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Homework answers / question archive / Question 2 Given that the following information about the Ghanaian economy; C = 100+0
Question 2 Given that the following information about the Ghanaian economy; C = 100+0.7Yd I = 110 G= 200 TR = 80 X = 40 M= 20+0.5Y T= 60+0.37Y a) Calculate the equilibrium national income. b) Calculate the amount of consumption and import at equilibrium income level. c) If government expenditure falls by 20%, calculate the new equilibrium national income, hence the new level of consumption and import. d) Find the induced tax and interpret it. e) Calculate the private savings, government savings and the national savings.
a)
C = 100 + 0.7Yd
I = 110
G = 200
TR = 80
X = 40
M = 20 + 0.5Y
T = 60 + 0.37Y
Equilibrium national income is given by
Y = C + I + G + X - M
Y = 100 + 0.7Yd + 110 + 200 + 40 - 20 - 0.5Y
Y = 430 + 0.7(Y - T + TR) - 0.5Y
Y = 430 + 0.7(Y - 60 - 0.37Y + 80) - 0.5Y
Y = 430 + 0.7(0.63Y + 20) - 0.5Y
Y = 430 + 0.441Y + 14 - 0.5Y
Y = 444 + 0.441Y - 0.5Y
Y + 0.5Y - 0.441Y = 444
1.059Y = 444
Y = 419.26
Thus equilibrium national income is 419.26
b)
C = 100 + 0.7Yd
Yd = Y - T + TR
Yd = Y - 60 - 0.37Y + 80
Yd = 0.63Y + 20
Yd = 0.63(419.26) + 20
Yd = 284.1338
C = 100 + 0.7(284.1338)
C = 298.8936
M = 20 + 0.5Y
M = 20 + 0.5(419.26)
M = 229.63
c)
G = 200
Since government expenditure falls by 20% so change in government expenditure is
G = 20% of 200 = - 40
Y/G = 1/(1 - c + ct + m)
where c = 0.7
t = 0.37
m = 0.5
Y/G = 1/(1 - c + ct + m)
Y/G = 1/(1 - 0.7 + 0.7
0.37 + 0.5)
Y/G = 1/(1 - 0.7 + 0.259 + 0.5)
Y/G = 1/1.059
Y = G/1.059
Y = - 40/1.059
Y = - 37.77
New equilibrium national income = 419.26 - 37.77 = 381.49
C = 100 + 0.7Yd
C = 100 + 0.7(Y - T + TR)
C = 100 + 0.7(Y - 60 - 0.37Y + 80)
C = 100 + 0.7(0.63Y+ 20)
C = 100 + 0.441Y + 14
C = 100 + 0.441(381.49) + 14
C = 282.2370
M = 20 + 0.5Y
M = 20 + 0.5(381.49)
M = 210.745
d)
Induced tax = tY
The amount of tax which depends upon the income , known as induced tax
Equlibrium national income is Y = 419.26
Induced tax = tY
= 0.37Y
= 0.37(419.26)
= 155.1262
So 155.1262 is the amount of induced tax
e)
T = 60 + 0.33Y
T = 60 + 0.37(419.26)
T = 215.1262
private saving = Y - T + TR - C
= 419.26 - 215.1262 + 80 - 298.8936
= - 14.7598
Public saving or Govt. savings = T - G - TR
= 215.1262 - 200 - 80
= - 64.8738
National savings = private savings + public savings
= - 14.7598 - 64.8738
= - 79.6336
