Notesale: Turn your study into money

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EC201 Intermediate Macroeconomics
EC201 Intermediate Macroeconomics

Lecture 6: Money Market and the LM Curve

Lecture Outline:
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the LM curve, and its relation to the liquidity preference theory

Essential reading:
Mankiw: Ch
...
2
The Theory of Liquidity Preference
In discussing the money market in the long-run we showed how prices adjust to
maintain the money market equilibrium
...
Keynes argued that in the short-run the interest rate
adjusts to balance the supply and demand for the economy’s most liquid asset, money
...

We still assume that:

 ∂L 
a) 
>0
 ∂Y 
Demand for real money balances increases with total income (more income = more
transactions = more money needed)

 ∂L 
b)   < 0
 ∂r 
Demand for real money balances decreases with the interest rate since r represents the
cost opportunity of holding money (higher is the interest rate and higher is the return
people can obtain by putting their money into less liquid assets like bonds)
...

Furthermore, since in the short run prices are fixed, the supply of real money balances
s

 M  is completely exogenous in the short run:
 
 P
s

M
M 
  =
P
P


In equilibrium we must have that supply =demand:

M
= L(Y , r )
P
The theory of liquidity preference explains how the interest rate that will adjust to
keep the money market in equilibrium in the short-run
...
According to the theory of liquidity preference
people keeps some portfolios with many assets in them
...

Now suppose that there is an excess of money supply respect to the demand
...
Now people have an excess of money they
do not want to hold so they convert this excess of money into assets that pay an
interest rate
...
Adding more
complicated assets will not change the main results)
...
+
+
...
In that equation we assume
that the interest rate is constant over the entire period (this is clearly a strong
assumption, but it is made to simplify things
...
This means that the price and the return for
this asset are negatively related (this is a basic result in finance)
...
Given that people have excess money that they want to convert into
2

bonds, the demand for bonds will increase
...
In our case,
the only way the price of the bonds can increase is by a decrease in the interest rate
...
This movement in the
interest rate will increase money demand (if r decreases money demand increases)
until the equilibrium between money supply and money demand is restored
...
In that case people want to hold more money, so they convert their assets into
liquid money and so the demand for bonds will decrease and so the price of bonds
...


In the graph we have the supply of real balances that is a vertical line because it is
exogenous, while the demand is decreasing in the interest rate (Y is fixed for the
moment)
...

At the interest rate r2 there is an excess of supply of money
...


3

Using our simple model we can analyse what is the effect on the equilibrium interest
rate when the central bank increases or decreases money supply
...

How the central bank raises the interest rate in the short-run?
Looking at the graph, the obvious answer is by decreasing money supply
...

Why? The idea is given by the theory of liquidity preference
...
People will start converting their less liquid assets into
liquid money
...

As the interest rate increases, money demand will be reduced and the initial excess of
demand will be eliminated and the equilibrium restored with an interest rate that is
now higher than the previous one
...
In the long-run (with flexible prices) a decrease in money supply
will decrease the price level and therefore will decrease inflation
...
On the other hand in the short-run, given that prices are fixed in our
model, a decrease in money supply will INCREASE the nominal interest rate (in this
case remember that i = r )
...
In October 1979, the chairman of the FED Paul Volcker
announced that monetary policy would aim to decrease inflation
...
Between August 1979 and
April 1980 the FED reduced the money supply in such a way that

M
decreased by
P

8% during that period
...
4%
...
8%
...
In January 1983, that compared to August 1979 can be considered in the
long run, the nominal interest rate was 8
...
7%
...
Notice however, that
the inflation and the nominal interest rate did not fall by equal amounts
...
This example seems to confirm that the two
theories fit well the data
...
The Federal
Reserve used to change money supply to change the interest rate
...
Nowadays, monetary policy in many countries is the reverse of what is
described above
...
In this case money supply is endogenous since it depends on the
what the market is asking
...

Such a schedule is called the LM curve
...

How to derive the LM curve from the money market equilibrium:

5

The market for
real money
balances

(a)

r

(b) The LM curve

r
LM

r2

r2
L (r , Y2 )

r1

r1

L (r , Y1 )
M1
P

M/P

Y1

Y2

Y

Suppose an increase in real income Y, from Y1 to Y2
...
Given that the money supply is fixed, there is
now an excess of money demand at the initial interest rate
...
So the interest rate must
rise to restore equilibrium in the money market
...
Therefore, there is a positive
relationship between r and Y coming from the money market
...

The LM curve equation:
M
= L(Y , r )
P

1)

that is exactly the equilibrium condition in the money market
...

Notice that the LM equation gives you a relation between r and Y only IMPLICITLY
...
When we have an implicit function, we can use
∂Y

the Implicit Differentiation to obtain that derivative (see the Appendix)
...

P

Implicit differentiation says that given F (Y , r , M , P ) = 0 , the derivative

∂r
is given
∂Y

by:

∂r
F
=− Y
∂Y
Fr

3)

where Fr is the partial derivative of the function F with respect to r
...
Using those facts into equation 3) we can see that: ∂r > 0
∂Y

Mathematical Appendix
a) Geometric Series
A geometric progression is a sequence of numbers where each new number is
generated by multiplying the previous number by a constant term
...


The general form of a geometric progression is:
a, aR, aR2 , aR3 ,
...

where a is the initial value
...
+ aRn−1 + aRn +
...


Now consider the present value of a series of n payments or receipts:
PV =

y1
y2
y
yn
+
+ 3 3 +
...

This is the case of the bond we have considered in the lecture note
...

Result B) was:

a

∑= 1− R
∞

8

Where a is the first element of an infinte geometric series
...
+
+
...

An Implicit Function is a function like:
F ( x, y) = 0

meaning that we do not know how to express EXPLICITLY (or simply we do not
want to) one variable (for example y) as a function of the other (for example x)
...

2

An example of an IMPLICIT function is: ( x 2 + y 2 )2 − ( x 2 + y 2 ) = 0
In the second case to express directly y as a function of x can be particularly difficult
(in this particular case it is impossible)
...

Implicit

Differentiation

Rule:

given

an

implicit

variables F ( x1 , x2 ,
...
,n , and where Fi =

∂F ( x1, x2 ,
...
, xn )
is the partial
∂xi

derivative of the function F with respect to xi
...

For example: consider the explicit function y = a + bx
...

If you apply the implicit differentiation rule to this implicit version of the function
you have:

F
dy
= − x = 2bx
dx
Fy
where Fx =

∂F ( x, y)
∂F ( x, y)
= −2bx and Fy =
= 1

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