The Expanded Model of Income

Determination

The Expanded Model of Income

Determination

Expanded model of income determination

In chapter 14, a very basic Keynesian model of income determination was introducedThis model serves as an introduction to

income determination and capacity utilisation in the economy

If is far to simple to be of any use in the real world, but it establishes some important points nevertheless

Keynes, John Maynard, 1st Baron Keynes of Tilton (1883-1946)

Expanded model of income determination

Recall when Keynes was writing – mid thirties with massive unemploymentEstablished theory until then had assumed

that this would be a temporary phenomenon

In a world with flexible prices, in the long run equilibrium will exist in all markets

Keynes: In the long run, we are all dead

Expanded model of income determination

Keynes gave politicians theoretically sound arguments for intervening in the economyKeynes in particular focused on how the

authorities could affect aggregate demand through fiscal policy, i.e. government purchases of goods and services and taxes

In chapter 15, this is incorporated into the basic model of income determination.

Expanded Model of Income Determination

We introduce a public sector, with government purchases of goods and services G and taxes T. This model could be labelled a Keynes model for a closed economy with a public sector

Later in the chapter, another sector is introduced – the foreign sector. Only goods transactions takes place, exports (X) and imports (Z)

This chapter also provides a more satisfactory explanation of investment demand

Investment demand

Demand for investment goods (I) very much depends on the outlook for the economy

Profitability depends on: Investment outlay Increased income due to the investmentCosts of financing the investment

Increased income – cost of investment = MEI(marginal efficiency of investment)

Cost of financing: R

Time value of money

The investment outlay is paid for ”today”

Income will accrue in the future, and value may be reduced due to:impatience and postponement of demand

risk

inflation

Income must be discounted by an interest rate R

Net Present Value

Example:Investment outlay = 10 000

Income year 1: 6 000

Income year 2: 2: 6 000

Interest rate (R) = 5 % (0,05)

What is the PV of the income?

1115605,1

6000

1,05

6000PV

2

Marginal Efficiency of Investment (MEI)

Marg

inal e

fficie

ncy

of in

vestm

en

t

Rate

of re

turn

(R)

R2

I2

R1

I1I0

Expectations change

Marg

inal e

fficie

ncy

of in

vestm

en

t

Rate

of re

turn

(R)

I0

R0

I1 I2

The accelerator

changes in national income and induced investment

the accelerator coefficient

the instability of investment

The multiplier / accelerator interaction

Keynesian business cycle

-14

-12-10

-8

-6

-4-2

0

24

6

810

12

14

1618

20

1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

GD

P, I

nves

tmen

t (%

ann

ual c

hang

e)Fluctuations in UK real GDP and investment: 1978-2002Fluctuations in UK real GDP and investment: 1978-2002

-14

-12-10

-8

-6

-4-2

0

24

6

810

12

14

1618

20

1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

GD

P, I

nves

tmen

t (%

ann

ual c

hang

e)Fluctuations in UK real GDP and investment: 1978-2002Fluctuations in UK real GDP and investment: 1978-2002

GDP

-14

-12-10

-8

-6

-4-2

0

24

6

810

12

14

1618

20

1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

GD

P, I

nves

tmen

t (%

ann

ual c

hang

e)Fluctuations in UK real GDP and investment: 1978-2002Fluctuations in UK real GDP and investment: 1978-2002

GDP

Investment

Accelerator 1970-1999 in Norway

-30,0 %

-20,0 %

-10,0 %

0,0 %

10,0 %

20,0 %

30,0 %

1974 1978 1982 1986 1990 1994 1998

GDP Investment

Accelerator theorycapital output ratio = 2

Year SalesRequired

capital stockNet

investment1 1 mill 2,0 mill2 1 mill 2,0 mill 03 1,2 mill 2,4 mill 0,4 mill4 1,5 mill 3,0 mill 0,6 mill5 1,6 mill 3,2 mill 0,2 mill

Accelerator theory

Investments are dependent on expected changes in GDP or I = YAccelerator – a small change in income

gives a large change in induced investmentThis depends on the marginal ratio

between capital and productionIn addition, we will have multiplier effects

between I and Y

Introducing the public sector

Taxes T represent a withdrawal from the economic circulation (like savings S)

The Governments demand for goods and services G represent an injection (like investments I)

Equilibrium when realised withdrawals = realised injectionsS + T = I + G

Keynes expanded model - 1

The public sectors demand for goods and services G is always exogenousTaxes (T)Version 1: Lump sum taxes T = T

Version 2: Income taxes T = tY, where t is the (average) tax rate

The model version 1

TT

GG

II

bY C

GICY

d

Equilibrium

bT)GI(b1

1Y

bT G I b)Y(1

bTGIbYY

GIbTbYY

GIT)b(YY

GICY

An example

Assume we have the following:C = 0,8Yd

I = 60

G = 50

T = 50

35040)5060(0,81

1Y

The multipliers

Tb1

b

Ib1

1

Gb1

1

Y

Y

Y5010

0,2

1Y

10G :Assume

The model

Examplea 0I 60G 50T 50

b = MPC 0,8Y 350

Consumption 240Government 50Investment 60Y = GNP 350

Multiplier 5,00

Haavelmos theorem

What happens if an increase in public spending is financed by an equivalent tax increase, i.e. G= T?

1 is multiplier theG,Y

Gb1

b1Y

Gb1

bG

b1

1Y

gives thisT, G assumptionBy

Tb1

bG

b1

1Y

The Model Version 2

tY

T

GG

II

t)bY(1 C

GICY

Equilibrium

G)I(t)b(11

1Y

G I t)b(1Y(1

GI bYt bYY

GI bYt bYY

GIt)bY(1Y

GICY

The multipliers

taxesof form in the leakages

increased todue reduced is multiplier The

It)b(11

1Y

Gt)b(11

1Y

8,271078,2

)2,00,8(11

1Y

%) (20 0,2 t 10,G :Assume

The model

Examplea 0I 60G 50t 0,3

b = MPC 0,8Y 250,00

Consumption 140Government 50Investment 60Y = GNP 250,00

Multiplier 2,27

Built in stabilisers

Govern

ment

exp

end

iture

an

d

Taxes

Yb

G

G

T

T

Introducing the foreign sector

Imports: Z and Exports: X

Equilibrium when leakages = injectionsS + T + Z = I + G + X

It is assumed that imports are endogenous and dependent on income

Exports are exogenous

Economic circulation

The model

nYZ

XX

T

GG

II

t)bY(1 C

ZXGICY

tY

The multipliers

Xnt)b(11

1

Gnt)b(11

1

Int)b(11

1

X) G I(nt)b(11

1Y

Y

Y

Y

The open economy model

InputG 20I 16X 30t 0,2n 0,3b 0,8

Y = 100,00

G - T 0,00X - Z 0,00