THE KEYNESIAN THEORY OF INCOME DETERMINATION

CONSUMPTION FUNCTION:

C = f (DI)

Where C = Planned Consumption Expenditures; and

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

where S = Saving; and

(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