Question 2 Given that the following information about the Ghanaian economy; C = 100+0

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 + 0.70.37 + 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