1. National Income Determination Two-Sector National Income Model
Lecture 2
National Income Determination
Two-Sector National Income Model

2. Outline Output-Expenditure Approach to Income Determination
Expenditure Multiplier
Saving Function
Injection-Withdrawal Approach to Income Determination
Paradox of Thrift

3. Recap
2-sector model to explain the size of the national income and what causes changes to it
Planned expenditure is composed of Consumption and Investment
Functions and graphical illustrations
National Income identities
Y  E
C + S  C + I
 S  I
Changes in these components of expenditure lead to changes in national income (autonomous changes)
Changes in national income can cause changes in expenditure, and national income (induced change)

4. Output-Expenditure Approach
National income is in equilibrium when planned output = planned expenditure
We have planned expenditure E=C+I
Equilibrium income is Ye=planned E
A 45°-line is the locus of all possible points where Y = E

5. Output-Expenditure Approach: A Graphical Illustration
Planned E < Y
Y = E
C, I, E
Y= E
Planned E > Y Y Ye

6. Output-Expenditure Approach: Algebraic Solution
Let the level of Investment, I= 100
MPC= 0.8, implying that C= 0.8Y
Aggregate expenditure, E = C + I
E= 0.8Y + 100
In equilibrium, E= Y
Y= 0.8Y + 100
0.2Y= 100
Y= 500

7. Output-Expenditure Approach: More Generally
Y = planned E
Y = I* + cY
Y = I*+ cY
(1-c)Y = I*
Equilibrium condition
Y* = I* x
We can also solve for the equilibrium condition using the savings function… 1
1-c

8. Saving Function We have Y  C + S
Saving function can simply be derived from the consumption function
S = Y – C if C = cY
S = Y – cY
S = (1-c) Y
S = sY (recall that s = 1 – c)

9. Saving Function S S = sY S = (1-c)Y Slope of tangent = s =1- c Y
Slope of ray = slope of tangent

10. Saving Function Marginal Propensity to Save MPS = s
It is defined as the change in saving per unit change in disposable income
MPS = S/ Y
It is the slope of tangent of the saving function

11. Saving Function Average Propensity to Save APS
It is defined as the total saving divided by total income
APS = S/Y

12. Saving Function Average Propensity to Save APS (cont’d) When S= sY
 APS = MPS = s = constant

13. Saving Function Y = C + S Differentiate wrt. Y Y/Y=C/Y + S/Y
 1= MPC + MPS
 1 = c + s

14. Injection-Withdrawal Approach
Remember the national income identity S  I
The equilibrium income happens when planned Y= planned E as well as planned S = planned I

15. Saving Function Y= C+ S And… E= C + I In equilibrium, Y= E
Implying that C+ S= C + I
Indicating that S= I
Let I= I* and S= sY
If S= I at equilibrium, then
sY= I*
Y= I*(1/s) …same as (1/ 1-c)

16. Equilibrium Income
No matter which approach you use, you will get the same equilibrium condition.

17. What Forces Cause Income, Y, to Change in the 2-sector Economy?
Movements along the curve vs. Shifts of the curve
A movement along a curve represents a change in expenditure in response to a change in income
A shift of a curve represents a different level of expenditure associated with each level of income

18. Graphical Illustrations- Movements along the Curve
Income is initially at Y0 and rises to Y1.
Investment remains constant
Consumption increases from C0 to C1
Savings increases from S0 to S1
The slope of each expenditure line is a measure of the responsiveness of the flow to a change in income
The slope is called a marginal propensity eg. MPC, MPS

19. Graphical Illustrations- Shifts of the Curve
The curves themselves could shift, with no change in income
At each level of income, Y0, more is invested, consumed and less is saved

20. Shifts in Expenditure Functions
How does national income change when expenditure flows change?
Only two things in this model that can bring about a change in expenditure flows
Consumption
Investment

21. A shift in the Investment Function
Investments are an injection and have expansionary effects on economy
Illustrations using the output- expenditure and injection- withdrawals approaches

22. A shift in the Consumption Function
Assume that there is a rise in the proportion of income that people wish to spend
(and a corresponding fall in savings)
Illustrations using the output- expenditure and injection- withdrawals approaches

23. The Multiplier
By How Much Does Income Change in Response to Changes in Expenditure Components?

24. Output-Expenditure Approach
If I*   E*  E   Ye 
If c   E steeper  Ye 
What is c? Why might we expect Ye to increase?
We know that
Y = planned E
Y = I* + cY
(1-c)Y = I*
Equilibrium condition
Y = I* x
If we differentiate the equilibrium condition,
Y/I* = 1/(1-c)
Given 0 < c < 1, implies that 1/(1-c) > 1
I*   Ye by a multiple 1/(1-c) of I* 1
1-c 

25. The Expenditure Multiplier
K= 1/(1-c) is the expenditure multiplier
The multiplier is the reciprocal of one minus the marginal propensity to consume
Also the reciprocal of the marginal propensity to save (K= 1/s)
The multiplier is larger the smaller the value of s, or the larger the value of c 

26. Expenditure Multiplier 1/(1-c)
Assume that there is initially an increase in investment expenditure of $100m per year, where MPC= 0.8
i.e. c=0.8, I* = 100
National income initially increases by this $100m
The factors of production employed in producing the new investment receive the $100 as income and will spend 0.8($100)
then the one who receives 0.8($100) as income will spend 0.8*0.8($100)
The process continues and the total increase in income is
$ ($100) +0.8*0.8($100) +…

27. Expenditure Multiplier 1/(1-c)
The total increase in income is actually the sum of an infinite geometric progression which can be calculated by the first term divided by (1- common ratio)
The first term here is I* = $100 and the common ratio is c =0.8
The sum of geometric progression is I * multiplier
Y= I* x 1/ (1-c)
= 100 x (1/0.2)
= 100 x 5
= $500m

28. Paradox of Thrift
“Thriftiness, while a virtue for the individual, is disastrous for an economy”
Given I = I*
Given S = sY
Now, suppose S* 
Will Ye increase as well?

29. A rise in thriftiness causes a decrease in national income but no increase in realised saving.
S=S +sY
S= sY
I=I’ Ye

30. Paradox of Thrift
If a rise in saving leads to a reduction in interest rate and hence an increase in investment (Think of the loanable fund market), national income may not decrease
Ye will increase if I’ increase more than S’
Ye will remain the same if I’ increase as much as S’
Ye will decrease if I’ increase less than S’

31. I  > S
S=S+ sY
S= sY
I=I”
I=I’ Ye

32. I  = S
S=S +sY
S= S’+ sY
I=I”
I=I’ Ye
=Ye

33. I  < S
S=S +sY
S= sY
I=I”
I=I’ Ye

34. Next Class Three-Sector Model Fiscal Policy
Output-Expenditure Approach: Equilibrium National Income Ye
Injection-Withdrawal Approach: Equilibrium National Income Ye
Fiscal Policy