CHAPTER THREE
AGGREGATE DEMAND IN CLOSED ECONOMY
3.1. Introduction
Note: using expenditure approach of measuring GDP is given by:
(1) Y= C+I+G+GX
In a closed economy, NX=0 and GDP is given by the identity:
(2) Y= C+I+G
According to the national income identity, the income households receive (Y) = Total output of
the economy (Y) = Total expenditure of all economic agents.
Consumption: For simplicity, households require only to pay taxes (T) to left with their net
income (Y-T), called Disposable Income.
Y-T= C+S
(Keynesian) consumption function (CF).
(3)
C= C0+c1(Y-T),
Where c1=d C/ d(Y-T), 0<c1<1, showing a positive relationship between C&Y.
c1 = slope of CF, or MPC, measures a one unit change in income brings c1 unit change
in consumption. It is assumed constant (although varies among different income levels,
countries, etc, .)
C0 = autonomous consumption, unrelated to income; an intercept of CF.
1
Average Propensity to Consume (APC):
C  c (Y  T )
C
C
 0 1
 c1  0
Y T
Y T
Y T
Equation (4) shows, APC changes with changes in income or disposable income.
(4)
APC 
APC is the slope of a curve that starts from the origin and crosses the consumption function at
any given level of income. According to the equation, as income increases; saving will increase
with a larger fraction of income.
Fig 3.1: Consumption Function
C
C  C0  c1 (Y  T )
APC  c1 
C0
Y T
Y
HH saving is the difference between disposable income and consumption.
(5) S = (Y-T)-[C0+C1(Y-T)] = -C0+(1-c1)(Y-T)
MPS is given by:
MPS = d S /d(Y-T) = 1-MPC
APS is given by
(6) APS = [Y-T]-[C0-c1(Y-T)]/(Y-T)= (1-c1) –C0/(Y-T)
(2) Investment: Investments are often made by firms. Firms purchase new houses, buy
investment goods to add to their stock of capital, replace existing worn-out machinery and
equipment or change their inventories. Thus, investment includes these different types of
spending. Investment is made for profit and thus it has its own opportunity cost. Firms consider
the prevailing interest rate as an opportunity cost before they make investment decisions. In
other words, if they have financial capital in their hands, they would observe, for instance, the
2
bank interest rate and make a decision whether putting this money in the bank and get interest
or invest it would provide better returns. If they do not have money, they would consider the
bank lending interest rate before they get credit for investment, calculate cost of capital and
compare it with its return from the investment. Thus, investment function of households is
given by
(7) I  (r ) , r  (i   )
Where r is real interest rate, i nominal interest rate and π is inflation rate. Nominal interest rate
is the market or reported interest rate that investors or borrowers pay for the lender and real
interest rate is the nominal interest rate adjusted for inflation.
(3) Government expenditure (G): Government expenditure is of two types: (a) Goods and
services for capital investment or recurrent consumption by the federal and local government
agencies and (b) transfer payments to households such as welfare for the poor and social
security payments (including pension) for the elderly. Government will have a balanced budget if
its purchases or spending equals net tax or tax minus transfer payments:
(8) G  (T  TR )
If G  (T  TR ) , government runs budget deficit and if G  (T  TR ) , it runs budget surplus.
Transfer payments increase disposable income and consumption contrary to taxes. For
simplicity, for the time being, we set T to stand for taxes less government transfer payments.
Assume government spending ( G  G ), private investment ( I  I ) and taxes ( T  T ); AD or E
is given by:
(9) E  c0  c1 (Y  T )  I  G
Aggregate Demand, total demand for goods and services in the economy, is determined by the
interaction between product (goods) and money markets.
This interaction of the product and money market, it is represented by IS-LM.
The product market equilibrium is designated by the IS curve; where I and S stand for
investment and saving respectively.
3
Money market equilibrium is captured by the LM curve. L and M stand for liquidity and money
respectively. We will discuss the two markets separately.
3.2. The Product/Goods Market Equilibrium
First step use the Keynesian cross to assess the possible actions of firms when there is
disequilibrium in the product market.
Disequilibrium occurs when planned expenditure and actual expenditure are not equal.
Actual expenditure is the amount that households, firms and government actually spend on
goods and services.
Planned expenditure is the amount that households, firms and government would like to spend
on goods and services.
Planned expenditure is given by Equation (9) or displayed by Figure 3.2. Planned expenditure
increases less proportionately with an increase in income.
Figure 3.2: Planned Expenditure as a Function of Income
Planned
Expenditure, E
E  c0  c1 (Y  T )  I  G
MPC= c1
Birr 1
Income, Output, Y
On the supply side, for simplicity, we leave what determines the level of output supplied and
simply consider the total supply in the economy ( Y ).
4
Fig 3.3: The Keynesian Cross
Income (Y)
Planned
Expenditure, E
E  c0  c1 (Y  T )  I  G
A
E-Bar
MPC= c1
Birr 1
450
Income, Output, Y
Y-Bar
The 450 line divides the quadrant into equal parts along which output equals actual
expenditure. Product market equilibrium is at point A; Actual expenditure = Planned
expenditure. No excess demand; no excess supply.
If the economy is in disequilibrium, how could it get back to the equilibrium?
Fig 3.4: Disequilibrium in the Product Market
Actual Expenditure
Planned
Expenditure, E
Y2
Planned Expenditure
E2
E
A
E1
Y1
Income, Output, Y
Y1
Y
Y2
If the economy operates below point A towards the origin, planned expenditure ( E1 ) exceeds
output ( Y1 ); firms draw down their inventories to satisfy the excess demand ( E1  Y1 ) . They
5
also employ more workers and expand output; a movement towards A (high output and AD).
If the economy operates above point A, output (Y2 ) exceeds planned expenditure ( E2 ) ; firms
pile-up inventories by the amount (Y2  E2 ) to reduce their sales to the level of AD, a
movement towards A.
Equilibrium condition:
(10) Y 
1
(c0  I  G  c1T )  E
1  c1
Government fiscal policies may affect the equilibrium condition in the economy. Before we
consider changes in fiscal policy instruments, let us quantitatively indicate the
The parameter 1 /(1  c1 ) is called multiplier; because it multiplies changes in exogenous variables
such I or G to give resulting change in output.
Income of HHs is allocated for (a) consumption, (b) saving and (c) taxes.
(11)
Y  C  S T
(11)
On the expenditure side, AD equals
(12)
Y C  I G
(12)
At equilibrium, we have
(13)
(13)
Y  C  S T  C  I G  S T  I G
From Equation (13),
(14)
S  I  (G  T )
If government has a balanced budget, G  T , this equals
(15)
SI
Equation (14) is called Saving-Investment Identity. If government runs a budget deficit or
(G  T )  0 ,
6
(16) S  I
Equation (16) shows that part of the saving is siphoned off to finance government budget deficit.
It is called crowding out of private investment. Because of excess government spending, private
investment is constrained.
If government has a budget surplus, (G  T )  0 , then private investment exceeds saving.
(17)
SI
Thus, private investment is finance by household saving ( S H ) and government saving ( S g ) ,
which is equal to government budget surplus.
(18) I  S H  S G
We have seen that an increase in “I”, “C” and “G” increases AD. What is the effect of saving
on investment? In the short-run, increase in saving has contractionary or negative effect on
output.
An increase in saving requires C0 or c1 to decline or (1-c1)) to increase. Lowering C0 decreases
AD by the amount C0/ (1-c1). A decrease in c1 reduces the multiplier and also has a stronger
negative effect on AD. This is called the saving paradox or the Paradox of Thrift.
In the short-run, there is an inverse relationship between AD and saving, because an increase in
S given Y and T, comes by reducing C. In the long-run, as S increases, supply for loan-able funds
increase; and interest rate falls. Decline in interest rate leads to an increase in I and also AD.
The Effect of Fiscal Policy on AD: If government increases its spending G, (G  0) brings;
(18)
Y 
1
(G )
1  c1
7
 1

where 
 1 1is government expenditure multiplier. Thus, the positive change in
 1  c1

government spending raises planned expenditure by ( 1 /(1  c1 )G) for any given level of
income. This leads to a move for the equilibrium position from A to B and income raises from
Y1 to Y2 .
Fig 3.5: The Effect of Increased in Government Spending on Equilibrium Output
Y
Planned
Expenditure, E
E2
B
E2
E1
E1
A
Income, Output, Y
Y1
Y2
The multiplier increases as MPC ( c1 ) increases.
If tax is reduced by T , disposable income increases by the change in tax and increase
consumption by (c1T ) . Planned expenditure becomes higher for any given level of income (Y)
and thus shifts the planned-expenditure schedule upward from point A to point B as in Fig 3.4.
1
Based on Equation (13), the multiplier is derived from the total effects of changes in government spending on
income as follows.
dY  d c1 (Y  T )  dI  dG
dY  c1dY  dG , because dI  0 and dT  0
(1  c1 )dY  dG
dY
1

dG (1  c1 )
8
Output increases from Y1 to Y2 by the change in tax times the multiplier for the tax rate or
  c1

Y  
.T  2.
 (1  c1 )

Let I be endogenously determined in the model as:
(19)
(20)
I  (r ) , where r  (i   ) or
(20)
(21)
I  I  br ,
where I is autonomous investment, independent of income and interest rate;
b is the slope, measuring the responsiveness of investment to changes in interest rate.
The investment function or schedule is shown in Fig 3.6a. The curve shifts upwards, other
things remain the same, with the change in intercept or autonomous investment.
We also assume that other components of the AD or planned expenditure are assumed
constant or government is not using its fiscal policy instruments such as G and T. Given this
assumption, investment (I) and real interest rate (r) are inversely related as discussed above.
The change in interest rate affects investment and investment in turn affects planned
expenditure or equilibrium level of output. Fig 3.6a, Fig 3.6b and Fig 3.6c capture (a) the
relationship between r & I, (b) between r & E and (c) between r and Y respectively.
Fig 3.6a shows that a decrease in interest rate from r1 to r2 motivates business entities to boost
their demand for investment from I (r1 )  I1 to I (r2 )  I 2 , which leads to a change in the
equilibrium position from point A to point B across the investment – interest curve and the
Given Y  c0  c1Y  c1T   I  G
A change in T with I and G being constant leads to
dY  c1dY  c1dT 
dY  c1dY  c1dT
(1  c1 )dY  c1dT or dY / dT  c1 /(1  c1 ) or tax multiplier.
2
9
increase in investment in turn causes an upward shift of planned expenditure curve from E1 to
E2 and a change in the equilibrium position from A to B across the Keynesian cross, with higher
level of output Y2 than Y1 . Because of an inverse relationship between interest rate and
investment, which is the component of planned expenditure or AD, we observe an inverse
relation between income or output with real interest rate. Thus, IS curve relates interest rate
and income or output, and it is a downward sloping slope as indicated in Fig 3.6c.
Fig 3.6b: Keynesian Cross
Y
E
E2
B
E2  Y2
E1
E1  Y1
A
Fig 3.6a: Investment
Function
Y
r
Y1
r
Y2
Fig 3.6c: IS Curve
A
r1
A
B
B
B
r2
I1
I (r )
Y
I
I2
Y1
Y2
What is the IS curve? IS curve (or schedule) shows the combinations of interest rate and output
(income) such that planned spending equals income.
The Effects of Fiscal Policy Change on Interest Rate and Income: If, for instance,
government spending increases (∆G>0), AD or planned expenditure line shifts upwards in the
Keynesian cross. Equilibrium output increases by ∆Y=[1/(1-c1)]*∆G); IS curve shifts upwards.
The transmission mechanisms and the chain effects are seen in Fig 3.7a and 3.7b respectively.
10
Fig 3.7a: Keynesian Cross
Expenditure, E
Actual Expenditure
E2
B
Y2
E1
A
Y1 3.7B: The IS Curve
Fig
Interest Rate
45 0
Income, Y
Y1
Y2
B
IS2
r
A
IS1
Income, Output, Y
Y1
Y2
IS curve below is negatively slopped because a higher interest rate reduces investment and AD
and equilibrium income. The slope of IS curve depends on sensitivity of investment to changes
in r and also the multiplier.
Relaxing the assumptions imposed on the multiplier: Normally, consumption is a
function of disposable income, which is output (income) plus, given level of government transfer
( R ) less taxes (T). We assume government collects its tax revenue at a rate of t per a fraction
of income (Y), where 0  t  1 .
(21)
C  c0  c1 Y  R  (tY ) or or
C  c0  c1 R  c1 (1  t )Y
Incorporate new C and I functions in (21) to AD gives:
11
(22)
(23)
Y  c0  c1 R  c1 (1  t )Y  I  br  G  (1  c1 (1  t )Y  c0  c1 R  G  I  br
If we collect autonomous spending together, we would get
A  br
(23)
(24) Y 
  g [ A  br ]
1  c1 (1  t )
1
where A  c0  c1 R  I  G and  g 
(1  c1 (1  t )
Both equations (23) and (24) are called the IS Equations. The change in income due to a one
unit change in interest rate is given us:
(24)
(25)
Y
b

  g b
r 1  c1 (1  t )
The IS equation as normally depicted in mathematics is given by:
(
Y
g
 A )  br  r 
A
1

Y
b  gb
or
r
A Y [1  c(1  t )]

b
b
IS represents a combination of interest rates and income levels at which the goods market
clears or becomes in equilibrium. IS curve shows the negative association between AD and
interest rate through investment function. The slope of IS curve is
(25)
(26)
dr
 (1 /  g b)
dY
The larger the multiplier (  g ), the smaller or flatter the slope of the IS curve becomes and the
larger the effect of fiscal policy on income.
Changes in the IS curve: An increase in autonomous spending (TR, I, G, C0), shift both
planned aggregate spending and the IS curve.
If government increases spending by ∆G and given multiplier
G 
1
1

1  c1 (1  t ) 1  c1  c1t
Government spending change on output across the Keynesian cross or IS curve becomes:
12
(26)
(27)
Y   G G
(a) What would happen if the business entities change their autonomous investment spending?
The effect of autonomous investment on income is similar to change in government
spending.
(27)
(28)
Y   G I
The introduction of the tax rate (t) reduced the size of the multiplier and thus the effect of
government spending on income.
(b) The effect of change in government transfer on aggregate output:
c1
R
1  c1 (1  t )
Tax rate change on the multiplier and on income or output:
(28)
(29)
Y  c1R  c1 (1  t )Y  Y 
Two effects will arise: (a) direct effect on consumption spending and (b) induced effect because
of change in income through change in the multiplier is:
(29)
The direct effect on consumption spending  c1 (t )Y  c1Y * t
(30)
Induced effect because of income change through multiplier  c1 (1  t ' )Y
 c1Y
Y  c1Yt  c1 (1  t ' )Y 
t
1  c1 (1  t ' )
Y
 c1Y
t
The change in output per unit tax rate cut ( ) 
t
1  c1 (1  t ' )
(31)
(32)
The change in tax rate affects the slope of the IS curve through the multiplier. If tax rate
increase, total tax revenue collection could increase. However, this will reduce the multiplier
 g and thus steeper the IS curve; thus the change in autonomous spending brings lower amount
of change in income.
Expansionary fiscal policy instruments such as increased government spending and tax cut
become more effective if the economy is in recession to let economy recover.
When the economy is overheating, tax rates may increase or government may cut its spending
to get back to equilibrium.
13
What will be the effect of change in government spending on government budget balance?
The effect of change in G on income ( Y )   G G
The effect of change in G on tax revenue T  tY  t g G
(33)
(34)
The
effect
of
change
in
G
on
government
budget
balance
(GBB )  T  G  (t g G  G )  (t g  1)G
3.3. The Money Market and the LM Curve
Assets of an economy could be broadly classified into two categories; financial assets and
tangible assets. Real assets or tangible assets are (a) properties owned by firms or corporations
such as machines, land, and structures and buildings (b) consumer durables (such as cars,
washing machines, stereos, etc.) and (c) residences owned by households. These assets are
called real to distinguish them from financial assets (money, stocks and bonds).These assets
carry a return that differs from one asset to another. Owner-occupied residences provide a
return to owners who enjoy living in them and not paying monthly rent. However, they have
opportunity costs. Machines of a firm produce output and thus make profits.
Financial assets are money; bonds or credit market instruments (and other interest-bearing
assets and equities or stocks.
Bonds: A bond is a promise by a borrower to pay the lender a certain amount (the principal)
at a specified date (the maturity date of the bond) and to pay a given amount of interest per
year in the meantime. Bonds are issued by many types of borrowers such as governments,
municipalities, and corporations. The interest rates on bonds issued by different borrowers
reflect the differing risks of default. Default occurs when a borrower is unable to meet the
commitment to pay interest or principal.
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Perpetuity: It is a bond which promises to pay interest forever, but not to repay the principal
on the bond.
Treasury Bills: Promissory notes by a borrower/central bank to pay the lender the principal at
a specified maturity date (often within 90 days) and interest.
Equities or Stocks: Equities or stocks are claims to a share of the profits of an enterprise or
organization. For example, a share in the Abyssinia Bank or Raya Brewery entitles the owner to
a share of the profits of the bank or the factory. The shareholder, or stockholder, may receive
the return on equity in two forms.
(a) In the form of dividends: firms may pay regular dividends to their stockholders a
certain amount for each share they own.
(b) In the form of capital gains: When business enterprises become profitable, people will
want to hold higher number of shares from this enterprise. When this occurs, the
shares become more valuable since they now represent claims on the profits.
Therefore, the price of the stock in the market will rise, and stockholders can make
capital gains. A capital gain is an increase, per period of time, in the price of an asset.
Return to stock = dividend +capital gain
(c) Firms may also decide not to distribute profits to the stockholders but rather retain the
profits and reinvest them by adding to the firms' stocks of machines and structures. This
is called retained earnings.
Money: It is the most convenient means of payment. What is money? Money is the stock of
assets that can be readily used to make transactions and can be immediately used for payments.
Money Functions:
 Medium of exchange: we use it to buy goods and services;
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 Store of value: transfers purchasing power from the present to the future and
 Unit of account: the common unit by which everyone and measures prices and values.
Money Types
a) Fiat money: This has no intrinsic value. It is nothing but the paper currency or cheque we
use.
b) Commodity Money: This has intrinsic value; for instance, silver, gold coins, etc. What does
money stock constitute?
There are two types of money stock. Based on composition, we have different components and
deposits.
 Currency in Circulation: The fiat money and commodity money that we see circulating
in the market.
 Demand Deposit: Demand deposit is non-interest bearing deposit; it can be
transferred easily to bearer of the check.
 Saving Deposit: It is the common kind of deposits that we know, a deposit that bears
interest but can be drawn at any time (depending sometimes on the amount).
 Time Deposit: It is interest bearing deposit, cannot be withdrawn from banks before
the agreement set between the bank and the client.
Following these components, we have three types of money
1. Narrow money (M1)
(36) M1 = C + DD, where C = currency in circulation,
DD = demand deposit.
2. Quasi Money:
(37) SD +TD
16
SD = Saving deposits and
DT = Time deposit
3. Broad money (M2)
(38) M2 = M1 + SD + TD
where SD = saving deposit, TD = time deposit, or M2= Narrow Money + Quasi Money
The Demand for Money
There are three motives for holding money.
 Precautionary demand for money
 Speculative demand for money
 Transaction demand for money
(1) Precautionary Demand for Money: It is a demand for money kept aside for
precautionary (for fear of risks) and it is affected by transaction and speculative demand
for money. For simplicity, we assume precautionary demand for money is zero for the
time being.
(2) Speculative Demand for Money: A person can put his liquid assets into either bonds
or money. An increase in interest rate, which is a return on bonds, induces to hold
assets in the form of bond and hold less in the form of money. Such demand for money
depends, therefore, on the cost of holding money – interest and called speculative
demand for money. At low interest rate, the speculative balance increases while at
higher interest rate the speculative balance declines.
Thus, demand for money for speculative purposes is a negative function of interest rate.
(39) LS  l (r ),
dLs
0
dr
where Ls = speculative demand for money, l = liquidity preference, r = interest.
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Fig 3.8: Speculative Demand for Money
r
L(r, Y1)
L(r, Y0)
M/P
Figure 3.8 indicates that speculative demand for money is negatively related with interest rate
and each curve is drawn with level of income or assume income to be fixed at a certain level.
As income increases, the speculative demand for money increases for any given level of interest
rate. This is shown by a shift in the speculative demand for money towards the right.
Transaction Demand for Money: It is the motive for holding money to bridge the time gap
between receipt of income and payments that have to be made for transaction purpose. The
transaction demand for money increases with an increase in income. However, the transaction
demand for money curve portrays the relationship between income and transaction demand for
money assuming interest rate constant.
(40) LT  K (Y ),
dLT
0
dY
Fig 3.9: Transaction Demand for Money
Y
L (Y , r )
M/P
The demand for money and also called the demand for real balances (sum of the two functions)
is given by:
(41)
L = l (r ) + k (Y )
18
The specific function of demand for real money balances is a decreasing function of interest
rate.
(42)
L = kY - hr ,
k , h > 0.
Real money balances (real balances) are the quantity of nominal money divided by the price
level. It is money expressed in terms of the number of units of goods that the money will buy.
Money Supply: It is to be exogenously determined by the central bank regardless of the
interest rate (assumption). At equilibrium, money supply equals the demand for money.
(43)
M
 l (Y )  h(r )
P
where M/P is real money supply and the other part of the equation is money demand. The
specific functional form could become:
(44) ( M / P)  kY  hr
1
r  [ M / P  kY ]
h
This is LM – equation representing equilibrium in the money market. The LM curve represents
the pairs of interest and income that keep the money market in equilibrium with the given level
of money supply, M, and a given price level P. It is derived as follows.
Fig 3.10: Derivation of LM Curve
r
r
E2
r2
LM
E1
r1
L1
L2
Y
M /P
LM is positively sloped because an increase in Y raises the transaction demand for money and
so of the total money demand. LM is drawn for constant money supply balances, while income
19
changes or increases. There is now excess demand in the money market at the initial interest
rate ( r  r1 ). Interest rate must rise to restore equilibrium in the money market at r  r2 .
The LM curve represents the pairs of interest and income that keep the money market in
equilibrium with the given level of money supply, M and a given price level P.
Fig 3.11: The Speculative and Transaction Demand and LM Curve
r
LM
Ls  h(r )
Y
Ls
M / P  h(r )  k (Y )
LT  k (Y )
LT
The slope of the LM – curve is:
(45)
dr k
 0
dY h
LM curve is drawn by changing the income level for a given supply of real money balances. If
National Bank (NB) changes the real money balances, the LM curve shifts. Suppose NB reduces
nominal money supply from M1 to M2 and real income remain constant as Y . This leads to a
fall in real money balances from M1/P to M2/P and shifts the real money supply curve towards the
left. The reduction in the supply of real money balances creates scarcity in money circulated in
the economy and people will have no option but reduce the speculative demand for money.
Interest raises and a new equilibrium occurs in the money market in Figure 3.12 a. This leads to
a shift in the LM curve upwards in Figure 3.12 b. If there is an increase in the supply of real
money balances, there will be shift in the LM curve towards the right or downwards.
20
Fig 3.12a: Money Market Equilibrium
Fig 3.12b: Shift in LM Curve in Response to Money Policy Changes
LM 2
Interest rate, r
Interest rate, r
LM1
r2
r1
L = (r, Y
)
Income, Y
M2/P
M1/P
Y
What determines the slope of the LM curve?
The slope of the LM curve is given by
dr / dy  k / h in Equation (45). The greater the responsiveness of the demand for money to
income as measured by k and/or the lower the responsiveness of the demand for money to the
interest rate, h, the steeper or (the higher the slope of) the LM curve will be. If the demand for
money is relatively insensitive to the interest rate or h is close to zero, the LM curve is nearly
vertical. If the demand for money is very sensitive to the interest rate, so that h is large, then
the LM curve is close to horizontal. In that case, a small change in the interest rate must be
accompanied by a large change in the level of income in order to maintain money market
equilibrium.
What causes the LM curve to shift? The real money supply is held constant along the LM
curve. It follows that a change in the real money supply will shift the LM curve. If the real
money supply increases, which is represented by a rightward shift of the money supply
schedule, the interest rate has to decline in order to restore money market equilibrium. This
will lead to a rightward/downward shift in the LM curve. What happens on points where we are
not on the LM curve?
21
Figure 3.13: Points on the LM Curve
E2
Interest rate
r2
r1
i
LM
E3
E1
E4
LT(Y1)
LT (Y2)
Y
Income
The money market is in equilibrium at point E1. Assume an increase in the level of income to Y2.
This will raise the demand for real balances and shift the transaction demand curve for money
to the right. At the initial interest rate (i1), therefore, the demand for real balances would be
higher. On all points below and to the right of the LM curve, there is an excess demand for real
balances. Conversely, points above and to the left of the LM schedule correspond to excess
supply of real balances.
3.4. Short-Run Equilibrium in the Economy
The Keynesian cross in the product market is the foundation for IS curve. The theory of
liquidity preference as applied in the money market is the basis for LM.
Goods Market: IS
Money Market: LM
Y  C (Y  R  T )  I (r )  G
M / P  L( r , Y )
(46)
(47)
Fig 3.14: Equilibrium in the IS-Model
Interest Rate, r
Equilibrium
Interest
Rate,
LM
A
r
IS
Income, Y
22 Y
Equilibrium Income,
Figure 3.13 represents a simultaneous equilibrium in both the product/goods market and the
money market. The equilibrium is at point A, with interest rate ( r ) and income ( Y ). At this
interest rate and income level, (a) the public holds the existing stocks of money and (b) planned
spending equals output. On the IS curve, the demand for goods is equal to the level of output.
On the LM curve, the demand for money equals the supply of money. The simultaneous
equilibrium of the product and money market is maintained given constant government
spending, taxes, government transfer, autonomous private investment spending, money supply
and the price level for the time being. If there is a change in government expenditure,
government transfer, private spending or tax, there will be a shift of the IS curve depending on
the direction of change of these variables or policy instruments. On the other hand, if there is a
change in money supply or price levels, this will affect the amount of real balances and thus
shifts the LM curve. Because of a shift in IS, LM or both, there will a change in the equilibrium of
level if interest rate and income or output.
3.4.1. Monetary and Fiscal Policy Analysis Using the IS-LM Framework
This section examines how changes in policy and shocks to the economy can cause these
curves to shift.
Effect of Fiscal Policy Changes
Changes in fiscal policy measure such as government spending or tax rates shift the IS Curve
and change the short-run equilibrium in the two markets.
Changes in Government Spending
Suppose government has increased its purchases of goods and services by (ΔG). Planned expenditure
(E) in the economy increases and the line for planned expenditure shifts upwards in the
Keynesian cross. The increase in planned expenditure stimulates firms to increase their goods
and services and this leads to an increase in income (Y). The change in income is the product of
the multiplier and the change in government spending.
23
(a) If the model assumes taxes to be unrelated to income (or) ( T  T ), then the multiplier
would be  g  1 /(1  c1 ) , where c1  MPC and the change in income becomes
(48) Y 
1
.G
(1  c1 )
(b) If the model assumes taxes to a function of income (or) ( T  tY ), then, the multiplier
1
becomes  * g 
and change in income becomes changes in government
1  c1 (1  t )
spending multiplied by the multiplier as:
1
.G
(49) Y 
1  c1 (1  t )
The change in government spending causes a change in equilibrium income in the product
market. This leads to a shift in the IS curve to the right by the change in government spending
and the multiplier within given interest rate ( r1 ) to point B in Figure 3.15. However, this point
will not ensure equilibrium in both markets immediately.
Figure 3.15: Effect of Change Government Spending in the IS-LM Model
Interest Rate, r
LM
C
r2
iii
A
B
r1
i
IS2
IS1
ii
Income, Y
Y1
Y2
However, a shift in the IS curve with increased in the level of income will cause changes in the
operation of the money market as well. The demand for money balances depends on income
(transaction demand for money) and also interest rate. As income increases, the quantity of
money demanded given interest rate increases although the supply of real money has not
changed. This will create disequilibrium or imbalance in the money market, which causes for an
24
increase in interest rate to r2 . On the IS side, as interest rate rises, firms cut back their planned
investment; thus reduce the total planned expenditure in the Keynesian cross and equilibrium
level of income. The final equilibrium point in the IS-LM model becomes at point C. Thus, the
fall in investment partially offsets the expansionary effect of the increase in government
purchases.
Note:
(a) If we leave the LM curve for the time being and assume tax to be unrelated to income, then
the change in income due to change in government spending would be:
(50) Y 
1
.G
(1  c1 )
(b) If we leave the LM curve for the time being and assume that tax is related to income, then
the change in income due to change in government spending would be:
(51)
Y 
1
.G
1  c1 (1  t )
Thus, an increase in income (51) is lower than (52) because of change in the introduction of
tax rate in the model.
(c) If we introduce the LM or the money market, assume tax is related to income, investment is
related to interest rate as I  I  br and then we have the following transmission
mechanisms.
 G  E  Y  Md  r  I  E  Y
The change in government spending in scenario (c) brings lower change in income than both
(a) and (b). The horizontal shift in the IS curve by amount (i) in Figure 3.15 equals the rise in
equilibrium income in the Keynesian cross assuming that investment is unrelated to interest
rate and larger than the increase in equilibrium income in the IS –LM model. This difference
is explained by the crowding out of private investment by increased government
expenditure, which is caused by the increase in interest rate.
25
Changes in Taxes
Assume for simplicity that tax is not functionally related with the income level. Government
wants to cut taxes by ( T ) from (T1 ) to (T2 ) . The tax cut increases the dispensable income of
consumers and increases their planned consumption expenditure. This in turn leads to an
upward shift in planned expenditure curve and leads to a change in equilibrium level of income
in the Keynesian cross. This leads IS1 to shift towards the left, IS2 in Figure 3.15. Given interest
rate, the IS curve horizontally shifts by the change in income ( Y ), which is the tax multiplier
times  c1 1  c1  and the change in tax ( T ). This is given by:
  c1 
(52) Y  
.T
1  c1 ) 
Equilibrium in the economy moves from point A to point B, with higher level of income and the
interest rate. As it was the case in government expenditure, an increase in income because of
tax cut leads to increased demand for real money balances. Given real money balances,
increased interest rate reduces planned investment expenditure, total planned expenditure and
income on the Keynesian cross.
Figure 3.16: The Effect of Change in Tax
Interest Rate, r
LM
Tax cut shifts IS1 to IS2:
at r
r2
 r1 ,
 c 
Y   1  * T
1  c1 
iii
r1
IS2
IS1
ii
Income, Y
Y1
Y2
The overall effect of tax cut on income in the IS–LM model is smaller than it is in the case of
the Keynesian cross, and it is Y2-Y1.
26
Monetary Policy Effects
As indicated above, price level (P) is fixed in the short run. Suppose there is an increase in
nominal money (M), which leads to an increase in real money balances M/P. For any given level
of income, an increase in real money balances leads people to have more money than they want
to hold at the prevailing interest rate. Interest rate falls until all the excess money vanishes. This
leads to an increase in the demand for holding real money balances with new equilibrium in the
money market. This leads to a downward shift in the LM curve from LM1 to LM2. The change in
money market equilibrium also brings a change in the product market equilibrium. Lower
interest rate stimulates planned investment, total planned expenditure and income Y. This
brings a new equilibrium point from point A to point B at lower interest rate and higher level of
income. This process is called the monetary transmission mechanism.
Figure 3.17: The Effect of Real Money Supply
Interest Rate, r
LM1
LM2
A
r1
B
iii
r2
C
IS
ii
Y2
Income, Y
Y1
The impact of the interaction between fiscal and monetary policies
The effect of a change in one government policy (either fiscal or monetary) depends on
whether or not other policies change and if so, what other specific policy change occurs. For
instance, if government wants to increase tax, the impact on the economy depends on the
27
policy that the Central Bank pursues in response for the fiscal policy. Central Bank could (a)
hold the money supply constant, (b) hold the interest rate constant or (c) maintain the level of
income constant. Consequently, the equilibrium outcome of the increase in tax depends on
which policy scenario that the Central Bank wants to pursue.
(a) Suppose the Central Bank holds the money supply constant: Phase 1: The economy
was at point A before the intervention. The tax increase shifts the IS curve to the left
from IS1 to IS2 because of the fall in planned consumption expenditure, total planned
expenditure and income. The fall in income reduces a fall in transaction demand and
thus a fall in money demand. This leads to a fall in interest rate and an increase in
planned investment expenditure and total planned expenditure; which consequently
leads to an increase in the level of income. The phase 1 effect of reduction in income
dominates the phase 2 effect of an increase in income. The equilibrium point will be at B.
Thus, net effect of tax increase could lead to a recession with low interest rate ( r2 ) and
low level of income ( Y2 ).
Fig 3.18a: Effect of Tax Increase on Equilibrium (Holding Money Supply Constant)
Interest Rate, r
LM
A
r1
r2
B
IS1
IS2
Income, Y
Y2
Y1
(b) Suppose the Central Bank decides to maintain the interest rate constant ( r  r1 ).
We have already witnessed that when tax increases the IS curve shifts to the left from
28
IS1 to IS2 and causes a fall in equilibrium level of income and interest rate ( Y2 , r2 ) . To
maintain the interest rate at its original level ( r  r1 ), the Central Bank must decrease
the money supply (M). This fall in the money supply shifts the LM curve upward and
causes the level of interest to pick up to its original level; ( r  r1 ). This brings a further
decline in income. Thus, the fall in income because of the tax cut; as money supply
varies to hold interest rate constant (scenario, b) is larger than the fall in income when
the money supply is constant as in scenario (a) above.
Fig 3.18b: Effect of Tax Increase on Equilibrium (Holding Interest Rate Constant)
Interest Rate, r
LM2
LM1
r1
C
A
r2
B
IS1
IS2
Income, Y
Y3
(c)
Y2
Y1
Suppose the Central Bank wants income to remain at it is: If Central bank wants to
prevent the tax increase from lowering income, it has to raise the money supply. This will
lead households to hold excess money than demand and causes interest rate to fall. The LM
curve shifts downwards to the extent that it offsets the effect of the shift in the IS curve to
the left. In this scenario, income remains constant and the tax increase does not cause a
recession, but it causes a fall in interest rate from r2 to r3 . A combination of fiscal policy (tax
increase) and a monetary policy (increase in money supply) maintain income constant but
change the allocation of the economy’s resources or the composition of planned
expenditure. Higher taxes depress consumption, while lower interest rate stimulates
29
investment. Thus, the need to keep income constant causes a greater fall in interest rate and
also the allocation of income away from consumption3.
Fig 3.18c: Effect of Tax Increase on Equilibrium (Holding Income Constant)
Interest Rate, r
LM1
LM2
A
r1
r2
B
IS1
r3
IS2
Income, Y
Y3
Y2
Y1
3.1.6. Aggregate Demand
The above discussion of IS, LM and IS-LM has been based on the assumption that in the shortrun price level is fixed. To derive the aggregate demand curve, we relax the fixed price
assumption and examine how IS and LM models shift to price changes. Suppose the money
market equilibrium and overall equilibrium was at point A on Figure 3.19a, when P  P1 .
Suppose price increases from P1 to P2 , where P2  P1 . For any given money supply M, a higher
price level P2 reduces the supply of real money balances from M P1 to M P2 . A lower supply
of real money balances shifts the LM curve upward or to the left. This move raises the
equilibrium interest rate from r1 to r2 and lowers the equilibrium level of income from Y1 to Y2
in Figure 3.20a. This implicit negative relationship between income and price level enables to
draw aggregate demand (AD) curve and price in Figure 3.19b. AD curve shows the set of
3
This policy move prevents income from falling in the short-run. The fall in interest rate may depress the
motivation of households to save in the long-run and constrain the amount of loanable funds for
investment.
30
equilibrium points of income on the IS–LM model as the price level varies. It also shows the
negative relationship between price and income.
Figure 3.19: Derivation of AD Curve
Price, P
(a)
Interest rate, r
(b)
LM2
B
LM1
B
A
A
AD
IS
Income, Y
Income, Y
Y2
Y2
Y1
Y1
A change in income in the IS–LM model resulted from a change in the price level represents a
movement along the aggregate demand curve.
What shifts the AD Curve? A change in income due to fiscal and monetary policy changes in
the IS–LM model for a fixed price level shifts the AD curve in either way. Any expansionary
policy (increase in government spending, increase in money supply and a decline in tax) brings
an increase in income given price level and shifts the AD curve to the right and leads to higher
level of income for given price level.
Effects of Expansionary Fiscal and Monetary Policy on AD
The Effect of Expansionary Monetary Policy on AD: As indicated above, the LM curve is
drawn for given real money balances. Any change on real money balances (either because of
change in money supply or price) will shift the LM curve. Suppose monetary authorities
increase money supply given the price level. This intervention by government shifts the LM
curve downwards or to the right from LM (P1) to LM (P2) in Panel (a) of Figure 3.20. This
movement of the LM curve will create excess supply of real money balances over the demand
in the economy. Given the equation, M / P  l (Y )  h(r ) , an increase in real money balances,
(M / P)  , would cause or require a decline in interest rate ( r  ) and thus an increase in the
31
demand for real money balances so as to bring back the money market to be at equilibrium.
The money market changes will have an impact on the product or commodity market. The
decline in interest rate will lead to a downward movement along the IS curve until we have a
new equilibrium between the new LM curve, LM (P2) and the IS curve at output level, Y2. The
movement along the IS curve towards a higher level of income arises because of the decline in
interest rate that boosts investment and thus aggregate planned expenditure (in the Keynesian
cross) and increases the equilibrium level of income or output in the product market.
Figure 3.20: Effects of Expansionary Monetary and Fiscal Policy
32
The Effect of Expansionary Policy on AD: In our previous discussion, we have indicated that
IS curve is drawn with changes in interest rate and investment; while keeping autonomous
consumption, government expenditure, autonomous investment and government expenditure
constant. If there is a change in one of these variables, which were assumed fixed, will shift the
IS curve. Suppose government increases its spending from G1 to G2 by the amount ( G ); the IS
curve will shift to the right from IS1 to IS2. An increase in government spending will increase
planned expenditure and thus will cause a change in equilibrium level of income, which is equal
to a change in government spending times the multiplier. On the money market, the increase in
income will lead to an increase in the transaction demand for money. However, the real money
balances (or real money supply) is constant. Given equation, M / P  l (Y )  h(r ) , the increase
in transaction demand for money, l (Y )  , needs interest rate and thus h(r ) to increase so as to
ensure that the money market is in equilibrium. This leads to an upward movement on the LM
curve. An overall equilibrium, both product and money market, is ensured at a new income
level, at Y  Y2 .
The IS–LM Model in the Short Run and Long Run
The IS–LM model is designed to explain the economy in the short run when the price level is
fixed. The short-run equilibrium of the economy is at point K in panel a; where the IS curve
crosses the LM curve. The short-run equilibrium income is less than its natural rate as it is
shown on the upward slopping long-run aggregate supply curve (LASC).
33
Figure 3.20: Effects of Fiscal and Monetary Policy Changes on AD Curve
Point K in Fig. 3.20, panel (b) describes the short-run equilibrium because it assumes that the
price level is stuck at P1. At this point, there is insufficient demand for goods and services to tap
the potential of the economy or operate at the natural level of output. Eventually, low
aggregate demand for goods and services causes prices to fall, and the economy moves towards
its natural rate. When the price level reaches P2, the economy moves to point C, which is the
long-run equilibrium. The aggregate supply and aggregate demand diagrams in panel b show, the
quantity of goods and services demanded equals the natural rate of output at point C. This
long-run equilibrium is also observed in the IS–LM diagram. The fall in the price level raises real
money balances and therefore shifts the LM curve to the right by a shift in the LM curve.
3.7. Conclusion
IS and LM model is a systematic representation of the interactions between demand and supply
both in the product and money markets. The model also helps to capture the fiscal and
monetary policy effects on the economy. The Keynesian cross helps to derive the IS curve that
represent the equilibrium conditions in the product market. The IS curve is drawn by
manipulating interest rate and investment, while holding government spending, tax and other
fiscal policy instruments constant. The change in the fiscal policy instruments will shift the
change in IS. The theory of liquidity preference helps to derive the LM curve, which gives the
34
combination of income and interest rate that maintains the money market at equilibrium. The
LM curve is drawn for given level of money supply. A change in real money balances will shift
the LM curve. Relaxing the assumption of fixed price levels and changes the price, changes the
real money balances and causes a shift to the LM curve. The equilibrium points at the
intersection of the IS curve and the LM curves at varied price levels will enable to derive the
AD curve. The overall equilibrium level of output of both the product and money market is
where the LM and the IS curves intersect. We have the slopes of IS and LM curves:
The IS schedule is represented by: Y   G [ A  br ] =
The LM schedule is given by = r 
 ( M / P) k
 Y
h
h
We can substitute the value of r in the LM equation into the IS equation to get equilibrium level
of income in terms of other parameters.
(53) Y   G [ A  b[
M /P k
 Y],
h
h
Thus, we find the equilibrium value of Y in terms of other parameters as:
Y
G
1  k G
b
h
A
 Gb
M
b
1  k G P
h
A captures the exogenous fiscal policy measures, autonomous private spending and
autonomous household consumption. Once we get equilibrium value of income in numbers, for
instance, we could find equilibrium level of interest rate. The change in income as a result of
change in A , for instance, G, will be given by:
Y 
G
b
1  k G
h
G
The new multiplier captures the effect of crowding-out effect of expansionary government
policy on private investment and it is expected to be lower than the previous multipliers and
the associated change in Y.
35
The IS-LM model is a very important tool to understand the movement of aggregate
macroeconomic variables and change in equilibrium conditions because of fiscal and monetary
policy instruments. As the model falls under the social science discipline, it has its own
limitations4. Thus, one should not necessarily assume that the predictions of the IS-LM would
exactly happen in reality.
4
The discussion of IS-LM model limitations is beyond the scope of the chapter.
36