Question

Suppose the Economy of Ghana is described by the following equations

Y =C +I+G+X. (income multiplier )

C= 100 + 0.8 Yd (consumption)

I= 200- 600r (investment)

X= 300-0.22Y -400r (Net Exports)

With government spending G = 400, the tax rate t = 0.15, Note that Yd = Y -tY

a) Derive the is curve

b) If r= 20 %. What is the level of income when spending balance occur?

c) What is the multiplier ?

d) Suppose that government spending increases to 700.What is the new level of income ? What is the change in income

Answer 1

Solution:

a.). IS curve = Y

Y = C + I + G + X

C = 100 + 0.8Yd = 100 + 0.8 (Y – tY) = 100 + 0.8 (Y – 0.15Y)

Y = 100 + 0.8(Y – 0.15Y) + 200 + 400 – 600r + 300 – 0.22Y – 400r

Y = 100 + 0.8Y – 0.12Y + 200 + 400 – 600r + 300 – 0.22Y – 400r

Y + 0.12Y + 0.22Y – 0.8Y = 100 + 200 + 400 + 300 - 600r – 400r

0.54Y = 1000 – 200r

Y = 1852 – 370r

IS curve: Y = 1852 – 370r

 

b.). r = 20% = 0.2

Y = 1852 – 370r

Y = 1852 – 370(0.2) = 1852 – 74 = 1,778

The level of income when spending balance occur = 1,778

 

c.). Multiplier = $\frac{1}{1 - MPC}$

MPC = 0.8

= $\frac{1}{1 - 0.8} = \frac{1}{0.2} = 5$

The Multiplier = 5

 

d.). Y = C + I + G + X

C = 100 + 0.8Yd = 100 + 0.8 (Y – tY) = 100 + 0.8 (Y – 0.15Y)

Y = 100 + 0.8(Y – 0.15Y) + 200 + 700 – 600r + 300 – 0.22Y – 400r

Y = 100 + 0.8Y – 0.12Y + 200 + 700 – 600r + 300 – 0.22Y – 400r

Y + 0.12Y + 0.22Y – 0.8Y = 100 + 200 + 700 + 300 - 600r – 400r

0.54Y = 1300 – 200r

Y = 2407 – 370r

New IS curve: Y = 2407 – 370r

Y = 2407 – 370(0.2) = 2407 – 74 = 2,333

The new level of income = 2,333

 

Change in income = $\frac{2333 - 1852}{1852} \times 100\% = 25.97\%$