CHAPTER THREE
AGGREGATE DEMAND IN CLOSED ECONOMY
3.1. Introduction
In chapter two, the expenditure approach of measuring GDP
gives us
Y= C + I +G +NX………………….(1)
where C, I, G and NX represent consumption, private
investment, government purchases and net exports
respectively.
Equation (1) gives components of Aggregate Demand (AD).
In a closed economy, NX=0 and GDP is given by the
identity:
Y = C + I +G………………………...(2)
Consumption: Households receive income from their labour
service and their ownership of capital.
According to the national income identity, the income
households receive equals the output of the economy (Y).
Households pay taxes (T) and the left over (Y-T) is called
Disposable Income. Disposable income is divided into
consumption (C) and saving (S). The higher is the disposable
income, the higher would be the consumption of households
as described by the following Keynesian consumption
function.
C
C  C0  c1 (Y  T )  0, c1 
, (0  c1  1)..............(3)
Y
where C0 is autonomous consumption, which is unrelated to
income. The parameter c1 stands for the slope of
consumption function.
It measures the amount by which consumption changes
when disposable income increases by one Birr.
Average Propensity to Consume (APC): is the ratio of
consumption expenditure of households to their disposable
income.
APC 
C
c0

 c1.........................( 4)
(Y  T ) Y  T
In Equation (4), c1 is constant but c0/(Y-T) declines as
income or disposable income increases.
Thus, APC changes with changes in income.
 This is one of the axioms of Keynesian consumption
theory.
Investment: Households purchase new houses and firms buy
investment goods to add to their stock of capital, replace
existing worn-out machinery and equipment or change their
inventories.
Households and firms consider the prevailing interest rate
before making decisions.
Investment function of households is given by
I = (r) = (i-
)……………………….(5)
 Nominal interest rate, i, is the market or reported interest rate that
investors or borrowers pay for the lender and real interest rate, r, is
the nominal interest rate adjusted for inflation.
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:
G = (T-R)………………………………….(6)
If G < (T - TR) , government runs budget surplus and if G
> (T - TR), it runs budget deficit.
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.
Taxes and government purchases are determined by
government authorities, not in the model.
Given the above components and assuming government
spending (G  G ), private investment( I  I ) and taxes (T  T ) ;
AD is represented by E as follows.
E  c0  c1 (Y  T )  I  G................................(7)
Aggregate Demand is an outcome of the interaction
between product (goods) and money markets.
The product market is designated by the IS curve, while
money market interactions are captured through the LM
curve. Where: S= Saving, I =investment. L and M stand
for liquidity and money respectively.
The Product/Goods Market Equilibrium
Keynesian cross displays what possible actions firms take
when there is disequilibrium in the product market.
Disequilibrium may occur when planned expenditure and
actual expenditure are not equal.
Actual expenditure is the amount households, firms and
government actually spend on goods and services. It is
equal to GDP.
Planned expenditure is the amount households, firms and
government would like to spend on goods and services.
The actual and the planned expenditures may not
necessarily be equal.
The figure shows that planned expenditure increases with
an increase in income.
On the supply side, for simplicity, we leave what
determines the level of output and consider the total supply
in the economy (Y )
The 45 degree line divides the quadrant into equal parts
along which output equals actual expenditure.
The product market is in equilibrium at point A, where
actual expenditure equals planned expenditure.
If the economy is outside of the equilibrium, how could
the economy get back to the equilibrium?
If the economy operates below point A towards the origin,
planned expenditure ( E1) exceeds output or production in
the economy (Y1) and firms will strive to draw down their
inventories to satisfy the excess demand ( E1-Y1).
Moreover, this move will force firms to condense their
inventories and motivate them to employ more workers
and expand output; a movement towards A.
If the economy is operating above point A, output (Y2)
exceeds the planned expenditure (E2) and firms will pileup their stock of inventories by unsold products on the
amount (Y2 - E2 ) to reduce their sales to the level of AD.
Government fiscal policies may affect the equilibrium
condition in the economy.
Before we consider changes in fiscal policy instruments,
let us quantitatively indicate the equilibrium condition.
Y 
1
(c0  I  G  c1T )  E......................(8)
1  c1
1
1  c1
The parameter
is called the multiplier; because it
multiplies changes in exogenous variables such I or G to
give resulting change in output.
Digression: Saving Function
The saving of households is part of the disposable
income, which has not been consumed.
S = Y-T-C or S= -c0+(1-c1)(Y-T)………………….(9)
The income of households is allocated for (a)
consumption, (b) saving and (c) taxes.
Y=C+S+T………………………………(10)
On the expenditure side, AD equals consumption,
government expenditure and private investment spending.
Y=C+I+G………………………(11)
At equilibrium, we have
Y=C+S+T=C+I+G
S+T=I+G………………….(12)
From equation (12),
S=I+(G-T)…………………………………..(13)
If government runs a balanced budget, G = T, this equals
S = I…………………………………..(14)
Equation (14) is called Saving-Investment Identity.
If government runs a budget deficit or G>T,
S > I………………………………………….(15)
Equation (15) shows that saving exceeds investment
because part of the saving is siphoned off to finance
government budget deficit. It is called crowding out of
private investment or because of excess government
spending, private investment is constrained.
 If government runs a budget surplus, (G-T) < 0, then there
will be private investment spending exceeding household
saving.
S <I……………………………………(16)
Thus, private investment is finance by household saving
(SH) and government saving (SG), which is equal to
government budget surplus.
I = SH+SG……………………………………………(17)
What is the effect of saving on investment? In the shortrun, increase in saving has contractionary or negative
effect on output.
Based on Equation (15), lowering C0 decreases AD by the
amount [C0/(1-c1)].
An increase in saving requires c1 to decline or (1- c1) to
increase.
A decrease in c1 reduces the multiplier and also has a
stronger negative effect on AD.
This is called the saving paradox; because of the inverse
relationship between AD and S.
However, in the long-run, as saving increases, the supply
for loanable funds will increase; and causes interest rate to
fall.
Given equation 5, the decline in interest rate leads to an
increase in I and also AD.
The Effect of Fiscal Policy Changes on Output or Income
Given Equation (13), what would happen if government
uses one of its fiscal policy instruments, say an increase in
government expenditure (G)?
Increase in G, ∆G>0, brings
Y 
1
(G )........................................(18)
1  c1
Y
1

 1 is government expenditure multiplier
Where 
G
1 c
 Thus, the positive change in 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 to raise from Y1 toY2
1
The Effect of Increased in Government Spending on
Equilibrium Output
The multiplier increases as marginal propensity to
consume ( c1) increases.
The second fiscal policy instrument is change in tax.
If tax is reduced by ΔT, this will raise disposable income
by the change in tax and increase consumption by (c1ΔT).
Output increases from Y1 to Y2 by the change in tax
times the multiplier for the tax rate, [-c1/(1-c1) ΔT].
To derive the IS curve, let us relax the assumption
imposed on investment or I.
Investment is no more exogenous.
I=f(r)……………………………(19)
I  I  br...............................................( 20)
We also assume that other components of the AD constant
Given this assumption, investment (I) and real interest rate
(r) are inversely related.
 A decrease in interest rate from r1 to r2 boosts the demand
for investment from I2 to I1, which causes an upward shift
of planned expenditure curve from E1 to E2.
This leads to a change in the equilibrium position from A
to B.
 Because of an inverse relationship between interest rate
and investment, it is also inversely related to income or
output as well.
Thus, IS curve slopes downward.
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
What will be the effect of fiscal policy changes on
equilibrium level of interest rate and income?
The equilibrium level of output will increase by the
change in government spending (ΔG ) times government
expenditure multiplier [1/(1-c1)].
This effect will also shift the IS curve upwards.
Relaxing the assumptions imposed on the multiplier
We assume government collects tax revenue at a rate of t
per a fraction of income (Y), where 0 < t <1.
C  c0  c1[Y  R  (tY )]orC  c0  c1 R  c1 (1  t )Y ........( 21)
We incorporate the new consumption and investment
function to get the new planned expenditure or AD as:
Y  c0  c1 R  c1 (1  t )Y  I  br  G..................(22)
By collecting autonomous spending together, we would get;
Y 
A  br
  g [ A  br ].....................( 23)
1  c1 (1  t )
Where A  c0  c1 R  I  G
Equation (22) and (23) are called the IS equations.
g
Changes in the IS curve
What happens if government exercises its fiscal policy by
increasing public spending by ΔG, other things remaining
constant?
The effect of change in government spending on output is:
Y   g G......................................(24)
The effect of change in autonomous investment on
income is:
Y   g  I .........................................(25)
The effect of change in government transfer on aggregate
output or income?
Y  c1 R  c1 (1  t )Y  Y 
c1
R................(26)
1  c1 (1  t )
 The effect of change in G on income Y   G
 The effect of change in G on tax revenue is: T  tY  t g G
 Thus, the effect of change in G on government budget
balance is:
g
GBB  T  G  (t g G  G )  (t g  1) G
The Money Market and the LM Curve
Assets of an economy could be broadly divided 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 or buildings (b) consumer durables (such as
cars, washing machines, stereos, etc.) and (c) residences
owned by households.
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.
Money: money is the stock of assets that can be readily used
to make transactions and can be immediately used for
payments.
Money Functions as medium of exchange, store of value
and unit of account.
Types of money: fiat money and commodity money
 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.
Time Deposit: It is interest bearing deposit
It cannot be withdrawn from banks before the agreement set
between the bank and the client.
Following these components, we have three types of money
i. Narrow Money: M1 = C+DD
ii. Quasi money: SD + TD, Where:SD= saving and TD=
time deposit
iii. Broad money (M2): M2 = M1 + SD+TD
The Demand for Money
i. 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.
ii. Speculative Demand for Money: demand for money for
speculative purposes is a negative function of interest rate.
Ls =f(r), (dLs/dr) < 0.
Where Ls = speculative demand for money, I = liquidity
preference, r = interest rate.
As income increases, the speculative demand for money
increases for any given level of interest rate.
iii. 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.
 It increases with an increase in income
The demand for money also called the demand for real
balances (sum of the two functions) is given by:
L=L(r) +k(Y)
Specific demand for real money balances is a decreasing
function of interest rate
L = kY-hr,
k, h>0
Real money balances (real balances) are the quantity of
nominal money divided by the price level.
Money Supply: It is to be exogenously determined by the
central bank regardless of the interest rate (assumption).
M/P = l(Y)-h(r)
Where M/p is real money supply.
The specific functional form could become:
1
M / P  kY  hr  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.
LM is positively sloped because an increase in Y raises
the transaction demand for money and so of the total
money demand.
At (r=r1), the supply of real balances (M/P) is fixed.
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.
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
asY-bar.
Real money balance falls from M1/P to M2/P, which
shifts LM curve upward.
Panel (a): money
Market equilibrium
Panel (b): shifts in the LM curve in
response to MP changes
What determines the slope of the LM curve?
The slope of the LM curve is given by dr/dy = k / h.
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.
What causes the LM curve to shift?
A change in the real money supply will shift the LM
curve.
If the real money supply increases, which is represent 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.
 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.
 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.
Short-Run Equilibrium in the Economy
Goods Market IS: Y = C(Y+R-T)+I(r)+G
Money Market LM: M/P = L(r, Y)
This figure represents a simultaneous equilibrium in both the
product/goods market and the money market.
Monetary and Fiscal Policy Analysis Using the IS-LM
Framework
1. Effect of Fiscal Policy Changes
a. Changes in Government Spending
Change in government spending shifts the IS curve to point
B at r1.
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.
As income increases, the quantity of money demanded
given interest rate increases.
The supply of real money has not changed. This will create
in balance in the money market, and increases 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.
b. Changes in tax rate
2. Monetary Policy Effect
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 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
C at lower interest rate and higher level of income.
Aggregate Demand
To derive the aggregate demand curve, we relax the fixed
price assumption and examine how IS and LM models
shift to price changes.
AD curve shows the set of equilibrium points of income on
the IS–LM model as the price level varies. It also shows
the negative relationship between price and income.
Suppose the money market equilibrium and overall
equilibrium was at point A
Suppose price increases from P1 to p2 , where p1 > p2.
For any given money supply M, a higher price level P2
reduces the supply of real money balances from M/P1 to
M/P 2.
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.
This implicit negative relationship between income and
price level enables to draw aggregate demand (AD) curve
and price.
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.
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.