CHAPTER
3
NATIONAL INCOME MODELS (I)
Keynesian models try to explain what determines the level of national income of an
economy.
3.1
Introduction
A. General assumptions under the models : (p.30)
(1) Existence of unemployment
Output can be increased by using factors which are currently unemployed
without pushing up
.
(2) Constant price level
(3) Single concept of national income (Y)
- no distinction between various concept of GNP, GDP, NNP and NI.
- national income is at
price, i.e., it measures the real output.
(4) Constant level of potential national income (Yf)
Potential national income is what the economy could produce if all
were fully employed.
B. Equilibrium condition
National income of an economy is at equilibrium when :
=
At equilibrium, the aggregate expenditure (E) equals the actual volume of output
(Y). There is no tendency to change.
3.2
Model 1 : 2-sector Model
(p.32)
A. Assumptions
(a) 2 types of economic units - firms and households
(b) Income can either be spent or saved. That is,
1
(c) Expenditure is on either consumer goods or producer goods. That is,
B. Explanation (p.33)
(1) In equilibrium, planned (ex-ante) aggregate E must equal to national income.
Y=E
=

=
(i) Equilibrium income occurs when households are just willing to purchase
everything produced, Y=E; or when the amount of income households plan to
save is just equal to the amount of expenditure firms plan to invest,
=
.
(ii) Saving creating a
out of the income flow. Investment
representing the
into the income flow.
(2) Y-line
- It is a 45 line
- All points along the Y-line indicate that Y E.
(3) Consumption function
(i) It shows the relationship between planned consumption expenditure (C) and
disposable income (Yd). In this case Yd = Y ( since there is no
)
(ii) Linear C function
C=
- slope of the ray from the origin = C/Y =
- if a = 0,
= APC
- APC < / > MPC at each income level
- when Y rises  APC
(this reflecting fundamental psychological law)
This implies that the high-income group or the rich has a
APC than
that of the low-income group.
Although as Y rises, the portion (APC) of it will be spent decreases, the
absolute amount of C
.
Exercise 1
(1) - At Y1, Y = C (break-even)  APC =
- From 0 - Y1, C
Y (dissaving)  APC
1
- At income level above Y1, C
Y (saving)  APC
1
(2) In this case, MPC is not constant but
as Y increases 
high-income group has a
MPC than that of the low-income group.
2
Factors affecting consumption function
(a) Wealth
Wealth rises  autonomous C
 C function shifts
.
(b) Expectation
- expect future level of prices rise  rush to make purchases  shifts
- expectation about future levels of Y and employment opportunity is pessimistic
shifts

(c) Changes in the distribution of income
the rich have a
MPC than the poor  if a change in the distribution of
Y that favours the poor  shifts
(d) Terms of credit
lending rate falls  cost of borrowing
 consumption
(e) Existing stock of durable goods
the larger the stock of durable goods, the
 shifts
the aggregate C is likely to be
(since purchase of durable goods can be postpone)  shifts
(4) Investment function
It shows the relationship between
and
.
- exogenous function / autonomous function : I =
- endogenous function / induced function : I =
(5) Saving function (p.35, fig.6)
(i) It shows the relationship between
(ii) Similar with C function, if a = 0,
(iii) APS
MPS at each income level
(iv) APS
when Y increases
(v) Since Y = C + S 
and
=
We can derive a corresponding saving curve from a consumption curve
3
.
Both C and S
as Y rises.
(6) Aggregate expenditure function
It shows the relationship between
and
.
E=
(when I is autonomous, slope of E function is c)
(7) Income determination for a 2-sector model
(a) Algebraically
(i) Income-expenditure approach
(p.38)
Given functions : C = a + cY, I = I* (I is an
function)
In equilibrium, planned aggregate expenditure equals national income :
E=Y 
(ii) Injection-leakage approach
In equilibrium, planned
S=I 
= planned
Exercise 2
1. Given C = 20 + 0.75Y , I = 20
(a) What is the equilibrium income level ?
(b) Given the production function Y = 2L, at the equilibrium, the no. of labour
required is
.
(c) Suppose labour force in the economy is 100, What is the level of unemployment ?
(d) What is the potential income level ?
2.
Given C = 150 + 0.8Y, I = 100 + 0.1Y
(a) What’s the equilibrium income level ?
(b) Suppose the production function of the economy is Y = 10N (labour), if the
labour supply is 400,
(i) What’s the amount of people being unemployed ?
(ii) How much can the income level be increased so as to reach the potential
income level ?
(b) Graphically
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3.3
Two Meanings of S = I
(1) Ex-ante S = Ex-ante I
- Planned investment includes
inventory investment
- Consider that
(a) If planned aggregate E (= AD) > level of output (Y) (= AS)  use inventories
to meet unexpected excess
 unintended
in stocks  a signal
for firms to
their output  income
.
(b) If E < Y  put the excess
into stocks  unintended
stocks  a signal for firms to
their output  income
(c) If E = Y  only have
inventory investment.
in
.
 (p.43 table 1) In case (a), planned S (0) < planned I (40). That means, people
spend more than what is produced  E > Y  unintended
in inventories by
 a signal for firms to
output
Y
.
In case (b), planned S (80) > planned I (40). That means, people
E Y


.
In case (c), level of Y is in equilibrium when
=
(2) Ex-post S = Ex-post I
Actual I = planned I + unintended inventory I
E.g., Refer to case (a) above, actual I = 40 + (-40) = 0 = actual saving.

S must always equal
I.
Exercise 3
1. Suppose Y = 1000, C = 100 + 0.8Y, I = 80, what are the values of realized
investment and unplanned inventory investment ?
2. ‘Equality between saving and investment determines the equilibrium national
income.’
‘ Saving and investment are always equal.’
From the above statements, can it be inferred that national income is always in
5
equilibrium?
3.4
Autonomous Change In The Equilibrium Level Of National Income (Y*)
- Any autonomous change in C and I (and hence in E)  change in Y*
- Consider :
C = 20 + 0.75Y, I = 20  Y* =
Now given I’ = 40  Y* =
If represent the above situation
(a) graphically :
(b) verbally :
At the initial equilibrium Y*, there is an excess of
over the output (income)
 there is an unintended inventory
 a firm will raise its output
to meet the extra demand  eventually the new Y* will be
than the
initial one.
*We can observe that :
I only changes by $20 but Y* changes by
( 4 times) of the change in autonomous E !!
3.5
 change in Y* is a multiple
effect.
More About Multiplier
In a 2-sector model :
(a) if I is an autonomous function , k =
(b) if I is an induced function, k =
(For algebra derivation, please refer to p.48.)
(1) Mathematical approach to k (p.50)
Suppose MPC = 0.6 and there is an increase in autonomous E, say $1  Y rises
by $1 in the 1st round (since Y = E)  C will then rise by
(since C = a + cY,
nd
then C = a + 0.6 (1))  Y then rises by
in the 2 round (since Y = C + I)
 C increases by
( since C = a + (0.6)(0.6))  ……….
 total increase in Y =
6
The smaller the s, the
- If s = 1, = 0 , k =
autonomous AE.
- If s = 0, = 0, k =
the change in Y*.
 the increase in Y* = initial increase in the
 infinite increase in Y*
(2) Graphical approach to k
Refer to textbook p.52, fig.12-14
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