Answer to Question #227154 in Macroeconomics for Nyakio

Question

Given the following model of an Economy as follows:-
(10 marks)
C = 50 + 0.7 Yd (Yd = Y-T) (Consumption & Expend)
I = 100
(Investment Expend)
X = 20
(Exports )
M = 10 – 0.27
(Imports)
T=25 interepret the consumption Function
ii)
Determine Equilibrium level of National Income
iii)
Consumption level at Equilibrium level of Income
iv)
Total import at equilibrium Income
v

Answer 1

Given that ,

Consumption expenditure C= 50 + 0.7 ( Y - T )

Investment expenditure I = 100 

Government expenditure G =0

Export X =20

Import M = 10 - 0.27 

And tax = 25 

Here , equilibrium condition is 

Income = expenditure 

Y = C+I+G+ X-M

i) Determine equilibrium level of national income, where income = expenditure

$Y=C+I+G+X-M\\Y=50+0.7(Y-T)+0+20-(10-0.27)\\Y=50+0.7(Y-25)+20-10+0.27\\Y=50+0.7Y-17.5+20-10+0.27\\Y-0.7Y=70.27-27.5\\Y(1-0.7)=42.77\\0.3Y=42.77\\Y=\frac{42.77}{3}\\Y=142.567$

Equilibrium level of national income is 142.567.

ii)

$Consumption\space C=50+0.7(Y-T)\\=50+0.7(142.567)\\=50+82.29\\=132.29$

consumption level at equilibrium level of income is 132.29.

iii)

Total import

$M=10-0.27\\M=9.73$

Total import at equilibrium income is 9.73.