Answer to Question #191740 in Macroeconomics for Daisy

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. (a)Determine the equilibrium level of income/output. (b)Illustrate aggregate spending 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)Determine the value of the economy’s multiplier, which is applicable to government spending, and interpret it. 

(f)Use the multiplier applicable to export, to explain how a 100 –billion decline in demand for export could affect the economy’s:GDP/ income, Balance of payment & Government budget

Answer 1

Solution:

a.). Determine the equilibrium level of income/output:

Y = AE

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 = 1100

The equilibrium level of income or output: Y = 1100

 

b.). The aggregate spending and equilibrium level of income is illustrated as follows on the below graph:

 

 

c.). Determine the 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

Budget surplus or deficit = 600 – 150 = 450

Budget surplus = 450

 

d.). Determine trade balance at equilibrium:

Trade balance = Value of exports – Value of imports

Value of exports = 200

Value of imports = 50 + 0.25Y

Substitute with equilibrium output:

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

Value of imports = 325

Trade balance = 200 – 325 = - 125

The trade balance has a trade deficit of – 125

 

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

The value of economy multiplier is calculated as follows:

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

MPC = 0.75

 = $\frac{1}{1 - 0.75} = \frac{1}{0.25} = 4$

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

 

(f)Use the multiplier applicable to export, to explain how a 100 –billion decline in demand for export could affect the economy’s: GDP/ income, Balance of payment & Government budget.

The multiplier applicable to export is the export multiplier. It illustrates the amount by which the national income of a country will be raised by a unit increase in domestic investments in exports.

Export Multiplier = $\frac{1}{1 - MPC + M}$

MPC = 0.75

M = 0.5

= $\frac{1}{1 - 0.75 + 0.5} = \frac{1}{0.75} = 1.33$

A 100 billion decline in demand for export will decrease the real GDP by 1.3 billion.

The balance of payment will result in a trade deficit of 1 billion since the exports will be less than 1 billion compared to imports.

The Government budget will face a deficit of 1 billion due to a decrease in aggregate demand.