Transcript Document

Money and Interest Rates
MBA 774
Macroeconomics
Class Notes – Part 2
Money and Interest Rates
1
What is Money?

Medium of exchange
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Unit of account
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Allows transactions not based on barter
Avoids the need for a “double coincidence of wants”
Common measure of value for goods, services, and
contracts
Store of value
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Allows for transfer of wealth through time
Most liquid of all assets
Money and Interest Rates
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Types of Money
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Pure Commodity
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Commodity Standard
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Scarce commodity is agreed on as “money”
For example: gold, silver, cattle, cigarettes
Certificates representing claims on a commodity are
issued and used instead of the commodity itself
For example: the US was once on a “gold standard”
Fiat Money
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Money established by government decree
Fiat money has no intrinsic value
Money and Interest Rates
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US Measures of Money

Currency = Bills and coins outside U.S. Treasury, Federal
Reserve Banks and the vaults of depository institutions
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M1 = Currency plus travelers’ checks, demand deposits,
other checkable deposits
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M2 = M1 plus savings deposits, small-denomination time
deposits, retail money market mutual funds, and overnight
repurchase agreements
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M3 = M2 plus large-denomination time deposits, institutional
money funds, and Eurodollars
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L = M3 plus other liquid securities such as savings bonds
and short-term Treasury securities
Money and Interest Rates
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US Money Supply Statistics
Measure
USD Billions
% of M3
1-yr %Chg
Currency
653
7.3%
5.6%
M1
1,288
14.5%
8.1%
M2
6,109
68.6%
7.2%
M3
8,900
100.0%
6.8%
Source: Federal Reserve Statistical Release H.6
Money and Interest Rates
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The US Federal Reserve

Federal Reserve System is the US “central bank”
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Foreign counterparts include the European Central Bank
(ECB), The Bank of England, and the Bank of Japan
Founded in 1913 by congress, “to provide the
nation with a safer, more flexible, and more stable
monetary and financial system.”
Primary functions are
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Monetary policy
Banking supervision and regulation
Providing certain services (e.g., check clearing)
Money and Interest Rates
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The US Federal Reserve (2)
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The “System” is composed of 12 regional banks
and a Board of Governors in Washington, DC
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Governors, the Chairman and Vice-Chairman are
appointed by the President and confirmed by the Senate
Monetary policy is overseen by the “Federal Open
Market Committee” or FOMC which includes
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Board of Governors
Fed Bank of NY President
4 other regional bank presidents on a rotating basis
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Monetary Policy (1)
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About every six weeks the FOMC meets to
determine monetary policy for the US
In practice, this means determining the target for
the “Federal Funds Rate” which is an inter-bank
overnight interest rate
Fed decreases (increases) the Fed Funds rate by
buying (selling) government securities which
increases (decreases) the available money supply
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The Federal Reserve Bank of NY makes these
purchases or sales on the open market--hence the name
Federal Open Market Committee.
Money and Interest Rates
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Money and Interest Rates
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Monetary Policy (2)
9.00%
Fed Funds Target
Fed Funds Actual
7.00%
6.00%
5.00%
4.00%
3.00%
2.00%
1.00%
0.00%
The Fed’s Actions around 9/11
4.00%
3.50%
3.00%
2.50%
Fed Funds Actual
Fed Funds Target
2.00%
1.50%
1.00%
0.50%
Stock Markets Re-open
9/
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0.00%
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Monetary Policy (3)
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The official objectives of US monetary policy are,
“economic growth in line with the economy's
potential to expand, a high level of employment,
stable prices (that is, stability in the purchasing
power of the dollar), and moderate long-term
interest rates.”
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Conceptually, the Fed will raise (the real) interest
rate if GDP is greater than “Potential GDP” and
vice-versa
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Aside: Real vs. Nominal Rates
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It is often said that the interest rate is the “cost of
money.” Is this true?
Ultimately, we use money to obtain consumption
goods
Think of the interest rate in terms of trading some
real amount of consumption in one time period for
some real amount of consumption in another time
period
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Note however, borrowing and lending contracts are
stated in nominal terms.
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Aside: Real vs. Nominal Rates
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The real rate of interest (R*) can be defined as
approximately,
Real Interest Rate =
Nominal Interest Rate - Anticipated Inflation
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Currently, what is R* in the U.S.? Japan?
Money and Interest Rates
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Monetary Policy (4)
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Potential GDP is the rate of economic activity that
leads to stable prices and employment
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Intuitively it is the amount of output that is
generated by utilizing all available resources at
there highest sustainable level.
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Algebraically, we can think of it as
PotGDP = (aggregate hours available for work) x
(average output per hour)
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Monetary Policy (5)
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Economists often discuss the Potential GDP
Growth Rate which is approximately
PotGDP Growth = Labor Force Growth Rate
+ Productivity Growth Rate
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We can calculate PotGDP Growth with this formula
for the last 50 years
Money and Interest Rates
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Historical Potential GDP
10.0%
Productivity Growth
Labor Force Growth
8.0%
6.0%
4.0%
2.0%
0.0%
Money and Interest Rates
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95
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90
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85
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80
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-2.0%
Better Estimates of PotGDP
6.0%
5.0%
4.0%
3.0%
2.0%
1.0%
PotGDP-Congressional Budget Office Estimates
PotGDP-( 5yr- Moving Average from Previous Graph)
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00
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0.0%
Monetary Policy and the GDP Gap
Note: GDP Gap = (Actual GDP - PotGDP) / PotGDP
10.0%
Real Fed Funds
GDP-Gap
5.0%
0.0%
-5.0%
Money and Interest Rates
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-10.0%
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Monetary Policy
Monetary
Policy
Regime
Change
Regime Change
NAIRU
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Another way of thinking about potential output is
the equilibrium rate of unemployment or NAIRU
(Non-accelerating Inflation Rate of Unemployment)
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NAIRU is the rate of unemployment below which
there will be inflationary pressures
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The exact level of NAIRU is an issue of debate.
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Most economists believe it is somewhere between 4%
and 6% in the US and Japan. Probably higher in Europe
(7-8%).
Money and Interest Rates
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Monetary Policy and NAIRU
Note: U-NAIRU is actual unemployment minus NAIRU and is sometimes called the employment gap.
10.0%
Real Fed Funds
U-NAIRU
5.0%
0.0%
Monetary Policy
Regime Change
Money and Interest Rates
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-5.0%
Other Mechanisms for Monetary Policy
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The Fed also has two other ways of controlling
monetary policy
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The discount rate
Reserve requirements
Reserve requirements (rr) directly affect the level of
money via the “money multiplier” (1/rr)
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Example, if the reserve requirement is 20% of deposits
then the money multiplier is 1/0.2 = 5
Money and Interest Rates
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Fractional Reserve Banking
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The Fed buys a $1,000 (market value) treasury
bond from a bond dealer
The dealer deposits the $1,000 proceeds into its
bank, FirstBank
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Money supply increases by $1,000
FirstBank only has to keep $200 as reserves and
loans the $800 balance:
FirstBanks Balance Sheet
Assets
Liabilities
Reserves
$200
Deposits
Loans
$800
Money and Interest Rates
$1,000
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Fractional Reserve Banking (2)
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Assume FirstBank made an $800 computer loan to
a student. Money supply increases to $1,800
The student buys a computer at BestBuy which
deposits the $800 at its bank, SecondBank
SecondBank also loans out all but 20%
SecondBank Balance Sheet
Assets
Liabilities
Reserves
$160
Deposits
Loans
$640
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$800
Now money supply = 1,000 + 800 + 640 = 2,440
Money and Interest Rates
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Fractional Reserve Banking (3)

This practice of keeping 20% reserves and loaning
out the rest continues indefinitely
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However, the ultimate increase in the money supply
(DMS) is finite and equal to
DMS = DD / rr
DMS = $1,000 / 0.2
DMS = $5,000
where DD is the original increase in money by the Fed
[ Mathgeeks note, its a converging geometric sequence:
1+x+x2+x3+... = 1/(1-x) where x = (1-rr) ]
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Fed Reserve Requirements
Type of Deposit
Net transaction accounts
$0 million-$6.6 million
$6.6 million-$45.4 million
More than $45.4 million
Nonpersonal time deposits
Eurocurrency liabilities
Requirement
% of Deposits
Effective Date
0
3
10
0
0
12/25/03
12/25/03
12/25/03
12/27/90
12/27/90
Required reserves must be held in the form of deposits with Federal Reserve Banks or vault
cash. Nonmember institutions may maintain reserve balances with a Federal Reserve Bank
indirectly, on a pass-through basis, with certain approved institutions. Under the Monetary
Control Act of 1980, depository institutions include commercial banks, savings banks, savings
and loan associations, credit unions, agencies and branches of foreign banks, and Edge Act
corporations.
See also: http://www.federalreserve.gov/monetarypolicy/0693lead.pdf
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Interest Rates
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There are lots of important USD interest rates
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Federal funds rate
Discount rate
Prime rate
Commercial paper rate
LIBOR and Eurodollar (similar for other currencies)
T-bill, T-note, T-bond rate
Swap rates
Corporate bond rates
Overnight repurchase rate or “Repo” rate
Rates depend on credit risk, liquidity, and maturity
Money and Interest Rates
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Government Issues
20
3-month T-Bill
20-year T-Bond
Term Spread
15
10
5
Thru
5/06
0
Money and Interest Rates
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20
04
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-5
Corporate Bonds
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Moody's AAA Corp
Moody's Baa Corp
Baa Credit Spread (over Treasuries)
15
10
Thru
5/06
5
Money and Interest Rates
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20
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0
A Model of the Money Market
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More detail about what affects interest rates
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For now consider “money” to be M1
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Also we assume that the money supply is
controlled by the central bank (e.g., the US Federal
Reserve)
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Specifically, the central bank fixes the amount of
money in the aggregate economy (MS) at a level it
desires regardless of other factors
Money and Interest Rates
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Individual Money Demand
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Individuals’ demand for money is based on
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The expected (real) return on money:
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The riskiness of the return
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Money (M1) pays little or no interest
=> higher interest rates will lead to less demand for money
The risk of holding money comes from variation in the price
level. Why?
Liquidity
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The primary value associated with money is derived from
liquidity
Since a primary use of money is as a medium of exchange, this
implies an increase in the value of individual transactions
increases the demand for money
Money and Interest Rates
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Aggregate Money Demand
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Aggregate money demand is the sum of demand
for money by all households and firms in the
economy
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In aggregate we can say the determinants of the
aggregate demand for money are
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The interest rate
The price level (think CPI)
Real national income (or GNP or GDP)
Money and Interest Rates
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Aggregate Money Demand

Define aggregate money demand as
MD
= P * L(R,Y)
or
MD / P = L(R,Y)
where,
MD = Aggregate money demand
P = Price level
R = Interest rate
Y = Real national income (or GNP or GDP)
and,
L decreases as R increases
L increases as Y increases
Money and Interest Rates
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Aggregate Money Demand
Interest Rate (R)
Interest Rate (R)
Increase in Y
L(R,Y2)
L(R,Y)
L(R,Y1)
Aggregate
Real Money
(M/P)
Money and Interest Rates
Aggregate
Real Money
(M/P)
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Equilibrium in the Money Market
In equilibrium, MS = MD = P*L(R,Y)
Interest Rate (R)
Real Money
Supply
R2
2
1
R1
3
R3
Q2
Money and Interest Rates
MS/P
Q3
Aggregate Real
Money Demand
L(R,Y)
Aggregate
Real Money
(M/P)
34
Increase in Money Supply
Suppose the money supply increases from M1/P to M2/P
Interest Rate (R)
Real Money
Supply Increases
R1
1
2
R2
M1/P
Money and Interest Rates
M2/P
Aggregate Real
Money Demand
L(R,Y)
Aggregate
Real Money
(M/P)
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Increase in GDP
Suppose real income (GDP) increases from Y1 to Y2
Interest Rate (R)
Real Money
Supply
R2
2
R1
1
1’
L(R,Y2)
L(R,Y1)
MS/P
Money and Interest Rates
Q1’
Aggregate
Real Money
(M/P)
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Determining the Real Interest Rate
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The interest rate is the price of future consumption
in terms of consumption today
Consider an individual with the following attributes
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Two-period time horizon (today and 1 future date)
Only cares about one nonstorable commodity, say beer
Endowment of concave production technology to produce
beer equals T(X)
Convex preferences for present and future consumption
No opportunities to save across time periods
Rational (implying she maximizes intertemporal utility)
Knows the future with certainty
Money and Interest Rates
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Intertemporal Preferences
Future
Consumption
(t=1)
U1 > U2 > U3
U1
U2
U3
Consumption Today (t=0)
Money and Interest Rates
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Intertemporal Production Possibilities Frontier
Future
Consumption
(t=1)
18
13
T(X)
10
Money and Interest Rates
20
Consumption
Today (t=0)
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Optimal Consumption Without Savings
Future
Consumption
(t=1)
C*1 = X*1
=14
U*
C*0 = X*0 =9
Money and Interest Rates
Consumption
Today (t=0)
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Optimal Consumption Without Savings

Optimal level of production comes at tangency
point of production function and indifference curves
(this is the highest level of utility possible)

Because there is no ability to borrow or lend,
production = consumption in both periods so
C*0 = X*0
Money and Interest Rates
and
C*1 = X*1
41
Savings: Borrowing and Lending
C’’1 = C’’0 (1+R)
Future Consumption (t=1)
C’1 = C’0 (1+R)
C1 = C0 (1+R)
Slope of Savings Lines = -(1+R)
C0
Money and Interest Rates
C’0
C’’0
Consumption
Today (t=0)
42
Optimal Production With Savings
Future
Consumption
(t=1)
C**1 = 17
14
U**
U*
U** > U*
X**1 = 8
C**0 = 8 9
Money and Interest Rates
X**1 = 16
Consumption
Today (t=0)
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Optimal Production With Savings

If we allow savings across time periods our
individual will:

Choose the production levels at t=0,1 that maximizes total
wealth at time 0 (W0) defined as
W**0 = X**0 + X**1 / (1+R)

Then chose the level of consumption in each period:
(C**0 , C**1)
that maximizes total utility given the level of total wealth

Note that production and consumption are unbundled:
C**0  X**0 and C**1  X**1
Money and Interest Rates
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Optimal Production With Savings

In this example, our individual is a lender
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This is because C**0 < X**0
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In effect, our individual takes the amount not
consumed (X**0 - C**0) and puts it in the bank to
earn interest at a rate of R

If our individual had different preferences, she
might prefer to be a borrower
Money and Interest Rates
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Optimal Production With Borrowing
Future
Consumption
(t=1)
X**1
C*1 = X*1
C**1
U** > U*
U**
U*
X**0 C* C**0
0
=X*0
Money and Interest Rates
Consumption
Today (t=0)
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Change in the Interest Rate
Future
Consumption
(t=1)
Interest Rate Declines from RH to RL
CH1
CL1
UH UH > UL
UL
XL1
XH1
-(1+RL)
-(1+RH)
CH0<CL0 XL0<XH0
LendingL
Money and Interest Rates
LendingH
Consumption
Today (t=0)
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Why Are We Doing This?!?

First, what have we established so far?
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The ability to lend or borrow increases utility
The ability to lend or borrow uncouples production and
consumption
Individuals can be either borrowers or lenders depending
on their intertemporal preferences
Changes in interest rates effect the demand for
borrowing and lending
But our goal was to figure out where interest rates
came from. How do these results help us?
Money and Interest Rates
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Equilibrium Interest Rate

Now consider an economy with two individuals with
different intertemporal preferences

one will be a lender and one will be a borrower

Lender will be supplier of funds and borrower will
be demander of funds

The interest rate in the economy will be set so that
the supply of funds equals the demand for funds
Money and Interest Rates
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Equilibrium Interest Rate
Future
Consumption
(t=1)
CL1
UL*
Lender
X1
Borrower
CB1
UB*
CL0
Money and Interest Rates
X0
CB0
Consumption
Today (t=0)
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Aggregate Economy
Interest Rate
Desired Lending
(Supply of Funds)
Desired Borrowing
(Demand for Funds)
R*
Supply =
Demand
Money and Interest Rates
Borrowing / Lending
51