Download three-sector keynesian model

THREE-SECTOR KEYNESIAN
MODEL:
• A Keynesian model of the macro economy
that includes the three domestic sectors, the
household sector, the business sector, and the
government sector. This Keynesian model
variation adds the government sector (or
public sector) to the household and business
sectors that make up the two-sector model.
• The three-sector Keynesian model is perhaps the most
commonly used representation of Keynesian economics. It
contains the three essential components of the
macroeconomics needed to analyze business-cycle instability.

First, consumption expenditures by the household sector
capture induced expenditures.


Second, investment expenditures by the business sector
incorporate autonomous private sector expenditure changes
that are considered a prime source of business cycles in
Keynesian economics.
Third, government purchases and taxes by the
government sector then highlight the use of policy actions
to address business-cycle instability.
• THREE-SECTOR, THREE-MARKET CIRCULAR FLOW:
• Three Sectors, Three Markets
• The three macroeconomic sectors included in this model are:

Household Sector: This includes everyone, all people, seeking to satisfy
unlimited wants and needs. This sector is responsible for consumption
expenditures. It also owns all productive resources.

Business Sector: This includes the institutions (especially
proprietorships, partnerships, and corporations) that undertake the task
of combining resources to produce goods and services. This sector does
the production. It also buys capital goods with investment expenditures.

Government sector: This includes the ruling bodies of the federal, state,
and local governments. Regulation is the prime function of the
government sector, especially passing laws, collecting taxes, and
forcing the other sectors to do what they would not do voluntary. It
buys a portion of gross domestic product as government purchases.
• The three macroeconomic markets in this version of the circular
flow are:

Product markets: This is the combination of all markets in the
economy that exchange final goods and services. It is the
mechanism that exchanges gross domestic product. The full name is
aggregate product markets, which is also shortened to the aggregate
market.


Resource markets: This is the combination of all markets that
exchange the services of the economy's resources, or factors of
production--including, labor, capital, land, and entrepreneurship.
Another name for this is factor markets.
Financial Markets: The commodity exchanged through financial
markets is legal claims. Legal claims represent ownership of
physical assets (capital and other goods). Because the exchange of
legal claims involves the counter flow of income, those seeking to
save income buy legal claims and those wanting to borrow income
sell legal claims.
This diagram presents the three-sector, three-market circular flow.
At the far left is the household sector, which contains people
seeking consumption. At the far right is the business sector that
does the production. At the top is the product markets that
exchange final goods and services. At the bottom is the resource
markets that exchange the services of the scarce resources. Just
above the resource markets are the financial markets that divert
saving to investment expenditures. In the very center is the
government sector.
• Illustration 1
• In a two sector economy, the basic equations are as
follows:
• The Consumption function is C = 200 + 0.8Y and investment
is I = 300 millions. The equilibrium level of income is 2500
millions. Presume the government is added to this two
sector model, which then becomes a three sector economy.
The government expenditure is at 100 millions
• Determine the equilibrium level of income in the three
sector economy
• What is the multiplier effect of the government
expenditure? Is it of the same magnitude as the multiplier
effect of a change in the autonomous investment?
• Presume the Consumption function is C = 200 + 0.8Yd that
there is a balanced budget in that the entire government
expenditure is financed from a lump sum tax. Find the new
equilibrium level of income in the three sector economy.
• Solution
• The equilibrium condition in the three sector economy is
given as
•
Y
=
C+I+G
Thus,
Y
=
200 + 0.8Y + 300 + 100
•
Or, Y
=
600 + 0.8Y
•
Or, Y – 0.8Y =
600
•
Or, 0.2Y =
600
•
Or, Y
=
600 / 0.2
• The equilibrium level of income in the three sector
economy is 3,000 millions, which is an increase by 500
millions over the two sector economy.
• Government Expenditure Multiplier
•
GM
=
ΔY =
1
ΔG
1–b
• Where, Δ G =
Change in government expenditure
•
b
=
Marginal propensity to consume
•
ΔY =
Change in income
•
GM =
Government expenditure multiplier
•
•
=
1 / 1 – 0.80
•
=
5
• Investment Multiplier, m
=
ΔY =
1
ΔI
1–b
• Where b is the marginal propensity to consume,
• Thus the magnitude of the multiplier effect is the same as
that of a change in government expenditure.
•
G
Thus,
C
=
=
T
200 + 0.8 (Y -100)
C
=
C
=
Y
=
Y
=
=
100 millions
we know (Yd=Y-T)
200 – 80 + 0.8Y
120 + 0.8Y
C+I+G
120 + 0.8Y + 300 +
•
•
• But,
•
100
•
Y – 0.8Y
=
120 + 400
•
0.2Y =
520
•
Y
=
520 / 0.2
• The new equilibrium level of income in the three
sector economy, when there exists a balanced budget
is 2,600 millions.
• Illustration 2
• In an economy, the full employment output
occurs at 2000 millions. The marginal propensity
to consume is 0.8 and the equilibrium level of
output is currently at 1600 millions. Suppose the
government aspires to achieve the full
employment output, find the change in
• The level of government expenditures
• Net lump sum tax
• Solution
• We have, GM =
• ΔY =
1
ΔG
1-b
• Where, Δ G =
Change in government expenditure
•
b
=
Marginal propensity to consume
•
ΔY =
Change in income
•
GM
=
Government expenditure multiplier
• For instance,
•
b
=
0.80
•
ΔY =
2000 – 1600
•
ΔY =
400
• Thus,
400 / Δ G
=
1 / 1- 0.8
•
ΔG =
400 (0.2)
• Thus, the level of government expenditures required to
achieve the full employment output is 80 millions
• We have, GF =
•
Where,
•
consume
ΔY
ΔT
=
-b
1–b
ΔT
b
=
=
Change in tax
marginal propensity to
•
ΔY =
Change in income
•
GF
=
Government tax multiplier
• As the tax multiplier is negative, an increase in tax leads to a decrease in
the equilibrium level of income.
• For instance,
b
=
0.80
•
ΔY =
2000 – 1600 = 400
Thus,
400 =
- 0.80
ΔT
1 – 0.80
•
-0.8 Δ T
=
400 (0.20)
• The net lump sum tax is – 100 millions. There should be a decrease in
lump sum tax by 100 millions