The circular flow of income and the Keynesian multiplier

The circular flow of income and the

Keynesian multiplier

Equilibrium in the goods market


The analysis of the goods market equilibrium is the starting point of Macroeconomic analysis (particularly from the Keynesian point of view)All the goods and services are aggregated

into a single market ⇒ 1 equationThe purpose is to find the equilibrium level

of output Y* on this market ⇒ 1 unknownA second issue is to describe how Y* varies

as a function of other macroeconomic variables


The circular flow of income

Aggregate demand and output

The multiplier and role of savings


Households Firms

Labour

Income €

Goods

Expenditure€


Households Firms

Labour

Goods

Real flows


Households Firms

Income €

Expenditure€

Monetary flows


The circular flow of income is what guarantees the 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






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 households

I : Investment of firms


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

C = C0 + cY

Where C0 is 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


For the moment, investment I is considered to be exogenous.

Its level is pre-determined and does not depend on output

This is a simplifying assumption that will be relaxed later on (when interest rates are introduced)

Aggregate demand Z is therefore a function of output Y, of the marginal propensity to consume c and of the exogenous level of investment I.

Z = C0 + cY + I


Income, output Y

Aggregate Demand (planned expenditure)

Z = C0 + cY + I

mpc: 0<c<1

Aggregate demand as a function of income

Autonomous demand (not a function of Y)

C0 + I

Aggregate Demand Z


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

slope < 1), There is only a single point for which the 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 full employment equilibrium !!

This will be examined later.


45°

Effective expenditure

Y = Z

Keynesian Equilibrium Output

Y* Income, output Y


Z = C0 + cY + I

Equilibrium on the goods market

Aggregate Demand Z


For each aggregate demand curve Z there is only a single point for which the planned expenditure is equal to the level of income Y But Z is determined by the plans of agents!

What happens if the level of planned expenditure Z is not equal to Y ? The goods market is not in equilibrium !! Output will adjust so that the equilibrium is

reached



Y* Income, output Y


Disequilibrium with Z > Y

Z

Y

Unplanned reduction in inventories

The firms are selling more than they are producing. They have to increase production in order to meet the aggregate demand, which brings the goods market back to Y*

Y

Aggregate Demand Z

45°

Y

Z



Y* Income, output Y


Disequilibrium with Z < Y

Y

Unplanned increase in inventories .

Firms are selling less than they are producing. They reduce output which brings the goods market back to Y*

Aggregate Demand Z

45°





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 ΔI ?

In fact, ΔY > ΔI !! Why is that?


45°

Y = Z

Y1Income, output Y

Z1 = C0 + cY + I1

Multiplier effect on the goods market

Aggregate Demand Z

Z2 = C0 + cY + I2

ΔY

Y2

ΔI

1. An increase in planned investment…

2. …leads to a more than proportional increase in income


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

ICc

Y

ICcY

IcYCY

0

0

0

1

1

1

cI

Y

1

1Multiplier

Autonomous demand

(exogenous)


Why do we observe ΔY > ΔI ?

Increase in planned investment

ΔI

Increase in income

ΔY

Increase in savings

ΔY × mps

Increase in consumption

ΔY × mpc

First interpretation: a multiplier effect due to the circular flow of income



Step 1 : output increases by ΔI Step 2 : output increases by c × ΔI Step 3 : output increases by c2 × ΔI Step 4 : output increases by c3 × ΔI ..... 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



Second interpretation: The economy is increasing output in order to balance investments and savings

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

These two equilibrium conditions are equivalent !


Aggregate demand can be decomposed into consumption and investment

Z = C + I Income can be decomposed into

consumption and savingsY = Y(c+s) = C + S

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

SIZY



Starting from equilibrium, if investment increases by ΔI, then we are no longer in equilibrium:

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

increase by the same amount (ΔS = ΔI).

Given the savings function,

So we have

YsS

sS

Y 1

sI

Y 1

⇒ ⇒ cI

Y

1

1



Both explanations (spending multiplier or savings/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 explanations of the real-life economic phenomena.

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The circular flow of income and the Keynesian multiplier