keynesian multiplier

7/30/2019 Keynesian Multiplier

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The circular flow ofincome and the

Keynesian multiplier

Equilibrium in the goods market


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The circular flow of income

Aggregate demand and output

The multiplier and role of savings


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Households Firms

Labour

Income

Goods

Expenditure


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Households Firms

Labour

Goods

Real flows


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The circular flow of income is what guaranteesthe central accounting identities

Three definitions of GDP (output)

Sum of the expenditures Z

Sum of the value added produced Q

Sum of the incomes distributed Y

Accounting identities

Production = Aggregate demand / expenditure

Q = Z

Production = Incomes of factors of production

Q = Y


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In the Keynesian model, the aggregate demand(also called planned expenditure) in a closed

economy with no government is:

Z = C + I

with Z : Aggregate Demand

C : Consumption of householdsI : Investment of firms


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Consumption C is not fixed. Its level depends onthe level of income Y, and is given by the

consumption function.

C = C0 + cY

Where

C0is the autonomous level of consumption, i.e. the

level of consumption that does not depend on income

c is the marginal propensity to consume (mpc) : the

amount spent out of an extra unit of income.

The converse is the marginal propensity to save (mps)

s, such that

c + s = 1


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For the moment, investment I is considered tobe exogenous.

Its level is pre-determined and does not depend

on output

This is a simplifying assumption that will berelaxed later on (when interest rates are

introduced)

Aggregate demand Z is therefore a function of

output Y, of the marginal propensity to consumec and of the exogenous level of investment I.

Z = C0 + cY + I


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Effective demand and equilibrium For any level of planned expenditure Z (with a

slope < 1), There is only a single point for whichthe planned expenditure is equal to the level of

income Y This gives the equilibrium condition on the

goods market: Y = Z

There is no guarantee that this point is a fullemployment equilibrium !!

This will be examined later.


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Effective expenditure

Y = Z

KeynesianEquilibrium Output

Y* Income, output Y

Aggregate Demand (planned

expenditure)

Z = C0 + cY + I

Equilibrium on the goods marketAggregateDemand Z


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For each aggregate demand curve Z there isonly a single point for which the plannedexpenditure is equal to the level of income Y

But Z is determined by the plansof agents!

What happens if the level of plannedexpenditure Z is not equal to Y ?

The goods market is not in equilibrium !! Output will adjust so that the equilibrium is

reached


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Y* Income, output Y


expenditure)

Disequilibrium with Z > Y

Z

Y

Unplanned reduction ininventories

The firms are selling more thanthey are producing. They have toincrease production in order tomeet the aggregate demand,which brings the goods marketback to Y*

Y

AggregateDemand Z

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Y

Z



Y* Income, output Y


expenditure)

Disequilibrium with Z < Y

Y

Unplanned increase ininventories .

Firms are selling less thanthey are producing. Theyreduce output which bringsthe goods market back to Y*

AggregateDemand Z

45


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The multiplier and the role of savings

So aggregate demand is given by

Z = C + I

And the equilibrium condition is

Y = Z

So what happens to output Y if investment I

increases by an amount I ? In fact, Y > I !!

Why is that?


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Y = Z

Y1 Income, output Y

Z1 = C0 + cY + I1

Multiplier effect on the goods marketAggregateDemand Z

Z2 = C0 + cY + I2

Y

Y2

I

1. An increase in plannedinvestment

2. leads to a more thanproportional increase in income


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Aggregate demand is given by : Z = C0 + cY + I And Y = Z

Solving for the equilibrium level of output gives us :

There are 2 equivalent interpretations to this result

IC

c

Y

ICcY

IcYCY

0

0

0

1

1

1

cI

Y

1

1

MultiplierAutonomous

demand

(exogenous)


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Why do we observe Y > I ?

Increase in plannedinvestment

I

Increase in income

Y

Increase in savings

Y mps

Increase inconsumption

Y mpc

First interpretation: a multiplier effect dueto the circular flow of income


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Step 1 : output increases by I

Step 2 : output increases by c I

Step 3 : output increases by c2 I Step 4 : output increases by c3 I

..... This continues forever ! The closer c is to 1, i.e.the less people save, the larger the effect. (why ?)

The aggregate size of the increase is equal to:

ccccc

1

1...1

432


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Second interpretation: The economy isincreasing output in order to balance

investments and savings

This is because the equilibrium condition Y=Z isequivalent to I=S (planned investment = savings)

These two equilibrium conditions are equivalent !


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Aggregate demand can be decomposed intoconsumption and investment

Z = C + I

Income can be decomposed intoconsumption and savings

Y = Y(c+s) = C + S

So one can see that setting Y=Z isequivalent to setting I=S !

SIZY


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Starting from equilibrium, if investment increasesby I, then we are no longer in equilibrium:

I + I > S To get back to equilibrium, we need savings to

increase by the same amount (S = I).

Given the savings function,

So we have

YsS

sS

Y 1

sI

Y 1

cI

Y

1

1


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Both explanations (spending multiplier orsavings/investment balancing) are equally

valid. The spending multiplier is usually easier to

understand, and is found in most manuals

The savings/investment balance, however,often brings more interesting explanationsof the real-life economic phenomena.

keynesian multiplier

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