THE KEYNESIAN THEORY OF INCOME DETERMINATION
CONSUMPTION FUNCTION:
C = f (DI)
DI = Disposable Income
In the short-run, the Keynesian Consumption Function can be described as:
C = a + mpcDI
where a = Autonomous Consumption Expenditures; and
mpc = Marginal Propensity to Consume; 0 < mpc < 1
SAVING FUNCTION:
S = - a + (1 - mpc) DI
(1 - mpc) = mps or Marginal Propensity to Save; mpc + mps = 1.
EXAMPLE:
Suppose that (a = 50) and (mpc = 0.80):
C = 50 + 0.80DI_{}, and apc = C / DI_{}
S = -50 + 0.20DI_{}, and aps = S / DI
apc = average propensity to consume
aps = average propensity to save
DI |
C | mpc | apc | S |
mps | aps |
0 | 50 |
0.80 | --- | -50 |
0.20 | --- |
100 | 130 |
0.80 | 1.30 | -30 |
0.20 | -0.30 |
200 | 210 |
0.80 | 1.05 | -10 |
0.20 | -0.05 |
250 | 250 |
0.80 | 1.00 | 0 |
0.20 | 0.00 |
500 | 450 |
0.80 | 0.90 | 50 |
0.20 | 0.10 |
1,000 | 850 |
0.80 | 0.85 | 150 |
0.20 | 0.15 |
10,000 | 8,050 |
0.80 | 0.81 | 1,950 |
0.20 | 0.19 |
AGGREGATE EXPENDITURE FUNCTION
AE = C + I + G + ( X - M )
Where, C = a + mpcDI
DI = Real Income (Y) - Personal Taxes
Personal Taxes = tY
DI = Y - tY = ( 1 - t )Y
Then, C = a + mpc(1 - t)Y
I = Autonomous
G = Autonomous
X = Autonomous
M = Autonomous
AE = a + mpc(1 - t)Y + I + G + ( X - M )
EXAMPLE:
Suppose you have the following numerical example for the macroeconomic model described above.
a = 100, mpc = 0.875, I = 60, G = 45, X = 15, M = 10, and t = 0.20
ASSIGNMENT:
Consider the following functions:
C = 50 + 0.75DI
where DI = Y - tY or DI = ( 1 - t )Y
I = $85, G = $150, X = $35, M = $40, and t = 0.20