K3
K
K1
K2
This increase in productivity not only raises total output for every unit of capital
employed, but increases the marginal product of unit of capital
K3
MPK
K
As events occur that influence the value of capital at the margin these businesses re-evaluate their
decisions and adjust their capital stock accordingly.
r
r
MPK
PK
 r1   
PY
r1
r1
MPK
K1
K2
K
KD
K1
K2
K
I
I1
I2
I1  K1  1    K
An increase in productivity raises
the optimal capital stock for the
firm
I 2  K 2  1    K
A larger capital stock requires a
larger amount of investment
Private borrowing isn’t the only borrowing taking place…there is also public borrowing
r
r
+
r1
I
MPK 
pK
r   
pY
r
=
r1
I  G  T 
Loans
I1
Private Borrowing
r1
G  T 
+
Loans
Public Borrowing (Note that
public borrowing is a policy
variable…not the result of an
optimization)
I1   G  T 
=
Total Borrowing
Loans
So, for example, an increase in public borrowing (the deficit) does not influence private borrowing but raises
total borrowing
r
r
+
r1
I
I1
Private Borrowing
r1
r
G  T 
=
r1
I  G  T 
Loans
Loans
Public Borrowing (Note that
public borrowing is a policy
variable…not the result of an
optimization)
I1   G  T 
Total Borrowing
Loans
Savings
Just as businesses make decisions to maximize profits, we make
decisions to maximize our utility
r
Make ourselves as happy as
possible
S
Total Utility
(Happiness)
U  U (C ', C )
Future
Consumption
Current
Consumption
S
We only have a couple requirements for utility functions
•Utility is increasing in both current and future consumption (i.e.
we like to buy things!)
•Utility exhibits diminishing marginal utility (the more we have of
anything, the less it is worth to us at the margin)
Financial markets give households the ability to reallocate their wealth over time
Income
Consumption
Without financial markets, savings is
restricted to be zero and consumption is a
function of current income
Time
Savings > 0
With financial markets, consumption is no
longer tied to current income, but instead is
related to wealth
Income
Consumption
Time
Savings < 0
Wealth equals the present value
of lifetime income
Let’s suppose the following…you have a job that currently pays you $80,000. Next year, will be retired and expect to collect
$20,000 in retirement benefits. Further, assume that the only good to buy is pizza and a pizza costs $10 (assume that there is
no inflation).
Without Financial
markets
With Financial
markets
C  8, 000
C '  2, 000
S 0
C  8, 000  S
C '  2, 000  1  r  S
C'
2, 000
C
 8, 000 
1 r
1 r
Wealth
Let’s suppose the following…you have a job that currently pays you $80,000. Next year, will be retired and expect to collect
$20,000 in retirement benefits. Further, assume that the only good to buy is pizza and a pizza costs $10 (assume that there is
no inflation). Finally, assume that you can borrow and lend at a 5% interest rate.
Future
Current Income = $80,000 (8,000 Pizzas)
Future Income = $20,000 (2,000 Pizzas)
Slope 
10, 400
Price of Pizza: $10
Interest Rate= 5%.
Inflation Rate = 0%
Real Interest rate = 5%.
10, 400
 1.05
9,904.7
Savings > 0
Savings < 0
2, 000
$80, 000 
0
Current Consumption = $0.
•
Savings =$80,000
•
Future Available Income = $80,000(1.05) + $20,000
8, 000
Current Consumption = $80,000
•
Savings = $0
•
Future Available Income = $20,000
9,904.7
$20, 000
 $99, 047
1.05
Current
Current Consumption = $99,047
•
Savings = - $19,047
•
Future Available Income =$0
What you choose to do depends on your preferences!
Total Utility
(Happiness)
U  U (C ', C )
Future
Consumption
If you save one pizza
(i.e. you consumer one
less pizza) what do you
lose?
If you save one pizza,
what do you gain?
Current
Consumption
Value of a pizza now
The utility (happiness)
that pizza would’ve
given you
A pizza next year, plus
the interest earned on
that pizza
MU C
1  r  MU C '
The pizza plus the
earned interest
Value of a pizza
next year
Just like with businesses, when we maximize our utility (happiness), we equate costs and benefits at the margin)
Benefits of Saving
1  r  MU C '
Let’s rewrite this…
Marginal Rate of
Substitution
1  r  
MU C
 MRS
MU C '
Cost of Saving
=
MU C
Marginal Rate of substitution measures the
value of current consumption in terms of
future consumption
Utility
MU C Current Pizza Future Pizzas
MRS 


Utility
MU C '
Current Pizza
Future Pizza
Total Utility
(Happiness)
U  U (C ', C )
Future
Consumption
We only have a couple requirements for utility functions
•Utility is increasing in both current and future consumption (i.e.
we like to buy things!)
•Utility exhibits diminishing marginal utility (the more we have of
anything, the less it is worth to us at the margin)
Current
Consumption
MRS
MRS
As you save more, current consumption falls
and the marginal utility of that consumption
increases
MRS2
• High marginal utility of current consumption
• Low Marginal Utility of future consumption
• High MRS
MU C
MRS 
MU C '
MRS1
As you save more, future consumption
increases and the marginal utility of that
consumption falls
• Low marginal utility of current consumption
• High Marginal Utility of future consumption
• Low MRS
S1
S2
S
Of all the affordable choices, the one that equates costs and benefits at the margin is the best choice!
Future
MRS
MRS
10, 400
1  r   MRS
1  r   MRS
5,100
1  r  1.05
1  r   MRS
2, 000
S
S *  3, 000
1  r   MRS
Utility is increasing
1  r   MRS
Utility is decreasing
0
5, 000
8, 000
Current Consumption = $50,000
•
Savings = $30,000
•
Future Available Income = $30,000(1.05) +
$20,000 = $51,500
Current
9,904.7
Suppose that the interest rate increases to 8% (real interest rate is now 8%)
Future
The substitution effect generates a
savings curve that’s upward sloping
(normal)
Possibility #1: Savings
Increases (Substitution Effect)
10, 400
6, 200
r
S
.08
5,100
.05
2, 000
0
4, 000 5, 000
8, 000
Current
9,904.7
3, 000
Current Consumption = $40,000
•
Savings = $40,000
•
Future Available Income = $40,000(1.05) +
$20,000 = $62,000
4, 000
S
Suppose that the interest rate increases to 8% (real interest rate is now 8%)
Future
The income effect generates a savings
curve that’s downward sloping
(weird)
Possibility #2: Savings
decreases (Income Effect)
10, 400
r
.08
5,132
5,100
.05
2, 000
0
5, 000 5,100
8, 000
S
Current
9,904.7
2,900 3, 000
Current Consumption = $51,000
•
Savings = $29,000
•
Future Available Income = $29,000(1.08) +
$20,000 = $51,320
S
So, which is it?
r
Possibility #1: Savings
Increases (Substitution Effect)
r
S
1.5
Possibility #2: Savings
decreases (Income Effect)
.08
OR
1.2
.05
S
3, 000
4, 000
S
We usually assume the substitution effect dominates!
2,900 3, 000
S
How would a change in income affect your spending decisions?
Future
Current Income = $80,000 (8,000 Pizzas)
Future Income = $20,000 (2,000 Pizzas)
10, 400
Price of Pizza: $10
Interest Rate= 5%.
Inflation Rate = 0%
Real Interest rate = 5%.
MU C
 1 r
MU C '
5,100
2, 000
0
5, 000
8, 000
9,904.7
Current Consumption = $50,000
•
Savings = $30,000
•
Future Available Income = $30,000(1.05) + $20,000 = $51,500
Current
Suppose that your current income increases to $90,000 …how
would your savings be affected?
Future
Recall what’s happening with the savings
decision at the margin…
10, 400
MU C  MU C ' 1  r 
OR
5,100
MU C
 1 r
MU C '
2, 000
Marginal Rate of
Substitution
0
5, 000
Current Consumption = $50,000
•
Savings = $30,000
•
Future Available Income = $30,000(1.05) +
$20,000 = $51,500
8, 000
Current
9, 000
Let’s back up and think about this optimality condition for a second…
MU C  MU C ' 1  r 
Real rate of return on
savings
Let’s imagine what optimal behavior would look like in a zero real interest rate
environment…
MU C  MU C '
You would be creating a savings plan so
that your marginal utility of
consumption is constant…
Income
During periods of
high income, your
savings is positive
Consumption
Time
During periods of
low income, your
savings is negative
Now, with a positive interest rate…
MU C  MU C ' 1  r 
You would be creating a savings plan so that your
marginal utility of consumption is always a little
bigger today than it is tomorrow (i.e. with a 5%
interest rate it would be 5% bigger today)
Income
Consumption
During periods of
high income, your
savings is positive
Time
During periods of
low income, your
savings is negative
With diminishing marginal utility, this implies a consumption path that is growing over time
Future
Y  90, 000
Y '  20, 000
W  $110, 000
At a zero interest rate, you would be dividing your wealth up evenly over
your lifetime..
r
S
Current Consumption = $55,000
•
Savings = $35,000
•
Future Available Income = $20,000 + $35,000 = $55,000
10, 000
0
5,500
5, 000
3, 000
2, 000
3,500
S
An increase in current income of $10,000 would
cause savings to go up by $5,000 (500 pizzas)
0
5, 000 5,500
8, 000
Current Consumption = $50,000
•
Savings = $30,000
•
Future Available Income = $30,000 + $20,000 = $50,000
9, 000 10, 000
Current
Future
Y  80, 000
Y '  30, 000
W  $110, 000
At a zero interest rate, you would be dividing your wealth up evenly over
your lifetime..
r
S
Current Consumption = $55,000
•
Savings = $25,000
•
Future Available Income = $30,000 + $25,000 = $55,000
10, 000
0
5,500
3, 000
2,500 3, 000
2, 000
S
An increase in future income of $10,000 would
cause savings to go down by $5,000 (500 pizzas)
0
5, 000 5,500
8, 000
Current Consumption = $50,000
•
Savings = $30,000
•
Future Available Income = $30,000 + $20,000 = $50,000
Current
10, 000
Future
Y  85, 000
Y '  25, 000
W  $110, 000
At a zero interest rate, you would be dividing your wealth up evenly over
your lifetime..
r
S
Current Consumption = $55,000
•
Savings = $30,000
•
Future Available Income = $25,000 + $30,000 = $55,000
10, 000
0
5,500
5, 000
2,500
2, 000
3, 000
S
An increase in current and future income of
$5,000 would have no effect on savings
0
5, 000 5,500 8, 000 8,500
Current Consumption = $50,000
•
Savings = $30,000
•
Future Available Income = $30,000 + $20,000 = $50,000
Current
10, 000
In all three cases, the effect on
wealth was the same and so
the effect on consumption is
the same (i.e. consumption is
a function of wealth, not
income)
Current Income = $80,000 (8,000 Pizzas)
Future Income = $20,000 (2,000 Pizzas)
Real Interest Rate = 0
Wealth = $80,000 +$20,000 = $100,000
Current Consumption = $50,000
Future Consumption = $50,000
Savings = $30,000
Consumption is a
function of wealth.
C  C Wealth 
S Y C
Savings = Income minus
consumption.
Case #1
Case #2
Case #3
Current Income = $90,000 (9,000 Pizzas)
Future Income = $20,000 (2,000 Pizzas)
Real Interest Rate = 0
Current Income = $80,000 (8,000 Pizzas)
Future Income = $30,000 (3,000 Pizzas)
Real Interest Rate = 0
Current Income = $85,000 (8,500 Pizzas)
Future Income = $25,000 (2,500 Pizzas)
Real Interest Rate = 0
Wealth = $90,000 +$20,000 = $110,000
Wealth = $80,000 +$30,000 = $110,000
Wealth = $85,000 +$25,000 = $110,000
Current Consumption = $55,000
Future Consumption = $55,000
Savings = $35,000
Current Consumption = $55,000
Future Consumption = $55,000
Savings = $25,000
Current Consumption = $55,000
Future Consumption = $55,000
Savings = $30,000
Capital Markets – Equilibrium
r
r
S
Households choose
how much to save
*
Businesses/Government
choose how much to
borrow
Using the accounting identities, the capital
market in equilibrium implies that every
good/service that’s produced gets used
Borrowing = Lending
S *  I *  G  T 
Output = Expenditures
Y *  C*  I *  G
I  G  T 
S  I  G  T 
*
*
Equilibrium savings
equals equilibrium
borrowing
Loanable
funds
Capital Markets – Long Run dynamics
As our incomes rise, our savings
increases
r
S
r*
I  G  T 
I
S *  I *  G  T 
Long term productivity growth raises
the value of capital at the margin –
increasing investment
Loans
C*  I *  G  Y *
Over the long term, real returns are constant and savings/investment rise
Capital Markets – Business cycle dynamics
r
S
r*
During economic expansions, capital productivity is
above trend…the pushes investment up
I  G  T 
S *  I *  G  T 
C*  I *  G  Y *
Loans
During recessions capital productivity is below
trend…this pushes investment down
During recessions,
productivity declines.
Investment falls – interest
rates decline
r
S
r
S
I  G  T 
I  G  T 
Loans
% Deviation From
Trend
During recoveries,
productivity
increases.
Investment rises –
interest rates rise.
Loans
Consumption
GDP
Peak
+
Predicted Correlations
Savings
+
Investment
Interest
Rate
+
+
Peak
GDP
Consumption
Savings
0
Investment
Real Interest rate
Trough
Recession
Recovery
Time
Productivity
+
Are we measuring real returns correctly?
Correlations With GDP
Savings
Actual
Consumption
Investment
+
+
+
-
(.83)
(.77)
(.78)
(-.35)
+
+
+
+
Predicted
r  i  e
Real Interest
Rate
?
Inflation expectations
(unobserved)
Maybe we need to take a closer look at savings behavior….
r
S
MRS  1  r 
S
Marginal rate of substitution measures the value to you of
current consumption in terms of how much you need to
be compensated in the future to give it up. We need to
take a closer look at this
Given your objective to “smooth out” your consumption as much as possible, how would you respond to an
unexpected drop in your income? Depends on your expectations…
r
r
S
r
S
S
S
S
S
Income
Income
Time
1
2
Case #1: You expect your
income to rebound quickly
1
2
Income
Time
Case #2: You expect your
income to remain low
permanently
Time
1
2
Case #3: You expect things
to get worse
Correlations With GDP
Savings
Actual
Predicted
Consumption
Investment
Given the empirical evidence, it seems as
though consumers see economic
downturns as temporary phenomena and
“smooth out” their consumption by
lowering their savings during a recession.
Real Interest
Rate
+
+
+
-
(.83)
(.77)
(.78)
(-.35)
+
+
+
+
r
S
r*
I
S I
*
*
S, I
Example: Oil Price Shocks in the 1970’s
Dollars per Barrel
1979 Iranian
Revolution
(Temporary Shock)
1973 Arab Oil
Embargo
(Permanent Shock)
Just as with labor markets, we
can examine the effect of high
oil prices on capital market
decisions. Remember, high
energy prices can be looked at as
a decline in productivity
r
r
S
I
I
I
Real Interest Rate
Investment (% Dev. From Trend)
I
Interest rates and Investment (1972 – 1982)
S
1973 Arab Oil
Embargo
1979 Iranian
Revolution
In both cases, the oil price
shocks resulted in large
declines in both investment
and interest rates – this
suggests there was a minimal
effect on savings