Answer to Question #184088 in Accounting for Seye Ogbons

Question

The following equations describes Nigeria economy. C=0.9(I-t)y, I=300-600r, G=300, t=3y, L=0.25y-150r, M=375.

Find: 1. IS LM FUNCTIONS AND SLOPE

2. Equilibrium level of income and interest rate

Answer 1

Solution:

1.). IS and LM functions and slope

IS function: Y = C + G + I

Y = 0.9(1-t)y + 300 + 300-600r

Y = 0.9(1-3y)y + 300 + 300-600r

Y = 0.9Y-3Y² + 600-600r

Y = 0.9Y-6Y + 600-600r

Y-0.9Y+6Y = 600-600r

6.1Y = 600-600r

Y = 98.36 – 98.36r

Slope: r= $1 - \frac{Y}{98.36}$

LM function:

Money demand (L) = Money supply

0.25y – 150r = 375

0.25y – 375 = 150r

150r = 0.25y – 375

r = 0.002y – 2.5

Slope: y =$\frac{r}{0.002} + 125$

2.). Equilibrium level of income and interest rate:

Substitute in IS function:

Y = 98.36 – 98.36r

Y = 98.36 – 98.36 (0.002y – 2.5)

Y = 98.36 – 0.20y + 245.9

Y+0.20Y = 98.36 + 245.9

1.20Y = 344.26

Y = 286.88

Equilibrium level of income = 286.88

Interest rate:

Substitute in IS function:

Y = 98.36 – 98.36r

286.88 = 98.36 – 98.36r

98.36r = 286.88 – 98.36

98.36r = 188.52

r = 1.92

Interest rate = 1.92