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

2. Outline Equilibrium Conditions: Output-Expenditure Approach
Graphical approach
Algebraic approach
Saving Function
Equilibrium Conditions: Injection-Withdrawal Approach
Changes in income
Expenditure Multiplier
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 actual output = planned expenditure
We have planned expenditure, E equal to C+I
Equilibrium income is Ye=planned E
A 45°-line is the locus of all possible points where Y = E
Above the line, E>Y
Below the line, E<Y
Graphical Illustration

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

6. Output-Expenditure Approach: More Generally
Y = planned E
Y = I* + cY
Y = I*+ cY
(1-c)Y = I*
Equilibrium condition
Y* = I* x 1
1-c

7. 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

8. Savings Functional form
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

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. Withdrawals-injections method: Algebraic approach
Equilibrium conditions under the withdrawals-injection approach
Graphical approach

14. Withdrawals-injections method: Algebraic approach
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) …compare with O/E method

15. Equilibrium Income
No matter which approach you use (i.e. output/ expenditure or withdrawals/injections), you will get the same equilibrium condition.

16. 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

17. Graphical Illustrations- Movements along the Curve: I,C,S functions/ expenditure flows
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

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

19. 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

20. 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

21. 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