Answer to Question #193850 in Macroeconomics for esther

Question

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 –MC = 160 + 0.6 YdT = 100 + 0.25YX = 80I = 150G = 150M = 22 + 0.25YWhere: Yis domestic incomeYdis 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. (b) Illustrate the aggregate spending curve and equilibrium level of income on a diagram. (c) Determine the surplus/ deficit in the government budget at equilibrium.(d) Determine trade balance at equilibrium. (e) Find the multiplier applicable to autonomous tax and interpret it.1.2 (a)Use the multiplier applicable to exports, to explain how a 100 billion decline in demand for exports could have affected the economy’s:(i)GDP/ output (ii)Balance of trade (iii)Government budget

Answer 1

1.1

(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)

 The surplus/ deficit in the government budget at equilibrium is equal to taxes because the government revenue source is tax.

$T = 100 + 0.25Y$

 $= 100 + 0.25(572.5)$

$= 100 + 143.125$

 $=243.125$

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. 

1.2

(i)

The export multiplier is calculated as follows:

Multiplier $= \frac{1}{[1 - c(1 - t) + m]}$

$= \frac{1}{[1 - 0.6(1 - 0.25) + 0.25]}$

$= 1.25$

Where,

c is marginal propensity to consume.

t is proportional tax rate.

m is marginal propensity to import.

The change in real GDP due to change in export by 100 billion is calculated as follows:

Change in GDP$= Export\space Multiplier \times Change\space in\space export$

$= 1.25 \times(-100)$

$= -125 \space billion$

Thus, the reduction in real GDP is equal to 125 billion.

New GDP = Old GDP + Change in GDP

$= 572.5 + (-125)$

$= 447.5$

ii.

The new balance of trade is calculated as follows:

Balance of Trade $= Export - Import$

$= 80 - 22 - 0.25 Y$

$= 58 - 0.25 \times447.5$

$= 58 - 111.87$

$= -53.87$

iii.

New government budget is calculated as follows:

Government Budget = Tax Revenue - Government Expenditure

$= 100 + 0.25Y - 150$

$= 100 + 0.25 \times 447.5$

$= 211.87$