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$:
(a) Determine the equilibrium level of income/output. (4)
An open economy is described by the following system of macroeconomic equations, in which all macroeconomic aggregate are measured in billions of Namibian dollars, N$:
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.
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