1. Lecture 3: Simple Keynesian Model
National Income Determination
Three-Sector National Income Model

2. Outline Three-Sector Model Fiscal Policy
Output-Expenditure Approach: Equilibrium National Income Ye
Injection-Withdrawal Approach: Equilibrium National Income Ye
Fiscal Policy

3. Three-Sector Model
With the introduction of the government sector (i.e. together with households C, firms I), aggregate expenditure E consists of one more component, government expenditure G.
E = C + I + G
Still, the equilibrium condition is
Planned Y = Planned E

4. Three-Sector Model Government expenditure is made up of two parts
Government expenditure on current production, G
Transfer payments, Q
Government also collects tax revenues, T
Government budget may be defined as
T- (G + Q)
When positive, there is a government surplus
When negative, there is a government deficit
When zero, there is a balanced budget

5. Three Sector Model Assumptions about the Government component of AE
Government expenditure on current production is assumed constant, G= G*
Transfer payments are also an autonomous expenditure flow, Q= Q*
Additional assumptions
All transfer payments are made to households
All taxes are direct taxes on personal and company incomes
Tax rate is levied at a flat rate, T= tY where 0<t<1
i.e. taxes are a constant proportion of national income

6. Three-Sector model
In the 2-sector model, all national income was paid out to households
Households decided to consume or save amounts
National income, Y= disposable income, Yd
Introduction of taxes and transfer payments drives a wedge between national income and disposable income
Yd= Y- T + Q

7. Three- Sector Model We continue to assume C= cYd Given that Yd= Y-T+Q,
Households spend a fraction of disposable income and save the rest
Given that Yd= Y-T+Q,
C= c(Y-T+Q)
=cY – cT + cQ, but T= tY
=cY – ctY + cQ
= c(1 – t) Y + cQ

8. The Income-Expenditure Approach
Aggregate expenditure has three components
E= C + I + G
At the equilibrium,
E = Y
Derive the aggregate expenditure function assuming the following
Yd = Y – T + Q
G= G*
Q= Q*
T= tY
I= I*
C= cYd

9. The Income-Expenditure Approach
E= C + I + G
= cYd + I* + G*
= c( Y – T+ Q*) + I* + G*
= c(Y – tY + Q*) + I* + G*
At equilibrium, Y= E
Y = c(1-t) Y+ cQ* + I* + G*
Y- c(1 – t) Y= cQ* + I* + G*
Y[1 – c(1 – t)] = cQ* + I* + G*
Y = 1/ [1 – c(1 – t)] (cQ* + I* + G*)
Expenditure depends on two main terms
The sum of the three autonomous flows: Q*, I*, G*
Behavioural patterns of consumption, c, and taxation, t

10. Changes in Equilibrium Income
What is the effect of changes in autonomous expenditure flows and the tax rate, t, on national income?

11. A change in G* and/or I*
An increase in G or I shifts the AE curve upwards
Increase in national income

12. A change in transfer payments
An increase in transfer payments will also increase national income
How?
However, an extra Ghc1 spent on final government expenditure, G, increases national income by more than Ghc1 spent on transfer payment, Q.
Why?

13. A change in tax rate
A cut in tax rates implies that a larger proportion of each Ghc1 reaches households as disposable income
Therefore, the propensity to consume increases
AE becomes steeper
Increase in national income

14. The Multiplier
How large is the change in national income from a given change in autonomous expenditure?
To determine this, we need to solve the following algebraically:
Ye/I
Ye/G
Ye/Q

15. The Multiplier Recall from the income expenditure approach
Equilibrium national income is given by
Y = 1/ [1 – c(1 – t)] (cQ* + I* + G*)
Solution?
Ye/I
Ye/G
Ye/Q
What do you notice about the change in income from a change in investment, I*, or government expenditure, G*?
What do you notice about the value of the transfer payments multiplier, Q*?
Is it larger or smaller? Why?
Under what conditions are al three multipliers equal?

16. Injection-Withdrawal Approach
In a 3-sector model, national income is either consumed, saved or taxed by the government
Y = C + S + T
Given E = C + I + G
In equilibrium, Y = E
C + S + T = C + I + G
 S + T = I + G , but G= G + Q (Q= cQ)
 S + T = I + G + cQ
i.e. withdrawals = injections

17. Injections- Withdrawals Approach: Equilibrium national income
Graphical Approach

18. Injections- Withdrawals Approach: Equilibrium national income
Graphical Approach
An increase in any component of aggregate expenditure shifts the injections curve upwards
And vice versa
A fall in the tax rate increases the amount of disposable income, and the propensity for increased consumption
This is illustrated by a flatter (i.e. smaller value of t) withdrawals curve, leading to increased equilibrium national income

19. Injections- Withdrawals Approach: Equilibrium national income
An algebraic approach
We define savings, S= s(Y- T)
i.e. the part of national income that is saved
Other assumptions
T= tY
Q= Q*
I= I*
G= G*
At the equilibrium, Withdrawals = Injections
Withdrawals = s(1- t)Y + tY = Y[s(1- t) + t]
Injections = I* + G* + cQ*
At the equilibrium,
Y =1/ [s(1- t) + t] x (I* + G* + cQ*)
Is this the same equilibrium as obtained under the income-expenditure approach?
Derive the multipliers for investment and government expenditures, and transfer payments.

20. Limitation of the Simple Keynesian model
Y = Multiplier* G*
There are several problems with this method of analysis, i.e., Y may be less
Sources of financing G*
Effects on private investment I*
Productivity of government projects

21. The Problems of the Simple Keynesian Multiplier k E
Sources of financing G’
Increasing Tax
will exert a contractionary effect on the economy
Increasing Money Supply
will generate an inflationary pressure
Prices assumed constant
Increasing Debt/ Private sector borrowing
will increase the demand for loanable fund as well as interest rate  affect private investment

22. The Problems of the Simple Keynesian Multiplier k E
Effects on Private Investment I’
Private investment may be crowded out when government increases its expenditure
It is questionable that the government can really produce something which is desired by the consumers
Besides, government investment projects are usually less productive than private investment projects

23. The Problems of the Simple Keynesian Multiplier k E
Productivity of Government Projects
Government projects may not yield a rate of return (MEC / MEI) exceeding the market interest rate.

24. Take- Home Assignment
Using the mechanistic Keynes Theory of National Income, explain the causes and solutions to the Great Depression of 1929.

25. Next Class Money and its Functions The origin of money
Modern money and definition of monetary aggregates
Commercial Banks and Money Creation
The Central Bank and its functions