Keynesian Model Of Income Determination
Introduction
This model assumes that the aggregate supply curve is perfectly elastic up to the full employment level of output after which it becomes perfectly inelastic. Hence price level, until the full employment level, will be determined solely by the height of the supply curve. Hence, the price variable gets less attention while entire focus is on the determination of equilibrium level of income, which is determined solely by the aggregate demand.
Aggregate Demand in a Two Sector Economy
The following are the postulations for the above analysis.
 The prices are constant or invariable
 Given the price level, the firms are willing to sell any amount of the output at that price level
 The short run aggregate supply curve is perfectly elastic or flat
 Investment is assumed to be autonomous and thus independent of the income level
 There exist only two sectors in the economy, the households and the firms
Aggregate demand is the total amount of goods demanded in an economy. The aggregate demand function can be expressed as
AD = C + I
Where, C = aggregate demand for consumers goods
I = aggregate demand for investment goods
Determination of equilibrium income or output in a Two Sector Economy
In the most basic terms, an economy can be said to be in equilibrium when the production plans of the firms and the expenditure plans of the households are realized.
Below are the postulations of the analysis
 There exists only two sectors of the economy, there is no government sector and foreign sector
 All the factors of production are owned by the households who sell the factor services to earn an income. With a part of this income, they purchase goods and services and save the rest
 As there is no government in the economy there are no taxes and subsidies and no government expenditure
 As there are no foreign sectors in the economy there are no exports and imports and external inflows and outflows
 As far as the firms are concerned there are no undistributed profits
 All the prices are constant and does not change
 The technology and the supply of capital are given
 According to Keynesian theory, there are two approaches, they are Aggregate Demand  Aggregate Supply Approach and Saving Investment Approach
Let us see few illustrations which explain the two sector models
Illustration 12
The fundamental equations in a two sector economy are given as consumption function C = 400 + 0.75 Y, investment Ī = 400. You are required to ascertain the following.
 Equilibrium level of income
 Equilibrium level of consumption
Solution
In a two sector economy, the equilibrium level of income is
Y = 1 (
Ca + Ī )
1 – b
In the equation, Ca = 400, Ī = 400, b = 0.75
By substituting the above we get
Y = 1 (400
+400)
1 – 0.75
Y = 1 / 0.25 (800)
Y = 4 x 800
(a) Thus, the equilibrium level of income is 3,200
In a two sector economy, the consumption function is
C = Ca + b Y
In the above equation, Ca = 400, Ī = 400 and b = 0.75
By substituting the above values we obtain,
C = 400 + 0.75Y
C = 400 + 0.75 (3,200)
C = 400 + 2400
(b) Thus the equilibrium of level of consumption is 2,800
Illustration 13
The fundamental equations in a two sector economy are given as: Consumption C = 300 + 0.8Y and the investment function Ī = 400.
 Derive the saving function
 Find the equilibrium level of productivity the equating the saving leakages to the investment injections
Solution
The saving function is given by
S = Y – C
S = Y – 300 + 0.8Y
S = – 300 + 1Y – 0.8Y
S = – 300 + 0.2Y
(a) Hence, the saving function is given by S =  300 + 0.2Y
The equilibrium level of productivity can be determined by equating the saving leakages to the investment injections.
Thus,

300 + 0.2Y = 400
 300 – 400 =  0.2Y
 700 =  0.2Y
Or 0.2Y = 700
(b) Thus, the equilibrium level of productivity is 3,500
Illustration 14
For a two sector economy we have the following equation for consumption function
C = 120 + 0.75Y, determine the following
 If investment in a year is $70 millions what will be the equilibrium level of income or productivity
 If full employment level of income is $920 millions what investment is required to be undertaken to ensure equilibrium at full employment
Solution
Y = C + I
Y = 120 + 0.75Y + 70
Y – 0.75Y = 120 + 70
Y (1 – 0.75) = 190
0.25Y = 190
Y = 190 / 0.25
(a) Thus, if the investment in a year is $70 millions, then the equilibrium
level of
income or Productivity (Y) will be 760
To ensure full employment equilibrium investment should be equal to the saving gap at full employment income. With the given full employment income equal to $920 millions,
SF
= YF – CF
Thus,
YF – (120 + 0.75YF)
920 – (120 + 0.75 (920))
800 – 0.75 (920)
SF = 800 – 690
(b) Thus, investment required for full employment equilibrium is S110 millions
Illustration 15
If in a two sector economy Consumption C = 900 + 0.8Y and Investment I = 1,080 then
 Determine the equilibrium level of income and consumption
 Derive the saving function and determine the saving at the equilibrium level
 Determine the equilibrium level of income by equating planned investment
Solution
The equilibrium condition is given as Y = C + I
Thus,
Y = 900
+ 0.8Y + 1,080
Y = 1,980 + 0.8Y
Y – 0.8Y = 1,980
0.2Y = 1,980
Y = 1,980 / 0.2
(a) Thus, the equilibrium level of income (Y) is 9,900
The consumption function C = 900 + 0.8Y
When Y = 9,900
C = 900 + 0.8(9,900)
C = 900
+ 7,920
 Thus, the equilibrium level of consumption C is 8,820
 Thus the saving function is given by S = 0.2Y – 900
 The saving function at Equilibrium will be S = 1080
 Thus, the equilibrium level of income (Y) is 9,900
The saving function is given by S = Y – C
S = Y – (900 + 0.8Y)
S = Y – 0.8Y – 900
S = 0.2Y – 900
At equilibrium level,
S = 0.2
(9,900) – 900
S = 1980 – 900
The planned saving is given by S =  900 + 0.2Y
In equilibrium, planned saving equals planned investment
Thus,

900 + 0.2Y = 1080
0.2Y = 1080 + 900
0.2Y = 1980
Y = 1980 / 0.2
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 Say's Law of Market
 Shifts In The Aggregate Demand and The Multiplier