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

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

3. Outline
Graphical approach
Algebraic approach

4. The multiplier Key prediction of Keynes national income theory
Change in expenditure flow will cause a change in national income that is greater in initial change in expenditure flow (C or I)
Why?
Investment expenditure of Ghc1m on new factories and people to work in factories.
Workers take salaries and buy goods and services (i.e. induced rise in consumption expenditure)
Firms respond to increase in purchases and increase output
In order to produce more, firms hire more workers and pay them
….etc….
The multiplier is the ratio of change in national income to change in autonomous expenditure flow (i.e. investment, in the current model) that caused it

5. The multiplier: graphical approach
Illustration
The change in investment is less than the final change in income

6. Output-Expenditure Approach
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.e. an increase in investment leads to an increase in income than is greater than the initial change in investment, by as much as (1/1-c) 1
1-c 

7. 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
Illustrate this graphically using both the OE and the WI approach 

8. Expenditure Multiplier 1/(1-c): Numerical illustration
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) +…

9. 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

10. The Multiplier- summary
Multiplier predicts the magnitude of change in national income that will accompany change in autonomous expenditure
Autonomous expenditures change often
An economy with a large multiplier will result in large swings in national income, and subsequently employment and unemployment

11. Paradox of Thrift What is this?
Equilibrium national income increases when the desire to save falls; and decreases when the desire to save rises.
Paradox because growth theory teaches us that countries that save grow faster!
“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?

12. A rise in thriftiness causes a decrease in national income
S=S +sY
S= sY
I=I’ Ye

13. Paradox of Thrift
If a rise in saving leads to a reduction in interest rate (i.e. cost of borrowing) and hence an increase in investment, national income may not decrease
(Recall that for this model, we assumed interest rates constant, though)
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’

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

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

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

17. Next Class Modifying the Simple consumption function
Determinants of consumption
Three-Sector Model- Introducing the Government Sector
Output-Expenditure Approach: Equilibrium National Income Ye
Injection-Withdrawal Approach: Equilibrium National Income Ye
Fiscal Policy