Topic2:- The L-M Curve1/ 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 Moneyand MS 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 levelMD/P id the demand for real balancesMS/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

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 Δ (MDT/P)/Δy > 0

This expression says that, as real incomes rise, the demand for real balances for 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 MDP is the amount of money held by an individual in a period in order

to 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,

Δ (MDP/P)/Δy > 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 MD

S 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 interestBonds 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….

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 high and people will economise on money holdings (MD

S0)

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

MD/Pre

Figure 2- Equilibrium in the Money Market

MS/PMD/PMD

S/PMD

T/P +MD

P/PMD/P = MS/P

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 than those required to finance known and precautionary transactions. Agents will attempt to purchase bonds driving up their price and down the rate of interest

r

MD/P& MS/P

MS1/PMS

0/P

re0

re1

Figure 3 – Increase in the Money Supply

r

from re0 to re

1. 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-equilibriate the 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 balances increases 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)

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

r2L-M

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 money market 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.

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 schedule3. 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 constant when deriving the L-M curve)

Jim StevensOCTOBER 2004