Question

Assume the Zambian economy is determined by following functions:

Y = Real GDP or national income

T = Taxes = 0.3Y

C = Consumption = K140 + 0.9(Y – T)

I = Investment = K400

G = Government spending = K800

X = Exports = K600

M = Imports = 0.15Y

1. Find the equilibrium level of income.                                                             

2. Fill in the blanks:                                                                                            

National Income	Tax	After-Tax income	Consumption	I + G + X	Minus Imports (M)	Aggregate Expenditures
k300			K236			k388
k400						k444
k500						k500
k600						k556
k700						k612

Answer 1

a.

T = 0.3Y

C = 140 + 0.9(Y-T)

I = 400

G = 800

X = 600

M = 0.15Y

Equilibrium Income is given by:

Y = C + I + G + X - M

Y = 140 + 0.9(Y-T) + 400 + 800 + 600 - 0.15Y

Y = 140 + 0.9(Y - 0.3Y) + 400 + 800 + 600 - 0.15Y

Y = 140 + 0.63Y + 1800 - 0.15Y

Y - 0.63Y + 0.15Y = 1940

0.52Y = 1940

Y = 3730.769231

Hence, the equilibrium icnome is 3730.769231

b.

Assume tax = 0.3Y and Imports = 0.15Y

Since, C = 236 at Y = 300

Assume , Autonomous Consumption = C_hat = 140

Tax = 0.3*300 = 90

After-tax income = 300-90 = 210

The marginal propensity to consume = (236-140)/(300-90) = 0.457143

Thus, Consumption C = C_hat + 0.457143(Y-T)

I + G + X = Aggregate Expenditure - Consumption + Imports

Thus,

National Income	Tax = 0.3*National Income	After-Tax income	Consumption = 140 + 0.457143(Y-T)	I + G + X	Minus Imports (M)	Aggregate Expenditures
300	90	210	236	197	45	388
400	120	280	268	236	60	444
500	150	350	300	275	75	500
600	180	420	332	314	90	556
700	210	490	364	353	105	612