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

2. outline Equilibrium in the 3 sector model The Multiplier Fiscal Policy
Output Expenditure Approach
Withdrawals Injections Approach
The Multiplier
Fiscal Policy

3. The Income-Expenditure Approach: equilibrium conditions (algebraic 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

4. The Income-Expenditure Approach
E= C + I + G
= cYd + I* + G*
= c( Y – T+ Q*) + I* + G*
= c(Y – tY + Q*) + I* + G*

5. Equilibrium : The Income-Expenditure Approach
Algebraic approach
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

6. Equilibrium: The income-expenditure approach
Graphical illustration

7. Changes in Equilibrium Income
What is the effect of changes in autonomous expenditure flows (G, I and cQ) and the tax rate, t, on national income?

8. A change in G*, I* or cQ* Graphical illustration
An increase in G, I or cQ shifts the AE curve upwards
Increase in national income

9. A change in transfer payments
An increase in transfer payments (Q) 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? Discuss…

10. 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

11. 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

12. 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?

13. 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

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

15. 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

16. Injections- Withdrawals Approach: Equilibrium national income
An algebraic approach
We define savings, S= s(Y- T)
i.e. the part of disposable 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.

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

18. Next Class Dr Monica P. Lambon-Quayefio 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