Answer to Question #306041 in Macroeconomics for katrichie

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 − 𝑀

C = 100 + 0.75𝑌𝑑

T = 50 + 0.5𝑌

I = 200

X = 200

𝑀 = 50 + 0.25𝑌

𝐺 = 150

Where:Y is domestic income

Y is private disposable income

C is aggregate consumption

T is government tax revenue

I is investment spending

X represents exports

M represents imports of goods and service

(a) Determine the equilibrium level of income/output.(4)

(b)Illustrate aggregate spending and equilibrium level of income on a diagram(4)

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

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

(e) Determine the value of the economy’s multiplier, which is applicable to government spending, and interpret it.(5)

Answer 1

a)

$Y = C + I + G + X – M$

$C = 100 + 0.75(Y – T) = 100 + 0.75(Y – (50 + 0.5Y) = 100 + 0.75Y – 37.5 – 0.375Y$

$I = 200$

$G = 150$

$X – M = 200 – (50 + 0.25Y) = 150 – 0.25Y$

$Y = 100 + 0.75Y – 37.5 – 0.375Y + 200 + 150 + 0.25Y$

$Y = 100 + 200 + 150 – 37.5 + 0.75Y + 0.25Y – 0.375Y$

$Y = 412.50 + 0.625Y$

$Y – 0.625Y = 412.50$

$0.375Y = 412.50$

$Y = \frac{412.50}{0.375} = 1100$

$Y = 1,100$

Hence, the equilibrium level of income is 1,100

b)

c)

Surplus/deficit in the government budget at equilibrium:

Budget surplus or deficit = Tax revenues (T) – Government spending (G)

Budget surplus or deficit = T – G

$G = 150$

$T = 50 + 0.5Y = 50 + 0.5(1100)$

$= 50 + 550 = 600$

$600 – 150 = 450$

Hence, Budget surplus = 450

d)

Trade balance = Value of exports – Value of imports

Value of imports = 50 + 0.25Y

Value of exports = 200

Substitute with equilibrium output:

$50 + 0.25Y = 50 + 0.25(1100) = 50 + 275 = 325$

The value of imports = 325

Hence, the Trade balance is;

$200 – 325 = - 125$

The trade balance has a deficit of - 125

e)

The value of the economic multiplier is calculated as follows;

$The \space spending\space multiplier = \frac{1}{1 - MPC}$

$MPC = 0.75$

$MPC = 0.75$

The spending multiplier represents the multiple by which GDP increases or decreases in response to an increase and decrease in government expenditures and investment.

In the above case, a change in spending of 100 multiplied by the spending multiplier of 4 is equal to a change in GDP of 400.