mtopic 2 - the l-m schedule

7/30/2019 MTopic 2 - The L-M Schedule

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Topic2:- The L-M Curve

1/ Introduction

The L-M schedule sets out all of the possible combinations of real output, y

and the rate of interest, r consistent with equilibrium in the money market.

The money market will be in equilibrium if

MD = MS

where MD is the Demand for Money

and M

S

is the Money Supply

In the foregoing analysis, we will be examining the demand and supply of real

balances.

i.e. MD/P = MS/P

where P is the price level

MD/P id the demand for real balances

MS/P is the real money supply

To make progress, we will examine the determinants of real money demand

and real money supply.

2/ The Demand for Money

In general, we can write that

MD/P = g(y, r)

where y is income and r is the rate of interest.

This expression indicates that the demand for real money balances depends on

real income and the rate of interest. To examine this more closely, we follow

Keynes and partition money demand into 3 components or motives for holding

money. Viz


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Transactions motive

Precautionary motive

Speculative motive

A/ The Transactions Motive for Holding Real Balances

Let the real money demand for transactions purposes be MDT/P

MDT is the amount of money carried around by an agent in a period in order to

undertake known transactions.

Keynes argued that the demand for real transactions balances will depend on

the level of real income.

i.e. MDT/P = f(y)

As real incomes rise, people will be able to afford to satisfy a greater range of

wants and needs and will plan to make a greater level of known expenditures

in a period.

Therefore (MDT/P)/y > 0

This expression says that, as real incomes rise, the demand for real balancesfor transactions purposes will also rise.

B/ The Precautionary Motive for Holding Real Balances

Let the real money demand for precautionary purposes be denoted by

MDP/P

Where MD

P is the amount of money held by an individual in a period in orderto cater for unforeseen or unpredictable transactions.

The demand for real balances for precautionary purposes will also depend on

the level of real income. Thus

MDP/P = g(y)

As real incomes rise, the type and price of unforeseen or impulse purchases

will also increase. Thus,


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(MDP/P)/y > 0

i.e. as real incomes rise, the demand for real precautionary balances will

likewise rise.

C/ The Speculative Motive for Holding Real Balances

Denote the money demand for speculative balances as

MDS/P

It is this motive for holding money that links money demand to the rate of

interest. Recall that the classical economists regarded the interest rate as being

determined in the capital market by

The flow of savings (supply of loanable funds)

The flow of investment (demand for loanable funds)

Classicists viewed that the rate of interest adjusted quickly to balance savings

and investment.

Keynes rejected this view by arguing that the rate of interest was determined in

the money market

There are several accounts/models which can be deployed to justify a

relationship between MDS and r. We will consider a simple account based on

the notion of the Opportunity Cost (OC) of Holding Money. There is a slightly

fuller account in Appendix L-M

The opportunity cost of holding money can be regarded as what is lost by not

holding your wealth in the form of interest bearing assets. In simple

approaches, there are 2 ways of holding wealth

Money pays no interest

Bonds pay a rate of interest per period

Clearly, the OC of holding money is the interest payments foregone

N.B. You can conceptualise money as notes, coins and zero interest bearing

bank accounts such as cheque accounts. The alternative to this would be to

hold interest bearing accounts (deposit or savings accounts) or less liquid

assets such as bills, bonds shares etc.


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The argument is simple. If interest rates rise, the OC of holding money rises

and people will hold less money and more bonds. We can represent this insight

graphically in Figure 1. At a low rate of interest, r1 the incentive to switch

from money into bonds is not great and people will tend to hold (demand)

more money, MD

S1. At a high interest rate, r0 ,the OC of holding money is highand people will economise on money holdings (MDS0)

3/ The Supply of Money

The real money supply / supply of real balances is denoted by MS/P. As prices

rise the real money supply falls and vice versa.

The money supply is taken to be exogenously determined and controlled by

the monetary authority / central bank. Thus, the money supply does not depend

on either r or y and is a policy instrument which can be changed at the behest

of the authorities.

4/ Equilibrium in the Money Market

We can take our expressions for transactions, precautionary, speculative

balances and the money supply and set them out in Figure 2 . Here, re is the

rate of interest/ price of bonds at which agents in the economy willingly hold

the issued real money stock.

MDS1/PMD

S0/P

MDS/P

r1

r0

Figure 1- Speculative Demand for Money


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Changes in the Money Supply

Suppose the Central Bank decided to increase the money supply from MS0 to

MS1. This would cause the money supply line to shift out as seen in Figure 3.

The money supply schedule shifts but the money demand curve is unaffected

because income, which determines transactions and precautionary holdings

has not changed.

Following the increase in the money stock, money holdings are greater thanthose required to finance known and precautionary transactions. Agents will

r

MD

/P

re

Figure 2- Equilibrium in the Money Market

MS/P

MD/P

MDS/P

MD

T/P +MDP/P

MD/P = MS/P

MD/P

& MS/P

MS1/PMS

0/P

re0

re1

Figure 3 Increase in the Money Supply

r


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attempt to purchase bonds driving up their price and down the rate of interest

from re0 to re1. The price of bonds will rise/ rate of interest fall until the

increased money stock is willingly held.

Thus, changes in r, the rate of interest, are the mechanism which re-equilibriatethe money market. There is no a priori reason why r should also serve to

equate savings and investment as the classical school believes.

5/ Deriving the L-M Schedule

The L-M curve is defined as all values of r and y consistent with equilibrium

in the money market. This suggests that to derive the L-M schedule we should

vary y and establish what happens to r in order to restore money market

equilibrium.

If y increases, both the transactions and speculative demand for money will

increase out of a fixed real money stock. This will require agents to sell bonds

in order to finance higher known and precautionary purchases. If there is

increased selling pressure on the fixed stock of bonds, then the price of bonds

will fall (i.e. the interest rate will rise). This is set out in Figure 4a for the case

when income rises from y0 to y1 to y2 and where we assume a linear money

demand curve

We obtain the L-M curve by mapping r versus y. As real income

increases the transactions and precautionary demand for real balancesincreases out of a fixed real money stock. This necessitates bond sales

r

MD/P

Figure 4a Deriving the L-M Curve

MD/P (y=y2)

MS/P

MD/P (y=y1)

MD/P (y=y0)


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which drive down the price of bonds/ up the rate of interest in order to

restore equilibrium in the money market.

6/ What Determines the Slope of the L-M Schedule

The slope of the L-M curve depends on

1. the interest sensitivity/ elasticity of the speculative demand for money

2. the income elasticity of money demand

You should attempt to construct L-M schedules for different interest and

income elasticities

7/ What causes the L-M Schedule to Shift

The L-M curve is sets out all the combinations of r and y consistent with

equilibrium in the money market. Equilibrium in the money market results

when MD/P = MS/P. The L-M curve is derived by varying real income given a

fixed real money stock and examining the changes in r required to maintain

money market equilibrium. If the real money stock changes, then a new L-M

curve will be engendered.

The real money stock is the nominal money supply deflated by some measure

of the price level. Thus:-

r

y

Figure 4b Deriving the L-M Curve

y0

y1

y2

r0

r1

r2

L-M


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1. A rise in the real money stock results when either the nominal money

supply rises or the price level falls.

2. A fall in the real money supply results when either the nominal money

supply falls or the price level rises.

Consider a rise in the real money supply from (MS/P) to (MS/P)*.

At the original level of the money stock, MS/P, the equilibrium rate of interest

when y = y0 is r0. As income increases to y1, the money demand schedule shifts

up to MD/P(y1). The higher money demand from a fixed money stock causes

agents to sell bonds to obtain money for increased transactions and

precautionary purposes. This causes the interest rate to rise until the moneymarket returns to equilibrium at the higher interest rate, r1. Mapping r versus y

we obtain L-M.

When income is y0, an increase in the money stock from (MS/P) to (MS/P)*

causes an excess supply of money for transactions and precautionary purposes.

Agents attempt to purchase bonds, increasing the demand for bonds from a

fixed supply. This drives up bond prices and down interest rates from r0 to r0*

until the expanded money supply is willingly held.

MD/P(y0)

MD/P(y1)

y0

y1

r0*

r0

r1*

r1

(MS/P) (MS/P)*r

real MD & Ms

r

y

L-M*

L-M

Figure 5: An Increase in the Money Stock

causes the L-M Curve to Shift Outwards.


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If income rises from y0 to y1 and the money supply is at the higher level

(MS/P)*, there is an increased demand for money for transactions and

precautionary purposes. Agents attempt to sell bonds driving down the bond

price and pushing up the rate of interest from r0* to r1*. The L-M schedule for

the expanded money stock is L-M*.

Thus, at any level of income, lower interest rates are necessary to equilibriate

the money market given a rise in the money supply. The higher money stock

results in excess balances for transactions and precautionary purposes which

agents use to attempt to increase purchases of bonds. This drives up bond

prices and down the rate of interest. Therefore at any level of income, interest

rates must fall to restore money market equilibrium. Hence, a rise in the real

money stock causes the L-M schedule to shift outwards.

Learning Objectives

On reading this and the accompanying Appendix L-M, you should be able

to:-

1. Understand the Money Market. What are the determinants of Money

Demand. Why is the speculative demand for money thus named. How

does the money market return to equilibrium following a shock to

either money demand or money supply

2. Derive the L-M schedule

3. Understand the factors which determine the slope of the L-M curve

4. Understand what causes the L-M curve to shift (i.e. what factors are

held constantwhen deriving the L-M curve)

Jim Stevens

OCTOBER 2004

mtopic 2 - the l-m schedule

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