The Simple Keynesian Model of Income

Determination

2

Session Outline

• Consumption Function

• Planned Investment (I), Government Purchases (G) and Net Exports (NX)

• Equilibrium Income

• Multiplier

• Income Determination in an Open Economy and the Foreign Trade Multiplier

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Introduction• Full employment level is one of the many

possible states of the economy i.e., it need not be automatically at this state.

• The model focuses only on the goods market and the influence of money market on the goods market is completely ignored.

• Key assumptions.– Prices remain constant– Firms are able to sell any amount of output at given

level of prices (that is, the aggregate supply curve is perfectly elastic)

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Determination of Equilibrium Output

Aggregate demand (AD) = total goods

demanded in an economy.

AD = C + I + G + NX

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Equilibrium Output

Equilibrium output is the output level at which the quantity of

output produced is equal to quantity of output demanded.

At any output level, Y, is equal to C + I + G + NX.

Does it mean all output levels are equilibrium output levels?

– The answer is ‘No’.

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Equilibrium Output

The concept of aggregate demand, AD is ‘ex-ante’, national

income accounts are all in the ‘ex-post’ sense.

In other words, aggregate demand refers to the total goods

and services that people want to buy, while national

income refers to the total goods and services that are

actually bought.

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Equilibrium Output

Desired aggregate demand may not be equal to

actual output at all times.

Equilibrium level of output refers to the output at

which total desired spending on goods and

services (desired aggregate demand) is equal to

the actual level of output (Y).

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Determination of Equilibrium Output

• Aggregate Demand (AD):

AD = C + I + G + NX

• Equilibrium Output:

Y = AD

Or,

Y = C + I + G + NX

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Consumption Function

Consumption expenditure (C) is one of the important components of aggregate demand. Although many factors influence the consumption expenditure, income (Y) is considered to be the most important influencing factor.

The relationship between consumption and income can be described using consumption function, C = f(Y).

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Consumption and income are positively related i.e., greater the income, greater is the consumption.

Let us assume that consumption demand increases linearly with an increase in the income level. Thenwe have, C = a + bY; a > 0, 0 < b < 1Where ‘a’ is the consumption when the income level is zero and ‘b’ is the slope of the consumption function. ‘b’ represents the marginal propensity to consume (MPC) i.e., the rate at which consumption changes for a unit change in income.

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Consumption Function

C = a + bY; a > 0, 0 < b < 1

Where b = MPC

C = a +bY

a

C

Y

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Derivation of Savings Function• If we assume a two-sector economy, income has

to be either spent or saved and there are no other alternatives to use the income. Thus, Y = C + S (or) S = Y – C

• S = Y – (a + bY)• S = – a + (1 – b) Y• Savings increase (decrease) with the increase

(decrease) in income. This relationship can also be seen from the above equation, S = - a + (1 – b) Y. In the equation, (1 – b) represents the marginal propensity to save (MPS). The sum of MPC and MPS must be equal to one. For example, if MPC is 0.4, then MPS = 0.6

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Savings Function

Y = C + S

S = Y – C

S = Y – C = Y – a – bY

= - a + (1 – b)Y

Where b = MPC

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Planned Investment (I), Government Purchases (G) and Net Exports (NX)

For deriving consumption function, we assume that other components of aggregate demand I, G and NX are constant and are independent of the income level. Let the constant levels of investment, government purchases and net exports be represented by I, G and NX respectively.

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Planned (I), Government (G) and Net Exports (NX)

( )

tan

AD C I G NX

a bY I G NX

a I G NX bY

A bY

Where

A a I G NX

and

A Cons t

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Planned Investment (I), Government Purchases (G) and

Net Exports (NX)

C = a +bY

AD = +bY

Y

AD

I G NX A

a

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In the figure, we have shown consumption

function and the aggregate demand

function. The parallel line above the

consumption function is the AD line. Part of

the aggregate demand, i.e. is autonomous

and is independent to the income level,

while remaining part ‘bY’ is dependent on

income and output.

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Equilibrium Income• Next , we use the aggregate demand function to

determine the equilibrium level of income and output.

• Equilibrium level of income is the level at which aggregate demand is equal to output, which in turn equals income.

• The 450 line drawn serves as a reference line on which at all points the level of aggregate demand is equal to the level of output.

• And, the point at which 45 line cuts AD line is the equilibrium point and the corresponding income level is the equilibrium income

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At output levels below Y, aggregate demand exceeds output. Consequently, the level of inventory with firms decreases. This unintended (undesired) decline in inventories makes firms to increase their production, resulting in increase in income levels.

Conversely, at output levels above Y, the output exceeds aggregate demand causing increase in level of inventories. This unintended increase in inventories makes firms to cut their production.

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Equilibrium Income

C = a +bY

AD = +bY

Y

AD

450

Y*

I G NX A

a

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Deriving Equation for Equilibrium Level of Income

b

NXGIa

b

AY

AbY

bYA

NXGIbYa

NXGICADY

11

)1(

)(

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From the above formula, we know that larger

the autonomous components (for a given

b), the higher is the equilibrium level of

income. Similarly, if b (slope of the AD

curve) is less, then higher is the

equilibrium level of income.

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Multiplier

Multiplier refers to a multiple by which

equilibrium income changes for a unit

change in autonomous spending.

Put differently, multiplier refers to the rate at

which the level of equilibrium income

increases (decreases) for a unit increase

(decrease) in autonomous spending. The

multiplier is denoted by .04/12/23

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Multiplier

AD2 = 2+bY

Y

AD

450

Y2*

AD1 = 1+bY

Y1*

A

AA

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From the above figure it is clear that

for a change in autonomous

expenditure (∆A), there would be a

greater change in equilibrium income

(Y), because of operation of multiplier.

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Deriving Equation for Multiplier

MPSb

Where

MPSbAAb

A

b

A

b

AY

ngSubstituti

AA

YY

1

1

1

1

111

1

12

12

12

12

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From the above multiplier equation we

know that larger the marginal propensity to

consume, larger is the value of the

multiplier.

Conversely, larger the marginal propensity

to save the lower is the value of the

multiplier.

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Government Sector

Note: Disposable Income (Yd) = Total Income (Y) – Tax (T) + Transfer Payments (J).

NXGIJbaAWhere

YtbA

GIJtYYbaAD

tYgTAssu

NXGIJTYbaAD

JTYYd

bYdaC

)1(

)(

min

)(

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Deriving Multiplier (with the inclusion of Government Sector)

Multiplierbtb

Where

btb

A

tb

AYtbAY

ADY

iumAtEquilibr

1

1

1)1(1)1(

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The Budget

Budget Surplus (BS) = Tax Revenue (T) – Government Expenditure (G) – Transfer Payments (J)

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Income Determination in an Open Economy and the Foreign Trade Multiplier

How to determine the equilibrium level of output in an open economy?

For determination of income in an open economy, we assume that the

volume of imports (M) is influenced by the total income of the country,

while exports (X) depend on foreign economic conditions that cannot be

influenced by the open economy (that is, exports are exogenous to the

country).

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Income Determination in an Open Economy and the Foreign Trade

Multiplier

)( MXGICAD

mYXGIbYaAD d )(

mYXGIJtYYbaAD )(

)( mbtbYJbGIaAD

])1([ mtbYJbXGaAD

JbXGIamtb

Y

.)1(1

1

mtb

)1(1

1

Y

MMPImwhereYmYMM

'',.)(

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