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$:

 

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

Answer 1

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

The calculation for the equilibrium level of output/income is as follows:

$C=100+0.75(Y-T)$

$=100+0.75[Y-(50+0.5Y)]$

$=100+0.75(Y-50-0.5Y)$

$=100+0.75Y-37.5-0.375Y$

$X-M=200-(50+0.25Y)$

$=200-50-0.25Y$

$=150-0.25Y$

Now put the values in the main equation of output.

$Y=C+I+G+X-M$

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

$Y=100-37.5+200+150+150+0.75Y-0.375Y-).25Y$

$Y=562.5+0.125Y$

$Y=642.85$

Hence, the equilibrium level of income is $642.85.