Answer to Question #222949 in Macroeconomics for katrichie

Question

The Namibian economy is described by the following equations, where: t is marginal tax, Y is income; I is investment spending; G is government spending; L is money demand; M/P is money supply, i is interest rate and C is consumption. The interest rate is measured in percentage terms while all the other variables are measured in millions of Namibian dollars:

C = 100 + 0.8 ( 1-t)Y

t = 0.25

I = 600 -80i

G = 900

L = 0.5y - 60i

M/P = 1500

(a) Derive the equation for the Is curve. (4)

(b) Derive the equation for the LM curve. (4)

(c)Determine the values of income (Y) and interest rate (i) and show these values on an IS –LM diagram. (8)

(d) What are the equilibrium levels of consumption and investment?

Answer 1

Solution:

a.). Equation for IS curve:

IS curve: Y = C + I + G

Y = 100+0.8(1 – 0.25) Y + 600 – 80i + 900

Y = 100 + 0.6Y + 600 – 80i + 900

Y – 0.6Y = 100 + 600 + 900 – 80i

0.4Y = 1500 – 80i

Y = 3750 – 200i

IS curve: Y = 3750 – 200i

 

b.). Equation for the LM curve:

LM curve: Md = Ms

0.5Y – 60i = 1500

0.5Y = 1500 + 60i

Y = 3000 + 120i

LM curve equation: Y = 3000 + 120i

 

c.). i.). The values of income (Y) and interest rate:

At equilibrium: IS = LM

3750 – 200i = 3000 + 120i

3750 – 3000 = 120i + 200i

750 = 320i

i = $\frac{750}{320}$ = 2.34375

Interest rate = 2.34%

Substitute the value of interest rate on the IS function to derive income Y:

Y = 3750 – 200i

Y = 3750 – 200(2.34)

Y = 3750 – 469

Y = 3281

Income (Y) = 3,281

 

ii.). The IS-LM curve is as follows:

 

 

d.). The equilibrium levels of consumption and investment are as follows:

Consumption = 100+0.8(1 – 0.25) Y

= 100 + 0.8 (1 – 0.25) 3281 = 100 + 0.8(0.75)3281 = 100 + 1969 = 2069

The equilibrium level of consumption = 2,069

 

Investment = 600 – 80i

I = 600 – 80(2.34) = 600 – 187 = 413

The equilibrium level of investment = 413