keynesian aggregate mode1 pdf

Lecturer : Javed Teelucksingh Unit 2 Keynesian Aggregate Model

Closed economy: is simply one that does not engage in international trade thus there is no imports and exports in a closed economy Open economy: is one that engages in international trade thus we would have imports and exports and injections and withdrawals

Keynesian Aggregate Model

To explain the determination of economic aggregates Keynes developed the Circular Flow of Income

model as an alternative to the supply and demand model of microeconomics. Recall the diagram below:

Consumers/Households

F.O.P G& S Exp 20m

Firms

Income 20m

Fig 1: Circular Flow

The diagram above represents a how income, expenditure and output flows throughout a closed economy

and more importantly how the economy is in equilibrium when income = expenditure = output. This can

be seen since in this diagram there are the consumers and there are the firms. Consumers have needs and

wants and thus firms try to satisfy them by producing goods and services to suit those needs and wants.

However in order to produce the goods and services firms need factors of production which are

essentially provided by the consumers/households. Now when household provide these factor services

they receive and equivalent income for it in our case 20 million at the same time firms are only able to

produce 20 million in goods and services since this is the total amount in factors that was provided to

them. On the other and when households receive this income they must consume and thus spend all there

income (20million expenditure) on the goods and services produced by the firms. Thus it can clearly be

seen that income = output = expenditure.

Nevertheless our purpose is to explain income determination using the Keynesian model, so that based on

our analysis so far we can say generally an economy is in equilibrium when total expenditure (E) is equal

to total income (Y) and since E = C + I + G + (X M) we get Y = C + I + G (X M).

Withdrawals and Injections

From the figure above Consumption (C) = Income (Y) in other words all of the income received in one

period is directly spent in the next. As a result it would appear that there would be no reason for the level

of Y to change and thus our economy would be in equilibrium. So that income in the first period is equal

to the consumption of the next period. If consumption is the only form of expenditure then expenditure in

this next period must be the same as this consumption. This expenditure, however is all received by firms

and all paid out again as income for factor services. So income and expenditure has a constant flow

throughout the circular flow of income. Thus we can write Ct = Et = Yt+1 = Ct+1 = Et+1 = Yt+2



where t is first time period and t+1 is the next time period. However there are various factors which cause

money to be withdrawn, or leak from the system and conversely there are also injections into it.

Withdrawals (W): is simply any part of income that is not passed on within the circular flow.

Withdrawals are also referred to as leakages of potential planned expenditures from the income-

expenditure stream. Withdrawals are savings, purchases of goods from other countries (imports) and

taxes. Savings (S) can be undertaken by households since they do not spend all their income or by firms

who choose to retain some of their profits for future expansion. Taxes (T) by government may or may not

be re-spent and hence is a withdrawal. Finally imports (M) these are purchases by domestic consumers of

foreign goods and services and because part of domestic consumers income is going abroad to foreign

firms it is being withdrawn from the circular flow and thus is a withdrawal. Essentially the sum of

savings, taxes and imports would give us the total withdrawal for an economy. i.e. W = S + T + M

Injections (J): these are additions of potential planned expenditures to the income-expenditure stream.

Another way of saying it is injections is an expenditure which is not the consumption of domestic

households so that it comes from outside into the circular flow of income. The most obvious example of

an injection is exports (X) because the income of the firm selling them comes not from domestic

households but from overseas. Also another form of injection is investments (I) an example would

include a firm that produces investment or (capital) goods and sells them to another firm, this is an

injection because the flow of income and expenditure has been increased, even though this increase is not

a result of extra spending by households. Lastly we have government spending (G) which again may or

may not be financed by current taxation, past taxation, borrowing or by simply printing money thus

government expenditure is an injection. As with withdrawals the total injection in the economy is given

by the sum of total exports, government expenditure and investments i.e. J = I + G + X.

Referring back to the circular flow diagram above we illustrated a situation where there was equilibrium

in the economy where Aggregate Expenditure = Income and thus this was a closed economy. However if

we were to consider an open economy we would be face with withdrawals and injections and we would

observe with the inclusion of these concepts the economy would be subject to situations of disequilibrium

unless off course total withdrawals were equal to total injections. (W = J)

Models of income Determination

Keynesian This model follows from the analysis of the circular flow of income and basically states that equilibrium

income is determined at the point where Aggregate Expenditure (E) is equal to Income (Y).

Diagrammatically we can illustrate this equilibrium however we have to utilize a tool Keynes developed

called the Keynesian cross or the 45 degree line. First of all we have met this tool before in our analysis of

the consumption function however Ill define it again. The Keynesian cross is a line constructed by connecting all points where desired consumption (which is reflected as our expenditure on goods and

services) equals our disposable income. It is a handy tool as it allows us or assists in the location of the

breakeven level of income at which consumption spending equals disposable income. We will now

illustrate this model as follows:



Expenditure

E = Y

AE

A

E1

Ye Income/output

The diagram above illustrate the keynesian model of income determination, we have already established

from our analysis of the circular flow that an economy is in equilibrium when E = Y we have also

introduced the Keynesian cross which would be used to determine equilibrium. The line labeled E = Y is

the Keynesian cross and each point on this curve shows a situation where total expenditure is equal to

income and is also known as the planned expenditure for the economy.

In other words it shows how all firms in an economy plan to allocate their income in the production of

goods and services so this curve essentially represents the supply of output. Now the reason I say this is

remember the 45 degree line shows a situation where expenditure is equal to income and the total income

generated within an economy is called GDP and thus GDP is sometimes referred to as the aggregate

supply.

On the other hand we have our actual expenditure which is labeled AE above this is also called the

aggregate expenditure of the economy and is given by the formula C + I + G + (X-M) and this formula

also defines the aggregate demand. So that in short equilibrium income would be determined where our

planned expenditure is equal to our actual expenditure. This is labeled as point A in the diagram above

with an associated income/output level of Ye and expenditure of E1.

Nevertheless now that we understand where equilibrium income is we need to understand how an

economy reaches equilibrium. Consider any point to the left of point A on the diagram; any point below

A show a situation where our actual expenditure is greater than our planned expenditure question is

how does the economy reaches equilibrium. Well lets consider whats happening if our actual

expenditure also called the aggregate demand is greater and our planned expenditure which is really a

reflection of supply then this is a type of disequilibrium known as a shortage. A shortage is said to occur

when the demand is greater than supply. So if what consumers are demanding is greater than the amount



firms had planned to produce then firms would react by stepping up on production. To do this they would

have to employ additional labor as well as more of the other factors and thus their expenditure would

increase but at the same time output would increase and this action continues until output and expenditure

is equal thereby re- establishing equilibrium.

Now consider the other side of the picture that is, any point to the right of A which shows a situation

where Planned Expenditure is greater than Actual Expenditure and this the other form of

disequilibrium known as a surplus. A surplus is said to exist when the supply is greater and the demand in

our case we have the total planned expenditure by firms in the economy is greater than the actual

expenditure so that firms would be faced with rising levels of stocks and thus would react by cutting back

on production. In the process of cutting back on production firms would lay off workers and thus overall

expenditure would fall and at the same time output would fall until it reaches equilibrium level again.

Injection and Withdrawal Approach

We have already introduced these two concepts and have thus established that W = S + M + T and J = I +

X + G and once the total withdrawals are equal to total injections (W = J) the economy would be in

equilibrium or equivalently we could also write where E = Y. Consider the diagram below:

Expenditure

Withdrawals

F Injection

Ye Income

So the diagram above illustrates equilibrium income using the withdrawal and injection approach. What

we observe is that the injection line is perfectly elastic (that is it is flat and thus it means it has a fixed

value) this because in this model we assume that injections in autonomous that is not influenced by

income. However we observe that withdrawal line is upward sloping meaning in our model withdrawal

are induced, that is it varies with the level of income and since it has a positive slope withdrawals

increases as income rises. So the point labeled F is where equilibrium occurs and thus any point to the

right of F would mean there would be an unplanned rise in stock levels in the firm and so they would



have to cut back on production to re-establish equilibrium. While any point to the left of F means that

households and firms are purchasing more of the real national output than firms had planned thus this

would cause a run down of stock levels encouraging firms to increase its output until equilibrium is

established again.

The Multiplier

The multiplier concept focuses on how responsive income is to changes in the level of aggregate demand.

For example, as economic activity starts to increase economics agents may become more optimistic about

economic prospects and hence this influences firms to increase investment and consumers to spend more.

So that what started off as just a small increase or decrease in aggregate demand is magnified by how

people interpret the situation and their belief of how it would affect their standard of living. To help

understand this better consider a decrease in government spending on domestically produced weapons,

this would cause an initial fall in output and thus income from weapons production. However the laid off

workers will in turn cut back on their expenditure on consumer goods, thus in the local areas around the

weapons factories, shops, cinemas, licensed drinking places etc will be faced with reduced demand and

perhaps may lay off workers or reduce their payments. This further reduces demand and so on, thus the

initial effect on aggregate demand is multiplied by a reduction in the income of consumers and demand

for consumer goods. Consider the diagrams below:

Expenditure

E = Y

B AE2 AE = 5% increase

A AE1

Y=15%

W

J2

J1

Y1 Y2 income



Above we show how the multiplier works using both the Keynesian aggregate model as well as the

injection withdrawal model. From the Keynesian model we observe as the aggregate expenditure

increases by 5% it resulted in a rightward shift of the Aggregate expenditure line from AE1 to AE2

establishing a new equilibrium point at B causing income/output to increase by 15% from Y1 to Y2. On

the other hand we also observe that if injections were to increase it would shift to a higher curve in our

case from J1 to J2 causing and increase in income also from Y1 to Y2.this is a diagrammatic example of

the multiplier principle. The numerical value of the change is known as the multiplier, the strength of the

multiplier or its coefficient is given by the symbol K.

Multiplier: this principle is that a change in the level of injection (or withdrawals) brings about a

relatively larger change in the level of national income.

Simple example of multiplier at work

Increase in income increase in consumption increase in savings Y C S 1

st recipients 1000 666.67 333.33

2nd

recipients 666.67 444.44 222.23

3rd

recipients 444.44 296.30 148.14

4th recipients 296.30 197.53 98.77

5th recipients 197.53 131.69 65.84

+ + +

. . .

. . .

Total Y = $3000 C = $2000 S = 1000

Assume that investment and savings are the only injection and withdrawal respectively. If a firm decides

to construct a new building costing $1000, then the income of builders and the suppliers of the raw

materials will rise (or change) by $1000. In addition let us assume that the recipients of the $1000 have an

MPC = 2/3 or 0.667 thus they would spend/consume 666.67 and save the rest which was from the table

$333.33. Nevertheless this $666.67 consumed by the builders and suppliers creates income for another

group of people and assuming their MPC is also 2/3 then they would consume 444.44 out of the 666.67

and save the rest. This process continues with each new round of spending being two thirds of the

previous round and thus a long chain of extra income, extra consumption and extra saving is set up. The

whole process comes to an end when the addition to savings total $1000 this is because only then will the



extra savings in equal to extra investment so S = I and economy is in equilibrium. At this point additions

to income are $3000 so that $1000 extra investment created $3000 rise in income, therefore the multiplier

in this case is 3 well see this in next section.

The Multiplier Formula

Based on our example above we have seen that the amount of income that goes back into the circular flow

is really governed by the MPC so we can thus say that the multiplier is governed by the MPC. We also

observed that the additions to income followed the following pattern or series: Y = $1000 + $666.67 +

$444.44 + 296.30 + ., and this was because the MPC was 2/3. Lucky for us such a series is well known

in maths as a geometric progression series and its value is given by the formula: 1/1-r where r is the value

of the common ratio. In the case of the multiplier the common ratio is the MPC so we get:

K = 1 and if MPC = 2/3 then we get K = 1 = 3

1 - MPC 1- 2/3

So now we see how we got the multiplier as 3 from last section. It is important to note that the larger

the MPC the larger the Multiplier will be.

Equilibrium and the Multiplier

In our example all extra income was either consumed or withdrawn we can write: MPC + MPW = 1

where the MPW is the marginal propensity to withdraw. Thus it follows that 1 MPC = MPW, and we

could also write the formula for the multiplier as: K = 1

MPW

So that if we know the value of MPW we can predict the effect of a change in injections upon national

income. The effect will be the change in injections multiplied by K, which we write as:

Y = K J or as Y = 1 J

MPW

To determine the overall MPW we must total all the other propensities to withdraw. That is:

K = 1

MPS + MPT + MPM

Where MPW = MPS + MPT + MPM and MPS is the marginal propensity to save, MPT is the marginal

propensity of taxation and MPM is the marginal propensity to import.

keynesian aggregate mode1 pdf

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