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

• What is the equilibrium level of income? Consumption? Saving?
• What is the value of the autonomous expenditure multiplier?
• Are leakages and injections equal in equilibrium?

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

• Determine the equilibrium level of income (Ye).
• Determine consumption and saving in equilibrium.
• Are leakages and injections the same at the equilibrium level of income? Explain and show.
• What is the value of the autonomous expenditure multiplier?
• Suppose that the full-employment level of income is \$800.
• Is there a GDP gap in this economy? Determine the gap. Is the gap recessionary or inflationary?
• Suppose the government wishes to achieve full-employment by changing its expenditures on goods and services. What is the necessary change? By how much should government expenditures (G) change? Show and explain.