1. Simple Keynesian Model
National Income Determination
Two-Sector National Income Model

2. Outline Macroeconomics [2.1] Exogenous & Endogenous Variables [2.3]
Linear Functions [2.6]
Aggregate Demand & Supply [3.2]
National Income Determination Model OR Simple Keynesian Model [3.3]

3. Outline National Income Identities [3.4]
Equilibrium Income [3.5 & 3.11]
Consumption Function [3.6]
Investment Function[3.7]
Aggregate Demand Function [3.8]

4. Outline Output-Expenditure Approach to Income Determination[3.9 ]
Expenditure Multiplier [3.9]
Saving Function [3.10]
Injection-Withdrawal Approach to Income Determination [3.10]
Paradox of Thrift [3.13]

5. Macroeconomics
National income, general price level, inflation rate, unemployment rate, interest rate and the exchange rate are the economic measures to be explained in the macroeconomic models / theories

6. Exogenous & Endogenous Variables
Exogenous Variable
the value is determined by forces outside the model
any change is regarded as autonomous
I, G, X ( Micro: Income/Population)
Endogenous Variable
the value is determined inside the model
factor to be explained in the model
Y, C, M ( Micro: Price/Quantity)

7. Linear Functions
A function specifies the relationship between variables
y is the dependent variable
x is the independent variable
y=f(x)

8. Linear Functions y=f(x) y= c y=mx y=c+mx m, c are exogenous variables
y, x are endogenous variables

9. Linear Functions
Consumption Functions
C= f(Y)
C= C’
C= cY
C= C’ + cY

10. Linear Functions C’, c are exogenous variables
C, Y are endogenous variables
Y is independent variables
C is dependent variables

11. Linear Functions
Can you express the 3 consumption functions graphically?

12. Linear Functions The parameter C’ is autonomous consumption
It summarizes the effects of all factors on consumption other than national income.
What is the difference between a change in exogenous variable (autonomous change) and a change in endogenous variable (induced change)?

13. Linear Functions C= f(Y, W)
If wealth is deemed as a relevant factor but is not explicitly included in the consumption function C=C’+ cY
a rise in wealth W  will lead to a rise in the exogenous variable C’
graphically, the consumption function C will shift upwards

14. Linear Functions
What happens if c  ?
What happens if Y  ?

15. Linear Functions
Consumption function can also be a relationship between consumption C and interest rate r.
What do you think of the relationship between the variables, i.e., consumption C and interest rate r?
Are they positively correlated or negatively correlated?

16. Aggregate Demand & Supply
the relationship between the total amount of planned expenditure and general price level (v.s. aggregate expenditure E)
Aggregate Supply
the relationship between the total amount of planned output and the general price level

17. Aggregate Demand & Supply
Price Level
Aggregate Supply
Equilibrium: no tendency to change and
the values of the endogenous variables
will remain unchanged in the absence of
external disturbances
Aggregate Demand
National Output

18. Aggregate Demand & SupplyAS
When AS is vertical
A shift of AD will cause a change
In P only but have no effect on Y
AD2
AD1 Y Yf

19. Aggregate Demand & Supply
AD1
AD2
When AS is horizontal
A shift of AD will cause a change in Y only but have no effect on P AS Y

20. Aggregate Demand & SupplyAS AD Ye Yf

21. Aggregate Demand & Supply
The Upward Sloping AS
When the economy is close to but below full employment level Y < Yf, the attempt to raise output by increasing aggregate demand will face supply side limitations
both price and output will increase

22. Aggregate Demand & Supply
The Vertical AS (slide 18)
When full employment is attained Y = Yf, an increase in aggregate demand can only cause prices to rise

23. Aggregate Demand & Supply
The Horizontal AS (slide 19)
When output is far below Yf, the equilibrium output is determined by AD
The supply side has no effect on income level as firms could supply any amount of output at the prevailing price level
The Keynesian Model analyses the situation of an economy with fixed prices and high unemployment Y < Yf

24. National Income Determination Model
Assumptions:
National income Y is defined as the total real output Q
A constant level of full national income Yf
Serious unemployment, i.e., there are many idle or unemployed factors of production

25. National Income Determination Model (cont’d)
Income / output can be raised by using currently idle factors without biding up prices
Price rigidity or constant price level
There are only households and firms (2-sector). No government and foreign trade

26. National Income Identities
An identity is true for all values of the variables
In a 2-sector economy, expenditure consists of spending either on consumption goods C OR investment goods I.
Aggregate expenditure (AE OR E) is ,by definition, equal to C plus I
E  C + I

27. National Income Identities
National income Y received by households, by definition, is either saved S OR consumed C.
Y  C + S

28. National Income Identities
Aggregate expenditure E is, by definition, equal to national income Y
Y  E
C + S  C + I
 S  I

29. Equilibrium Income
Equilibrium is a state in which there is no internal tendency to change.
It happens when
firms and households are just willing to purchase everything produced Y = E (v.s. Micro: Qs = Qd) [slide 30-36]
Income-Expenditure Approach [slide 37-60]
planned saving is equal to planned investment S = I
Injection-Withdrawal Approach [slide 61-74]

30. Equilibrium Income
What is the definition of GNP (/ GDP) in national income accounting?
The total market value of all final goods and services currently produced by the citizens (/within the domestic boundary) of a country in a specified period

31. Equilibrium Income Ex-ante Y > E  Excess supply
planned output > planned expenditure 
unexpected accumulation of stocks OR
unintended inventory investment OR
involuntary increase in inventories
In national income accounting, this amount Y-E is treated as (unplanned) investment by firms

32. Equilibrium Income Ex-post Y= E Firms will reduce output
Actual (Realised)= Planned + Unplanned
Expenditure Expenditure Investment
Actual (Realised) Output = Actual Expenditure
Firms will reduce output

33. Equilibrium Income Ex-ante Y < E  Excess Demand
planned output < planned expenditure 
unexpected fall in stocks OR
unintended inventory dis-investment OR
involuntary decrease in inventories
However, in national income accounting, this amount E - Y consumed is not currently produced

34. Equilibrium Income Ex-post Y= E Firms will increase output
Actual (Realised)= Planned - Unplanned
Expenditure Expenditure Dis-investment
Actual (Realised) Output = Actual Expenditure
Firms will increase output

35. Equilibrium Income Ex-ante Y= E  Equilibrium
There is no unintended inventory investment OR dis-investment
Ex-post Y=E

36. Equilibrium Income
When there is excess supply, i.e., planned output > planned expenditure, firms will reduce output to restore equilibrium
When there is excess demand, i.e., planned expenditure > planned output, firms will increase output to restore equilibrium
In the Keynesian model, it is aggregate demand that determines equilibrium output. Remember the horizontal AS [slide 19]

37. Consumption Function
Now, we will look at the 1st component of the aggregate expenditure E  C + I i.e. C
Empirical evidence shows that consumption C is positively related to disposable income Yd
Yd = Y since it is a 2-sector model
Remember the 3 consumption functions [slide 9 & 11]

38. Consumption Function Autonomous Consumption C’
It exists even if there is no income. This can be done by dis-saving, i.e., using the past saving
Then, saving will be negative when income is zero.
It is totally determined by forces outside the model
What happens to the 3 consumption functions if C’  ? Or C’  ?

39. Consumption Function C’ = y-intercept  In C’ C = C’ C = cY

40. Consumption Function Marginal Propensity to Consume MPC = c
It is defined as the change in consumption per unit change in income
MPC = C / Y
It is the slope of the tangent of the consumption function
For a linear function, MPC is a constant
What does the consumption function C look like if MPC is increasing? Decreasing?
It is assumed that 0 < MPC < 1
What happens to the 3 consumption functions if c ? or c  ?

41. Consumption Function MPC = slope of tangent  in MPC or  in c C = C’
C = cY
C = C’ + cY

42. Consumption Function Average Propensity to Consume APC
It is defined as the ratio of total consumption C to total income Y
APC = C / Y
It is the slope of ray of the consumption function
When C = C’ OR C = C’ + cY, APC decreases when Y increases.
When C = cY, APC = MPC = c = constant

43. Consumption Function
APC = slope of ray
C = C’
C = cY
C = C’ + cY

44. Consumption Function Relationship between APC and MPC
C = C’ Divide by Y
C/Y = C’/Y
APC = C’/Y
APC  when Y 
Slope of ray flatter when Y 
Slope of tangent = MPC = c = 0

45. Consumption Function Relationship between APC and MPC
C = cY Divide by Y
C/Y = c
APC = MPC = c
Slope of ray=Slope of tangent=constant=c

46. Consumption Function Relationship between APC and MPC
C = C’ + cY Divide by Y
C/Y = C’/Y + c
APC = C’/Y + MPC C’ +ve
APC > MPC
Slope of ray steeper than slope of tangent
Slope of tangent constant
Slope of ray flatter when Y 
APC  when Y 

47. Investment Function
Let’s look at the 2nd component of the aggregate expenditure E  C + I
An investment function shows the relationship between planned investment I and national income Y
It can be a linear function or a non-linear function

48. Investment Function Again, there can be 3 investment functions I = I’
I = iY
I = I’ + iY
Economists usually use the first one, i.e., I= I’ as investment is thought to be correlated with interest rate r, instead of Y
I’ , i are exogenous variables
I , Y are endogenous variables

49. Investment Function Autonomous Investment I’
It is independent of the income level and is determined by forces outside the model, like interest rate.
I’ is the y-intercept of the investment function

50. Investment Function Marginal Propensity to Invest i
It is defined as the change in investment I per unit change in income Y
MPI = I / Y
MPI would not correlate with Yd
It is the slope of tangent of I
It is also determined by forces outside the model

51. Investment Function MPI = i =slope of tangent I’ = y-intercept
API  when Y
MPI =0
I = I’
I = iY
I = I’ + iY

52. Aggregate Expenditure Function
Given E = C + I
C = C’ + cY I = I’
 E = I’ + C’ + cY
 E = E’ + cY

53. Aggregate Expenditure Function
C, I, E I C
Slope of tangent = c
Slope of tangent=0 Y
I = I’
C = C’+cY
E = I’ + C’+ cY

54. Aggregate Expenditure Function
Autonomous Change
When C’ or I’   E’   shift upward
When c   slope of E steeper  rotate
Induced Change
When Y   E   move along the curve

55. 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
When E = planned E, Y = Ye

56. Output-Expenditure Approach
Y = E
Planned E=C +I
C, I, E
Planned E < Y
Unintended inventory investment
Actual E = Y
Y=planned E
Planned E>Y
Unintended inventory dis-investment
Actual E =Y Y Y Ye Y

57. Output-Expenditure Approach
Y = planned E
Y = I’ + C’ + cY
Y = E’ + cY
(1-c)Y = E’
Equilibrium condition
Y = E’ 1
1-c

58. Output-Expenditure Approach
If C’ or I’   E’  E   Ye 
If c   E steeper  Ye 
If we differentiate the equilibrium condition,
Y/E’ = 1/(1-c)
Given 0 < c < 1 1/(1-c) > 1
E’   Ye by a multiple 1/(1-c) of E’ 

59. Expenditure Multiplier 1/(1-c)
Assume c=0.8, E’ = 100
The one who receive the $100 as income 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) +…

60. 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 E’ = $100 and the common ratio is c =0.8
The sum of GP is E’ * multiplier

61. Saving Function We have Y  C + S [slide 27]
Saving function can simply be derived from the consumption function
S = Y – C if C = C’ + cY
S = Y – C’ – cY
S = -C’ + (1-c) Y
S = S’ + sY S’= -C’ s = 1 - c
S’ < 0 if C’ >0 S’ = 0 if C’ = 0

62. Saving Function S S S = sY S = (1-c)Y S = S’+ sY S =-C’+(1-c)Y
Slope of tangent = s =1- c
Y > Y*  S+ve Y Y Y* S’
Slope of ray = slope of tangent
Slope of ray < slope of tangent

63. Saving Function Autonomous Saving S’ Since S= -C’ + (1-c)Y
If C’= 0 when C= cY
 S = (1-c)Y  S’ = 0
If C’ +ve when C = C’ + cY
 S = -C’ + (1-c)Y  S’ –ve
If Y= 0  S’ = -C’  Dis-saving

64. Saving Function Marginal Propensity to Save MPS = s
It is defined as the change in saving per unit change in disposable income Yd OR income Y (in a 2-sector model)
MPS = S/ Y
It is the slope of tangent of the saving function
MPS is a constant if the consumption / saving function is linear

65. Saving Function Average Propensity to Save APS
It is defined as the total saving divided by total income
APS = S/Y
It is the slope of ray of the saving function

66. Saving Function Average Propensity to Save APS (cont’d) When S= sY
 APS = MPS = s = constant
When S=S’+ sY
 APS < MPS as S’ –ve
 APS –ve when Y < Y* [slide 62]
 APS = 0 when Y = Y*
 APS +ve when Y > Y*
 APS  when Y 

67. Saving Function Y = C + S Differentiate wrt. Y Y/Y=C/Y + S/Y
 1= MPC + MPS
 1 = c + s [slide 61]
S = S’ + sY Divided by Y
S/Y = S’/Y + s
APS=S’/Y+MPS [slide 66]

68. How to determine Ye?
Y = E
C, S, I, E
Planned Y = planned E
+ve S
Planned I C
-ve S
Planned C Y
Y<C
Y*=C Ye
Y>C

69. Y = E
Y = C  S =0  No Dis-saving  Y < E  Unintended Inventory Dis-investment  Actual I =Planned I – Unintended I
E = C + I
Y < C
Y < E
Planned I C
Planned C
Planned Y < Planned E Ye

70. Y = E
Y > C  S +ve  Saving  Y > E  Unintended Inventory Investment  Actual I =Planned I + Unintended I
E = C + I
Planned I C
Planned C Ye
How about Y*<Y<Ye?
Planned Y > Planned E

71. Injection-Withdrawal Approach
Remember the national income identity S  I [slide 28]
The equilibrium income happens when planned Y= planned E as well as planned S = planned I [slide 29]

72. Injection-Withdrawal Approach
S’+ sY = I’
sY = I’ – S’ S’=-C’ s=1-c
(1-c)Y = I’ + C’ = E’
Equilibrium condition [slide 57]
Y = E’ 1
1-c

73. Equilibrium Income
No matter which approach you use, you will get the same equilibrium condition.
Can you derive the equilibrium condition if investment I is an induced function of national income Y, using the 2 approaches?

74. Equilibrium Income
Write down the investment function I first. Then write down the saving function S. Remember planned S = planned I when Y is in equilibrium {Injection-Withdrawal}
Write down the investment function I as well as the consumption function C. Together they are the aggregate expenditure function E. Remember planned Y = planned E when Y is in equilibrium {Output-Expenditure}

75. Injection-Withdrawal Approach

76. Output-Expenditure Approach

77. Y=C
Y=E
Y<C
Y>C
E=C+I
C=C’+cY
E’=C’+I’
S = S’ + sY C’
I=I’ I’
S’=- C’

78. Planned Y=Planned E
Unintended Inventory Investment
E=C+I
S=S’+sY
Unintended Inventory Disinvestment
E’=C’+I’
Unintended Inventory Investment
Unintended Inventory Disinvestment I’
I=I’
Planned S=Planned I

79. Paradox of Thrift This is an example of the “fallacy of composition”
“Thriftiness, while a virtue for the individual, is disastrous for an economy”
Given I = I’
Given S = S’ + sY OR S = -C’ + (1-c)Y
Now, suppose S’ 
Will Ye increase as well?

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

81. 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’

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

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

84. I  < S
S=S” +sY
The reduction in Ye is less than the case when I does not increase
S= S’+ sY
I=I”
I=I’ Ye
What about the case if I is an induced function of Y?