IS-LM EQUATION:A step by step approach

IS-LM EQUATION

UNDER TWO SECTOR MODEL

PRACTICAL EXAMINATION QUESTION

Given C=102 +0.7y, I = 150-100i,Ms = 300, Mt= 0.25y, and Mz = 124 – 200i.

Find (a) the equilibrium level of income and the equilibrium rate of interest (b) the level of C, I, Mt , and Mz , when the economy is in equilibrium.

Note:

Y= C + I at IS

Ms = Md= Mt + Mz at LM

Where

Y = Income, C= Consumption, and I = Investment

Ms =Money Supply, : Md = Money demand, Mt = transaction-precautionary demand for money, and : Mz = speculative demand for money

Solution

(a)

In commodity market under two-sector model, IS is in equilibrium when Y= C+I

But C=102 +0.7y and I = 150-100i

Thus, Y= 102+0.7y +150-100i

Collect like terms

Y-0.7y =102 +150 -100i

0.3y=252-100i

Divide through with 0.3

Y= 840 – 333. 33i …………….equation1 at IS

In the monetary, LM is in equilibrium when Ms =Mt + Mz

Thus, 300 = 0.25y+ 124- 200

Collect like terms

0.25y = 300 – 124 + 200i

0.25y= 176 +200i

Y = 704 + 800i …………equation 2 at LM

Under the general equilibrium IS=LM

Y= 840 – 333. 33i …………….equ1

Y = 704 +800i … …………equ2

840 – 333. 33i = 704 + 800i

840-704 = 800i +333.33i

136= 1,133.33i

I = 136/ 1133.33

= 0.12 ( the equilibrium interest rate)

Substitute y for 0.12 for interest rate in equ(1) 0r (2) to obtain the equilibrium income

Y= 840 – 333. 33i … …………equ 1

Y= 840 – 333. 33 (0.12)

Y 840 - 39.99

Y = 800

Thus, the equilibrium income (Y) is 800

While the equilibrium interest rate ( i) is 0.12

(b) Find the level of C, I, Mt , and Mz, when the economy is in equilibrium

Given C=102 +0.7y, I = 150-100i, Ms = 300, Mt= 0.25y, and

Mz = 124 – 200i

by substituting Y for 800 and i for 0.12,

C=102 +0.7y,

C=102 +0.7(800) = 662 I = 150-100i,

I = 150-100(0.12)= 138

Mt = 0.25y

Mt = 0.25(800) = 200

Mz = 124 – 200i

Mz= 124 – 200(0.12)= 100

Let’s run a check of our answers

C+I =Y= 800 at IS

But c= 662 and I= 138

Thus, 662 + 138 =800=Y

Under the money market

Mt + Mz =Ms = 300 at LM

200 + 100=300

Thus

C+I =Y = 800

Mt + Mz =Ms = 300

Thanks!

I HOPE YOU UNDERSTAND THE LESSON ON IS-LM EQUATION