Answer to Question #194243 in Macroeconomics for Selma Shilongo

Question

QUESTION 1 [30]

An open economy is described by the following system of macroeconomic equations, in which

all macroeconomic aggregate are measured in billions of Namibian dollars, N$:

Y = C + I + G + X – M

C = 160 + 0.6 Yd

T = 100 + 0.25Y

X = 80

I = 150

G = 150

M = 22 + 0.25Y

Where: Y is domestic income

Yd is private disposable income

C is aggregate consumption spending

T is government tax revenue

I is investment spending

X represents exports

M represents imports of goods and services

1.1

(a) Determine the equilibrium level of income/ output. (5)

(b) Illustrate the aggregate spending curve and equilibrium level of income on a diagram. (3)

(c) Determine the surplus/ deficit in the government budget at equilibrium. (4)

(d) Determine trade balance at equilibrium. (4)

(e) Find the multiplier applicable to autonomous tax and interpret it. (4)

Answer 1

(a)

$Y = C + I + G + X –M$

$= 160 + 0.6 Yd + 150 + 150 +80 - (22 + 0.25Y)$

 $=540 + 0.6 (Y - T) - 22 - 0.25Y$

$=540 + 0.6(Y - (100 + 0.25Y)) - 22 -0.25Y$

$=518 + 0.6Y - 60 - 0.15Y - 0.25Y$

$=458+ 0.2Y$

$Y - 0.2Y = 458$

    $Y = \frac{458}{0.8}$

      $Y = 572.5$

Equilibrium level of income is 572.5

(b)

(c)

$T = 100 + 0.25Y$

 $= 100 + 0.25(572.5)$

$= 100 + 143.125$

 $=243.125$

Hence the Government budget is in surplus of $243 billion

(d)

Trade Balance$= X - M$

$= 80 - 22 - 0.25Y$

$= 58 - 0.25 \times572.5$

$= 58 - 143.125$

$= -85.12$

(e)

$Multiplier = \frac{-c}{(1 - c)}= \frac{-0.6}{(1 - 0.6)}$

$= -1.5$

Where,

c is marginal propensity to consume. 

this means its operating on a deficit